适用于远程医疗信息系统的身份认证协议

适用于远程医疗信息系统的身份认证协议 An Authentication Protocol for Telecare Medicine Information System 1 first-author 屈 娟，女，副教授，现从事无线网络、身份认证的研究。E-mail：qulujuan@163.com 屈 娟，女，副教授，现从事无线网络、身份认证的研究。E-mail：qulujuan@163.com qulujuan@163.com 2 重庆三峡学院 数学与统计学院，重庆 404100 重庆三峡学院 数学与统计学院，重庆 404100 School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100, China School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100, China 陕西师范大学 数学与信息科学学院，陕西 西安 710119 陕西师范大学 数学与信息科学学院，陕西 西安 710119 College of Mathematics and Information Science, Shaanxi Normal University, Xi an 710119, Shaanxi, China College of Mathematics and Information Science, Shaanxi Normal University, Xi an 710119, Shaanxi, China 远程医疗信息系统中，身份认证是确保患者和医疗服务器之间安全通信的有效机制。对Sutrala等基于口令的适用于远程医疗信息系统的用户匿名认证协议进行了安全性分析，指出其协议不能抵抗离线口令猜测攻击、中间人攻击，不具备前向安全性。基于扩展混沌映射提出了一个新的三因素匿名用户身份认证协议，新协议克服了Sutrala 等协议的安全漏洞。利用BAN(Burrows-Abadi-Needham)逻辑对提出方案进行了形式化证明。此外，安全分析表明，新的协议能够抵御各种恶意攻击，适用于远程医疗环境。 Mutual authentication is one of the most efficient mechanisms to guarantee secure communication between the patient and the medical server in telecare medicine information system（TMIS）. We remark that Sutrala et al ’s scheme cannot resist offline password guessing attacks and man-in-the-middle attack and preserve forward secrecy . To overcome these limitations, we present a three factor user authentication protocol using extended chaotic maps for TMIS. Further, the proposed protocol is validated using BAN(Burrows-Abadi-Needham) logic. In addition, security analysis of our proposed protocol is to demonstrate its resilience against the well-known malicious attacks. Thus, it is more applicable to telecare medicine environments. 远程医疗信息系统 认证 智能卡 BAN逻辑 telecare medicine information system authentication smart card BAN(Burrows-Abadi-Needham) logic 0　 引 言 1 随着网络通信技术的快速发展，为患者和患者家庭提供医疗服务的远程医疗信息系统也得到了快速的发展，并成为现代医疗服务的一种新模式。远程医疗信息系统（telecare medicine information system，TMIS） [ 1 1 , 2 2 , 3 3 , 4 4 , 5 5 , 6 6 ] 是一种提供医生、护士和患者等使用者相互认证 [ 7 7 , 8 8 , 9 9 ] 身份并进行安全通信的网络系统。使用远程医疗信息系统来检测患者的健康状况可以大大地减少医疗费用，节约人力和时间。 2002年，Lee等 [ 10 10 ] 提供了一个基于指纹的三因子用户认证协议。然而，Lin和Lai [ 11 11 ] 指出Lee等的协议 [ 10 10 ] 不能抵抗冒充攻击，并给出了一个改进协议。2015年，Wu等 [ 12 12 ] 基于生物特征提出了一个可证明的三因子用户认证协议，并声称他们的协议可抵抗现有的所有安全攻击。不幸的是，Jiang等 [ 13 13 ] 发现文献[ 12 12 ]存在安全漏洞，易遭受用户冒充攻击和离线口令猜测攻击等，他们提出了改进协议。2016年，Moon等 [ 14 14 ] 提出了一个使用智能卡的基于扩展混沌映射的密钥协商协议。随后，Khan等 [ 15 15 ] 分析指出Moon等的方案 [ 14 14 ] 易遭受偷取验证者攻击，并且不能保护用户的匿名性，他们基于扩展混沌映射给出了保护用户匿名性的认证协议。2016年，Li等 [ 16 16 ] 基于扩展混沌映射提出了一个动态的身份认证方案。2018年，Madhusudhan等 [ 17 17 ] 深入分析Li等的方案 [ 16 16 ] ，指出其不能抵抗口令猜测攻击、用户冒充攻击、服务器冒充攻击和中间人攻击。此外，文献[ 16 16 ]不能保护用户匿名性。为了克服这些安全缺陷，文献[ 17 17 ]给出了改进方案。2016年，Sutrala等 [ 18 18 ] 基于RSA提出了一个适用于远程医疗信息系统的用户认证和密钥协商协议。 本文分析了Sutrala等 [ 18 18 ] 提出的基于口令的匿名用户认证协议，发现其易遭受离线口令猜测攻击、中间人攻击，不具备前向安全性。利用扩展的混沌映射给出了一个新的三因素（口令、生物特征、智能卡）认证协议，用BAN(Burrows-Abadi-Needham)逻辑给出了证明。新方案克服了Sutrala等方案的安全漏洞并具有较小的计算复杂度。 1　 基础知识 1 1.1　切比雪夫混沌映射 2 定义1 [ 19 19 ] 设 <math id="M1"><mi>n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413793&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413788&type= 1.86266661 2.79399991 是正整数， <math id="M2"><mi>x</mi><mo>∈</mo><mo stretchy="false">[</mo><mo>-</mo><mn mathvariant="normal">1,1</mn><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413803&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413798&type= 18.37266731 3.55599999 ， <math id="M3"><mi>n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413815&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413811&type= 1.86266661 2.79399991 阶切比雪夫多项式 <math id="M4"><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>:</mo><mo stretchy="false">[</mo><mo>-</mo><mn mathvariant="normal">1,1</mn><mo stretchy="false">]</mo><mo>→</mo><mo stretchy="false">[</mo><mo>-</mo><mn mathvariant="normal">1,1</mn><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413826&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413819&type= 42.07933426 4.48733330 定义为 <math id="M5"><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><mi>n</mi><mo>⋅</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413834&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413831&type= 42.24866486 4.48733330 。 由定义1可知， <math id="M6"><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413843&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413839&type= 9.90599918 4.48733330 的迭代关系为 <math display="block" id="M7"><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mtext> </mtext><mo>=</mo><mn mathvariant="normal">2</mn><mi>x</mi><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mtext> </mtext><mo>-</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>，</mo><mi>n</mi><mo>≥</mo><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413852&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413847&type= 56.89599991 4.57200003 其中， <math id="M8"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mtext> </mtext><mo>=</mo><mn mathvariant="normal">1</mn><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mtext> </mtext><mo>=</mo><mi>x</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413861&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413857&type= 33.95133591 4.48733330 。 1.2　切比雪夫多项式的半群性 2 切比雪夫多项式的一个重要特性是半群性 <math display="block" id="M9"><msub><mrow><mi>T</mi></mrow><mrow><mi>r</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>=</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">[</mo><mi>r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">[</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><mi>s</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo stretchy="false">]</mo><mo>=</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413870&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413867&type= 72.81333160 4.65666676 <math display="block" id="M10"><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">[</mo><mi>r</mi><mi>s</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>r</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413878&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413875&type= 41.31733322 4.65666676 <math display="block" id="M11"><mo>=</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413886&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413882&type= 3.72533321 2.79399991 <math display="block" id="M12"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi><mi>r</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">[</mo><mi>s</mi><mi>r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>r</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413893&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413890&type= 62.82266617 4.65666676 其中 <math id="M13"><mi>r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413901&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413897&type= 1.52399993 2.79399991 和 <math id="M14"><mi>s</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413908&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413905&type= 1.26999998 2.79399991 是正整数。2008年，Zhang [ 20 20 ] 证明了定义在 <math id="M15"><mo stretchy="false">(</mo><mo>-</mo><mi mathvariant="normal">∞</mi><mo>,</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413914&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413911&type= 19.47333336 3.55599999 上的切比雪夫多项式即扩展的切比雪夫多项式 <math id="M16"><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">[</mo><mn mathvariant="normal">2</mn><mi>x</mi><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>-</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo stretchy="false">(</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">d</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413921&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413917&type= 61.63733673 4.48733330 <math id="M17"><mtext> </mtext><mi>p</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413929&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413925&type= 2.62466669 3.64066648 ）仍然具有半群特性，其中， <math id="M18"><mi>n</mi><mo>≥</mo><mn mathvariant="normal">2</mn><mo>,</mo><mi>x</mi><mo>∈</mo><mo stretchy="false">(</mo><mo>-</mo><mi mathvariant="normal">∞</mi><mo>,</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413937&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413933&type= 34.12066650 3.64066648 ，且 <math id="M19"><mi>p</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413946&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413942&type= 1.86266661 3.64066648 是一个大素数。 1.3　扩展的切比雪夫多项式的计算难题 2 1) 离散对数问题(DLP):给定 <math id="M20"><mi>x</mi><mo>,</mo><mi>y</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413954&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413950&type= 5.67266655 3.72533321 和 <math id="M21"><mi>p</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413963&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413958&type= 1.86266661 3.64066648 ，且 <math id="M22"><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><mo stretchy="false">(</mo><mo>-</mo><mi mathvariant="normal">∞</mi><mo>,</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413972&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413968&type= 28.87133217 3.81000018 ，找到一个整数 <math id="M23"><mi>r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413979&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413976&type= 1.52399993 2.79399991 使得 <math id="M24"><msub><mrow><mi>T</mi></mrow><mrow><mi>r</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">d</mi><mtext> </mtext><mi>p</mi><mo>=</mo><mi>y</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413988&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413983&type= 26.07733345 4.74133348 。 2) 计算Diffie-Hellman问题(CDHP):给定 <math id="M25"><mi>x</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413997&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3413994&type= 2.03200006 2.79399991 ， <math id="M26"><msub><mrow><mi>T</mi></mrow><mrow><mi>r</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414005&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414001&type= 9.65199947 4.48733330 和 <math id="M27"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414013&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414009&type= 9.56733322 4.48733330 ，其中 <math id="M28"><mi>r</mi><mo>,</mo><mi>s</mi><mo>≥</mo><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414024&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414019&type= 11.17599964 3.47133350 ，且 <math id="M29"><mi>x</mi><mo>∈</mo><mo stretchy="false">(</mo><mo>-</mo><mi mathvariant="normal">∞</mi><mo>,</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414032&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414028&type= 25.23066711 3.55599999 ，计算 <math id="M30"><msub><mrow><mi>T</mi></mrow><mrow><mi>r</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>≡</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>r</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>≡</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>r</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">d</mi><mtext> </mtext><mi>p</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414040&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414036&type= 62.90733337 4.65666676 。 2　 Sutrala等方案的回顾 1 Sutrala 等 [ 18 18 ] 方案分为5个阶段：初始化、注册、登录、认证和密钥协商、口令更新阶段。方案包含两个参与者：用户 <math id="M31"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414048&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414044&type= 3.81000018 3.72533321 和服务器 <math id="M32"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414055&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414051&type= 2.20133328 2.79399991 。文中所用到的符号及含义见 表1 表1 。 符号 描述 <math id="M33"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> 第 <math id="M34"><mi>i</mi></math> 个用户 <math id="M35"><mi>S</mi></math> 医疗服务器 <math id="M36"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> 用户 <math id="M37"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> 的身份 <math id="M38"><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub></math> 用户 <math id="M39"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> 的口令 <math id="M40"><mi>h</mi><mo stretchy="false">(</mo><mo>⋅</mo><mo stretchy="false">)</mo></math> 安全的单向散列函数 <math id="M41"><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> 切比雪夫多项式， <math id="M42"><mi>x</mi><mo>∈</mo><mo stretchy="false">(</mo><mo>-</mo><mi mathvariant="normal">∞</mi><mo>,</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></math> <math id="M43"><mi>s</mi></math> 医疗服务器 <math id="M44"><mi>S</mi></math> 的私钥 <math id="M45"><mo>⊕</mo></math> 异或运算 <math id="M46"><mo>|</mo><mo>|</mo></math> 字符串的串接运算 <math id="M47"><mi mathvariant="normal">Δ</mi><mi>T</mi></math> 允许最大传输延迟 <math id="M48"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub></math> 用户 <math id="M49"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> 的生物特征 <math id="M50"><mi>A</mi></math> 攻击者 <math id="M51"><mi mathvariant="normal">G</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><mo>⋅</mo><mo stretchy="false">)</mo></math> 生物特征标识信息生成函数 <math id="M52"><mi mathvariant="normal">R</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">p</mi><mo stretchy="false">(</mo><mo>⋅</mo><mo stretchy="false">)</mo></math> 生物标识信息回复函数 2.1　初始化阶段 2 服务器 <math id="M53"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414072&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414067&type= 2.20133328 2.79399991 选取两个不同的大素数 <math id="M54"><mi>p</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414082&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414077&type= 1.86266661 3.64066648 和 <math id="M55"><mi>q</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414089&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414087&type= 1.86266661 3.64066648 ，计算 <math id="M56"><mi>n</mi><mo>=</mo><mi>p</mi><mo>×</mo><mi>q</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414098&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414094&type= 15.07066631 3.64066648 。然后，服务器 <math id="M57"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414109&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414105&type= 2.20133328 2.79399991 选取素数 <math id="M58"><mi>e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414120&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414117&type= 1.52399993 2.79399991 和 <math id="M59"><mi>d</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414130&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414124&type= 2.20133328 2.79399991 满足 <math id="M60"><mi>e</mi><mo>×</mo><mi>d</mi><mo>≡</mo><mn mathvariant="normal">1</mn><mo stretchy="false">(</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">d</mi><mo stretchy="false">(</mo><mi>p</mi><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>q</mi><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414139&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414136&type= 49.78400040 3.72533321 ，即 <math id="M61"><mi>d</mi><mo>≡</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">d</mi><mo stretchy="false">(</mo><mi>p</mi><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>q</mi><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414150&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414144&type= 46.65133286 3.97933340 ， <math id="M62"><mi>d</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414159&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414153&type= 2.20133328 2.79399991 为私钥。 2.2　注册阶段 2 第1步 用户 <math id="M63"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414169&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414167&type= 3.81000018 3.72533321 选择自己的身份 <math id="M64"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414179&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414176&type= 4.82599974 3.72533321 和口令 <math id="M65"><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414192&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414186&type= 5.41866684 4.57200003 ，随机数 <math id="M66"><msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414204&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414198&type= 2.62466669 3.72533321 ，计算 <math id="M67"><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414217&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414210&type= 24.46866608 4.48733330 并通过安全信道发送注册请求消息 <math id="M68"><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414229&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414223&type= 5.41866684 3.72533321 给医疗服务器 <math id="M69"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414239&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414234&type= 2.20133328 2.79399991 。 第2步 服务器 <math id="M70"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414249&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414245&type= 2.20133328 2.79399991 接收到注册请求消息 <math id="M71"><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414258&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414253&type= 5.41866684 3.72533321 后，计算 <math id="M72"><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi>d</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414267&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414263&type= 23.02933502 4.48733330 ， <math id="M73"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414275&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414271&type= 2.20133328 2.79399991 将含有 <math id="M74"><mo>{</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>e</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>h</mi><mo stretchy="false">(</mo><mo>⋅</mo><mo stretchy="false">)</mo><mo>}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414283&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414279&type= 22.69066620 4.48733330 的智能卡通过安全信道发送给用户 <math id="M75"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414292&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414289&type= 3.81000018 3.72533321 。 第3步 <math id="M76"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414299&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414296&type= 3.81000018 3.72533321 计算 <math id="M77"><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414306&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414302&type= 26.92399788 4.65666676 ， <math id="M78"><msub><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414314&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414310&type= 16.00200081 4.40266657 <math id="M79"><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>，</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>,</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414322&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414318&type= 53.00133133 4.91066647 <math id="M80"><mi mathvariant="normal">D</mi><mi mathvariant="normal">P</mi><mo>=</mo><msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414330&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414326&type= 27.17800140 4.65666676 <math id="M81"><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414340&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414335&type= 6.60399961 4.65666676 。最后， <math id="M82"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414347&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414344&type= 3.81000018 3.72533321 将 <math id="M83"><mo>{</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi mathvariant="normal">D</mi><mi mathvariant="normal">P</mi><mo>}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414356&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414351&type= 19.55799866 4.48733330 存储到智能卡中，删除 <math id="M84"><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414364&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414360&type= 3.47133350 3.72533321 。 2.3　登录阶段 2 第1步 用户 <math id="M85"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414371&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414367&type= 3.81000018 3.72533321 将智能卡插入读卡器，输入用户名 <math id="M86"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414374&type= 4.82599974 3.72533321 和口令 <math id="M87"><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414383&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414380&type= 5.41866684 4.57200003 ，智能卡计算 <math display="block" id="M88"><msubsup><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">D</mi><mi mathvariant="normal">P</mi><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414393&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414388&type= 33.10466385 5.16466665 ， <math display="block" id="M89"><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>'</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msubsup><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414399&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414396&type= 24.46866608 4.65666676 ， <math display="block" id="M90"><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msubsup><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414406&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414402&type= 26.92399788 4.91066647 ， <math display="block" id="M91"><msubsup><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414413&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414410&type= 29.29466629 5.16466665 ， <math display="block" id="M92"><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>|</mo><mo>|</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414419&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414416&type= 34.71333313 5.16466665 检验 <math id="M93"><msubsup><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414428&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414424&type= 3.21733332 3.97933340 是否和智能卡存储的 <math id="M94"><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414433&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414430&type= 3.21733332 3.72533321 相等。如果相等，继续执行协议下一步；否则，终止会话。 第2步 智能卡生成随机数 <math id="M95"><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414439&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414436&type= 4.06400013 3.81000018 ，记录当前时戳 <math id="M96"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414445&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414442&type= 3.72533321 3.72533321 ，并计算 <math display="block" id="M97"><msub><mrow><mi>C</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>|</mo><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>|</mo><mo>|</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414453&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414448&type= 36.23733139 4.91066647 ， <math display="block" id="M98"><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>|</mo><mo>|</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414461&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414457&type= 32.59666443 4.91066647 <math display="block" id="M99"><mo>⊕</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414467&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414464&type= 7.70466709 4.40266657 ， <math display="block" id="M100"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>|</mo><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>|</mo><mo>|</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>e</mi></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">d</mi><mtext> </mtext><mi>n</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414474&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414470&type= 54.44067001 4.91066647 发送登录请求消息〈 <math id="M101"><msub><mrow><mi>C</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414481&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414478&type= 14.05466652 4.14866638 〉到服务器 <math id="M102"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414487&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414484&type= 2.20133328 2.79399991 。 2.4　认证和密钥协商阶段 2 第1步 服务器 <math id="M103"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414491&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414490&type= 2.20133328 2.79399991 接收到登录请求〈 <math id="M104"><msub><mrow><mi>C</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414498&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414494&type= 14.05466652 4.14866638 〉后，获取当前时戳 <math id="M105"><msubsup><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414503&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414500&type= 4.14866638 3.97933340 ，使用其拥有的私钥 <math id="M106"><mi>d</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414509&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414506&type= 2.20133328 2.79399991 解密 <math id="M107"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414515&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414512&type= 3.30199981 3.72533321 ，即 <math id="M108"><msubsup><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>d</mi></mrow></msubsup><mo stretchy="false">(</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">d</mi><mtext> </mtext><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414522&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414519&type= 53.59399796 4.91066647 ，验证 <math id="M109"><mo>|</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>-</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>|</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414528&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414525&type= 14.13933372 4.65666676 <math id="M110"><mo>≤</mo><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414534&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414531&type= 9.31333351 3.30199981 。若成立，继续执行下一步；否则,终止会话。 第2步 <math id="M111"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414539&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414536&type= 2.20133328 2.79399991 计算 <math id="M112"><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi>d</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414545&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414542&type= 23.36800003 4.65666676 ，验证 <math id="M113"><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>=</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414552&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414549&type= 12.27666664 3.97933340 是否成立，若不成立则终止会话；若成立， <math id="M114"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414558&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414554&type= 2.20133328 2.79399991 计算 <math id="M115"><msubsup><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>=</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414563&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414560&type= 41.31733322 5.16466665 ，验证 <math id="M116"><msubsup><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>=</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414569&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414566&type= 13.46199894 4.06400013 是否成立。若成立，继续会话；否则，终止会话。 第3步 <math id="M117"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414575&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414572&type= 2.20133328 2.79399991 计算 <math id="M118"><msubsup><mrow><mi>C</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>|</mo><mo>|</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414581&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414579&type= 37.59199905 4.91066647 ，验证 <math id="M119"><msubsup><mrow><mi>C</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>=</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414587&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414584&type= 12.27666664 3.97933340 。若成立， <math id="M120"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414594&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414590&type= 2.20133328 2.79399991 认证 <math id="M121"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414600&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414597&type= 3.81000018 3.72533321 是合法用户且继续执行协议下一步；否则，终止会话。 第4步 <math id="M122"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414606&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414603&type= 2.20133328 2.79399991 生成随机数 <math id="M123"><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414612&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414609&type= 4.06400013 3.81000018 ，获取当前时戳 <math id="M124"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414618&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414614&type= 3.72533321 3.72533321 并计算 <math display="block" id="M125"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>|</mo><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414625&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414621&type= 50.63066864 4.91066647 ， <math display="block" id="M126"><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>⊕</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414630&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414627&type= 21.42066574 4.65666676 ， <math display="block" id="M127"><msub><mrow><mi>K</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>|</mo><mo>|</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>|</mo><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414636&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414633&type= 44.95800018 4.65666676 服务器 <math id="M128"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414644&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414641&type= 2.20133328 2.79399991 发送认证消息〈 <math id="M129"><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414650&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414646&type= 15.15533447 4.14866638 〉到 <math id="M130"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414654&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414653&type= 3.81000018 3.72533321 。 第５步 <math id="M131"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414660&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414657&type= 3.81000018 3.72533321 接收到认证消息〈 <math id="M132"><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414666&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414663&type= 15.15533447 4.14866638 〉后，获取当前时戳 <math id="M133"><msubsup><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414672&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414669&type= 4.14866638 3.97933340 ，验证 <math id="M134"><mo>|</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>-</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>|</mo><mo>≤</mo><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414678&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414675&type= 23.79133415 4.82599974 。验证通过后，计算 <math display="block" id="M135"><msubsup><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>=</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>⊕</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414685&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414681&type= 21.42066574 4.65666676 ， <math display="block" id="M136"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msup><mrow><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msup><mrow><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup><mo>|</mo><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>|</mo><mo>|</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414690&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414687&type= 52.49333191 4.91066647 ， <math display="block" id="M137"><msubsup><mrow><mi>K</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>|</mo><mo>|</mo><msup><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup><mo>|</mo><mo>|</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414696&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414693&type= 46.65133286 4.65666676 检测等式 <math id="M138"><msubsup><mrow><mi>K</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>=</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414702&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414699&type= 12.78466702 3.97933340 是否成立。若成立， <math id="M139"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414708&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414705&type= 3.81000018 3.72533321 认证 <math id="M140"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414714&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414711&type= 2.20133328 2.79399991 的合法性；否则， <math id="M141"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414720&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414717&type= 3.81000018 3.72533321 终止会话。 第６步 <math id="M142"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414726&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414723&type= 3.81000018 3.72533321 计算 <math id="M143"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mi mathvariant="normal">V</mi><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>|</mo><mo>|</mo><msup><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup><mo>|</mo><mo>|</mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414732&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414729&type= 45.46599960 4.65666676 ， <math id="M144"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414738&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414735&type= 3.72533321 3.72533321 为 <math id="M145"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414744&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414741&type= 3.81000018 3.72533321 当前的时戳。然后， <math id="M146"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414750&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414747&type= 3.81000018 3.72533321 发送〈 <math id="M147"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mi mathvariant="normal">V</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414756&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414753&type= 13.37733269 4.14866638 〉到 <math id="M148"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414762&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414759&type= 2.20133328 2.79399991 。 第７步 接收到消息〈 <math id="M149"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mi mathvariant="normal">V</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414768&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414765&type= 13.29266644 4.14866638 〉后，获取当前时戳 <math id="M150"><msubsup><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414772&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414770&type= 4.14866638 3.97933340 ， <math id="M151"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414778&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414775&type= 2.20133328 2.79399991 检测 <math id="M152"><mo>|</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>-</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>|</mo><mo>≤</mo><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414784&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414781&type= 23.79133415 4.82599974 ，若不成立， <math id="M153"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414790&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414787&type= 2.20133328 2.79399991 终止会话，否则， <math id="M154"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414794&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414792&type= 2.20133328 2.79399991 计算 <math id="M155"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><msup><mrow><mi mathvariant="normal">V</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>|</mo><mo>|</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>|</mo><mo>|</mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414798&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414796&type= 46.14333344 4.65666676 ，验证等式 <math id="M156"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><msup><mrow><mi mathvariant="normal">V</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup><mo>=</mo><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mi mathvariant="normal">V</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414802&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414800&type= 21.67466736 3.13266659 是否成立。若成立， <math id="M157"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414806&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414804&type= 3.81000018 3.72533321 和 <math id="M158"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414810&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414808&type= 2.20133328 2.79399991 将 <math id="M159"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414814&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414812&type= 4.91066647 2.79399991 作为以后通信的会话密钥；否则，会话终止。 2.5　口令更新阶段 2 当用户 <math id="M160"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414818&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414816&type= 3.81000018 3.72533321 想要更改自己的口令， <math id="M161"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414822&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414820&type= 3.81000018 3.72533321 将智能卡插入到读卡器中，输入用户名 <math id="M162"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414826&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414824&type= 4.82599974 3.72533321 和口令 <math id="M163"><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">d</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414832&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414829&type= 7.28133297 4.82599974 ， <math id="M164"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414835&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414834&type= 3.81000018 3.72533321 执行如下操作： 第1步 <math id="M165"><mi mathvariant="normal">S</mi><mi mathvariant="normal">C</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414840&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414837&type= 4.82599974 2.79399991 计算： <math id="M166"><msubsup><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">D</mi><mi mathvariant="normal">P</mi><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">d</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414845&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414843&type= 33.86666870 5.16466665 ， <math id="M167"><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414849&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414847&type= 9.31333351 3.97933340 <math id="M168"><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414853&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414851&type= 8.72066689 4.48733330 <math id="M169"><mo>|</mo><mo>|</mo><msubsup><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414859&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414856&type= 5.24933338 4.65666676 ， <math id="M170"><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">d</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">d</mi></mrow></msubsup><mo>|</mo><mo>|</mo><msubsup><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414864&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414861&type= 30.22600174 4.91066647 ， <math id="M171"><msubsup><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414868&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414866&type= 16.42533302 4.65666676 <math id="M172"><mo>⊕</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414871&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414870&type= 3.72533321 3.47133350 <math id="M173"><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">d</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414873&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414872&type= 10.32933331 4.91066647 ， <math id="M174"><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">d</mi></mrow></msubsup><mo>|</mo><mo>|</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414875&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414874&type= 36.57600021 5.16466665 ，检验 <math id="M175"><msubsup><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414877&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414876&type= 3.21733332 3.97933340 是否和智能卡存储的 <math id="M176"><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414879&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414878&type= 3.21733332 3.72533321 相等。若不相等， <math id="M177"><mi mathvariant="normal">S</mi><mi mathvariant="normal">C</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414881&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414880&type= 4.82599974 2.79399991 终止会话；否则， <math id="M178"><mi mathvariant="normal">S</mi><mi mathvariant="normal">C</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414883&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414882&type= 4.82599974 2.79399991 输入新口令 <math id="M179"><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414885&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414884&type= 8.12800026 4.82599974 ，执行下一步。 第2步 <math id="M180"><mi mathvariant="normal">S</mi><mi mathvariant="normal">C</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414887&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414886&type= 4.82599974 2.79399991 计算 <math id="M181"><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup><mo>|</mo><mo>|</mo><msubsup><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414889&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414888&type= 32.34266663 4.91066647 ， <math id="M182"><msubsup><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup><mo>=</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>⊕</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414891&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414890&type= 18.79599953 4.65666676 <math id="M183"><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup><mo>|</mo><mo>|</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414893&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414892&type= 21.42066574 4.91066647 ， <math id="M184"><msubsup><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414896&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414894&type= 34.71333313 5.16466665 ， <math id="M185"><mi mathvariant="normal">D</mi><msup><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msup><mo>=</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414898&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414897&type= 12.86933327 3.04799986 <math id="M186"><msubsup><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>⊕</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414900&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414899&type= 6.60399961 4.65666676 <math id="M187"><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414904&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414903&type= 19.47333336 4.91066647 。 <math id="M188"><mi mathvariant="normal">S</mi><mi mathvariant="normal">C</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414906&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414905&type= 4.82599974 2.79399991 用 <math id="M189"><msubsup><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414908&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414907&type= 14.22399998 4.40266657 和 <math id="M190"><mi mathvariant="normal">D</mi><msup><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414912&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414910&type= 8.46666718 3.04799986 替代智能卡中的信息 <math id="M191"><msub><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414914&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414913&type= 8.72066689 4.14866638 和 <math id="M192"><mi mathvariant="normal">D</mi><mi mathvariant="normal">P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414916&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414915&type= 5.07999992 2.79399991 。 3　 Sutrala 等方案的安全性分析 1 3.1　离线口令猜测攻击 2 离线口令猜测攻击是指攻击者采用遍历的方式穷举口令集合中的所有口令，并逐个验证来确认用户 <math id="M193"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414918&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414917&type= 3.81000018 3.72533321 的正确口令。假设攻击者 <math id="M194"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414920&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414919&type= 2.87866688 2.79399991 获取用户 <math id="M195"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414922&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414921&type= 3.81000018 3.72533321 的智能卡，并通过侧信道技术 [ 21 21 ] 提取智能卡中的信息 <math id="M196"><mo>{</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi mathvariant="normal">D</mi><mi mathvariant="normal">P</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>h</mi><mo stretchy="false">(</mo><mo>⋅</mo><mo stretchy="false">)</mo><mo>}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414924&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414923&type= 34.88266754 4.48733330 ，那么攻击者 <math id="M197"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414926&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414925&type= 2.87866688 2.79399991 可发起如下的口令猜测攻击： 第1步 <math id="M198"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414928&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414927&type= 2.87866688 2.79399991 从用户身份空间 <math id="M199"><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414930&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414929&type= 6.68866634 4.82599974 和口令空间 <math id="M200"><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414932&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414931&type= 7.70466709 4.82599974 猜测 <math id="M201"><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msubsup><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>,</mo><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414934&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414933&type= 15.49400043 4.91066647 ； 第2步 <math id="M202"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414936&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414935&type= 2.87866688 2.79399991 计算 <math id="M203"><msubsup><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">D</mi><mi mathvariant="normal">P</mi><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msubsup><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414938&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414937&type= 34.20533371 5.16466665 ， <math id="M204"><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>|</mo><mo>|</mo><msubsup><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414940&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414939&type= 27.94000053 4.91066647 ，其中 <math id="M205"><mi mathvariant="normal">D</mi><mi mathvariant="normal">P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414942&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414941&type= 5.07999992 2.79399991 是从智能卡中提取的； 第3步 <math id="M206"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414944&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414943&type= 2.87866688 2.79399991 计算 <math id="M207"><msubsup><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msubsup><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>⊕</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msubsup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414946&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414945&type= 38.09999847 5.16466665 是否成立。若成立，则猜测正确，否则，转第1步。直到猜测到正确的 <math id="M208"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414948&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414947&type= 4.82599974 3.72533321 和口令 <math id="M209"><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414950&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414949&type= 5.41866684 4.57200003 。 以上攻击的时间复杂度为 O ((3T <math id="M210"><msub><mrow/><mrow><mi>h</mi></mrow></msub><mo>+</mo><mn mathvariant="normal">2</mn><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">x</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414952&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414951&type= 13.29266644 3.81000018 )· <math id="M211"><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414954&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414953&type= 6.68866634 4.82599974 · <math id="M212"><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414956&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414955&type= 7.70466709 4.82599974 ),其中 <math id="M213"><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414958&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414957&type= 6.68866634 4.82599974 和 <math id="M214"><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414960&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414959&type= 7.70466709 4.82599974 分别表示身份空间和口令空间。从以上分析可看出，攻击者能够成功实施离线口令猜测攻击的原因在于，攻击者从用户的智能卡中获取了验证消息 <math id="M215"><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414962&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414961&type= 3.21733332 3.72533321 ，利用 <math id="M216"><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414964&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414963&type= 3.21733332 3.72533321 确认用户 <math id="M217"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414966&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414965&type= 3.81000018 3.72533321 正确的口令和身份。 3.2　中间人攻击 2 中间人攻击是指攻击者将自己处于通信双方的中间，伪装成通信中的一方或多方来欺骗其他通信方。在3.1小节中，攻击者 <math id="M218"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414968&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414967&type= 2.87866688 2.79399991 猜测到 <math id="M219"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414970&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414969&type= 3.81000018 3.72533321 正确的口令 <math id="M220"><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414972&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414971&type= 5.41866684 4.57200003 和身份 <math id="M221"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414974&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414973&type= 4.82599974 3.72533321 ，则他可计算 <math display="block" id="M222"><msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">D</mi><mi mathvariant="normal">P</mi><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414976&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414975&type= 33.10466385 4.91066647 ， <math display="block" id="M223"><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414978&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414977&type= 26.92399788 4.65666676 ， <math display="block" id="M224"><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414980&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414979&type= 34.71333313 4.91066647 其中 <math id="M225"><msub><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi mathvariant="normal">D</mi><mi mathvariant="normal">P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414982&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414981&type= 10.66799927 4.14866638 是通过侧信道技术从智能卡中提取的。接下来，攻击者 <math id="M226"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414984&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414983&type= 2.87866688 2.79399991 就可对Sutrala等协议发起中间人攻击（如 图1 图1 所示）。 成功实施中间人攻击的原因在于，攻击者 <math id="M227"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414989&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414988&type= 2.87866688 2.79399991 得到了用户 <math id="M228"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414991&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414990&type= 3.81000018 3.72533321 和医疗服务器 <math id="M229"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414993&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414992&type= 2.20133328 2.79399991 之间共享的秘密信息 <math id="M230"><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414995&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414994&type= 12.61533356 4.57200003 。 3.3　不具备前向安全性 2 依据3.1节中，攻击者 <math id="M231"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414997&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414996&type= 2.87866688 2.79399991 通过离线口令猜测攻击获得用户 <math id="M232"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414999&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3414998&type= 3.81000018 3.72533321 的身份 <math id="M233"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415001&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415000&type= 4.82599974 3.72533321 和口令 <math id="M234"><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415003&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415002&type= 5.41866684 4.57200003 ，则 <math id="M235"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415005&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415004&type= 2.87866688 2.79399991 计算 <math id="M236"><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415007&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415006&type= 32.85066605 4.91066647 可以获取 <math id="M237"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415009&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415008&type= 3.81000018 3.72533321 和服务器 <math id="M238"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415011&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415010&type= 2.20133328 2.79399991 之间的会话密钥，具体流程如下： 第1步 攻击者 <math id="M239"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415013&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415012&type= 2.87866688 2.79399991 从公开信道上截获用户 <math id="M240"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415015&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415014&type= 3.81000018 3.72533321 发给服务器 <math id="M241"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415017&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415016&type= 2.20133328 2.79399991 的认证消息 <math id="M242"><mo stretchy="false">(</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415019&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415018&type= 16.67933464 4.48733330 和服务器发给用户的应答消息 <math id="M243"><mo stretchy="false">(</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415021&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415020&type= 18.03400040 4.48733330 ，并计算 <math display="block" id="M244"><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415023&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415022&type= 40.55533218 4.91066647 第2步 攻击者 <math id="M245"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415025&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415024&type= 2.87866688 2.79399991 从公开信道上截获〈 <math id="M246"><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415027&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415026&type= 15.15533447 4.14866638 〉，并计算 <math id="M247"><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>⊕</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415029&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415028&type= 20.99733353 4.40266657 ； 第3步 攻击者 <math id="M248"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415031&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415030&type= 2.87866688 2.79399991 获得会话密钥 <math id="M249"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415033&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415032&type= 20.57399940 4.48733330 <math id="M250"><mi mathvariant="normal">p</mi><mi mathvariant="normal">w</mi><msub><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415035&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415034&type= 29.71799850 4.65666676 。 从以上分析可以看出，攻击者 <math id="M251"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415037&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415036&type= 2.87866688 2.79399991 可以获得所有登录过医疗服务器 <math id="M252"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415039&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415038&type= 2.20133328 2.79399991 的用户会话密钥。Sutrala 等认证协议存在无法抵抗离线口令猜测攻击、中间人攻击且不具备前向安全性。 4　 本文提出的协议 1 为改进安全缺陷，本文引入生物特征标识，结合智能卡和口令，提出了一个新的适用于远程医疗信息系统的身份认证协议。该协议由3个阶段组成：注册（见 图2 图2 ）、登录和认证（见 图3 图3 ）、口令更新。 4.1　注册阶段 2 第1步 用户 <math id="M253"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415047&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415046&type= 3.81000018 3.72533321 选取自己的身份 <math id="M254"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415049&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415048&type= 4.82599974 3.72533321 和口令 <math id="M255"><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415051&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415050&type= 5.41866684 4.57200003 ，选取随机数 <math id="M256"><mi>b</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415053&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415052&type= 1.86266661 2.79399991 ，提取生物特征 <math id="M257"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415055&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415054&type= 3.30199981 3.72533321 ，通过模糊提取技术得到 <math id="M258"><mi mathvariant="normal">G</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415057&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415056&type= 26.75466537 4.82599974 ，然后计算 <math id="M259"><mi mathvariant="normal">H</mi><mi mathvariant="normal">P</mi><msub><mrow><mi mathvariant="normal">W</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi>b</mi><mo>|</mo><mo>|</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415059&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415058&type= 31.83466721 4.65666676 。随后将消息 <math id="M260"><mo>{</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi mathvariant="normal">H</mi><mi mathvariant="normal">P</mi><msub><mrow><mi mathvariant="normal">W</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415061&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415060&type= 19.47333336 4.48733330 通过安全信道发给服务器 <math id="M261"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415063&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415062&type= 2.20133328 2.79399991 。 第2步 服务器 <math id="M262"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415065&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415064&type= 2.20133328 2.79399991 选取 <math id="M263"><msub><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415067&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415066&type= 2.28600001 3.72533321 ，计算 <math id="M264"><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415069&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415068&type= 21.08199883 4.48733330 ， <math id="M265"><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">)</mo><mo>⊕</mo><mi mathvariant="normal">H</mi><mi mathvariant="normal">P</mi><msub><mrow><mi mathvariant="normal">W</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415071&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415070&type= 35.89866638 4.65666676 ，然后将信息 <math id="M266"><mo>{</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>h</mi><mo stretchy="false">(</mo><mo>⋅</mo><mo stretchy="false">)</mo><mo>,</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415073&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415072&type= 16.00200081 4.48733330 <math id="M267"><mi>x</mi><mo>,</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415075&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415074&type= 3.89466667 3.21733332 <math id="M268"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415077&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415076&type= 11.42999935 4.48733330 写入智能卡 <math id="M269"><mi mathvariant="normal">S</mi><mi mathvariant="normal">C</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415079&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415078&type= 4.82599974 2.79399991 中，并将智能卡 <math id="M270"><mi mathvariant="normal">S</mi><mi mathvariant="normal">C</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415081&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415080&type= 4.82599974 2.79399991 通过安全信道发送给用户。 第3步 用户在收到智能卡 <math id="M271"><mi mathvariant="normal">S</mi><mi mathvariant="normal">C</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415083&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415082&type= 4.82599974 2.79399991 后，计算 <math id="M272"><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi mathvariant="normal">H</mi><mi mathvariant="normal">P</mi><msub><mrow><mi mathvariant="normal">W</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415085&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415084&type= 24.38399887 4.40266657 ， <math id="M273"><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>b</mi><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415087&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415086&type= 30.48000145 4.91066647 ， <math id="M274"><msub><mrow><mi>Q</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi>b</mi><mo>|</mo><mo>|</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415089&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415088&type= 19.30399895 4.48733330 并将 <math id="M275"><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415091&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415090&type= 8.72066689 4.14866638 加入到智能卡 <math id="M276"><mi mathvariant="normal">S</mi><mi mathvariant="normal">C</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415093&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415092&type= 4.82599974 2.79399991 中。最终，智能卡 <math id="M277"><mi mathvariant="normal">S</mi><mi mathvariant="normal">C</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415095&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415094&type= 4.82599974 2.79399991 包含的参数为 <math id="M278"><mo>{</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>h</mi><mo stretchy="false">(</mo><mo>⋅</mo><mo stretchy="false">)</mo><mo>,</mo><mi>x</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>,</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415097&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415096&type= 46.14333344 4.82599974 。 4.2　登录和认证阶段 2 第1步 <math id="M279"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415099&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415098&type= 3.81000018 3.72533321 插入智能卡 <math id="M280"><mi mathvariant="normal">S</mi><mi mathvariant="normal">C</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415101&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415100&type= 4.82599974 2.79399991 ，输入 <math id="M281"><mi mathvariant="normal">I</mi><msubsup><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>,</mo><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415103&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415102&type= 12.78466702 4.82599974 ，输入生物特征 <math id="M282"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415105&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415104&type= 3.30199981 3.72533321 ，通过模糊识别技术恢复 <math id="M283"><mi mathvariant="normal">R</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">p</mi><mo stretchy="false">(</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415106&type= 24.46866608 4.82599974 ，然后智能卡计算 <math display="block" id="M284"><mi>b</mi><mi>'</mi><mo>=</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msubsup><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415109&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415108&type= 31.24200058 5.16466665 ， <math display="block" id="M285"><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>|</mo><mo>|</mo><mi>b</mi><mi>'</mi><mo>|</mo><mo>|</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415111&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415110&type= 33.10466385 5.16466665 ， <math display="block" id="M286"><msup><mrow><msub><mrow><mi>Q</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi>b</mi><mi>'</mi><mo>|</mo><mo>|</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415113&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415112&type= 20.23533440 4.65666676 并与存储的 <math id="M287"><msub><mrow><mi>Q</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415115&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415114&type= 3.64066648 4.14866638 进行比较，若相等，智能卡产生 <math id="M288"><mi>u</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415117&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415116&type= 1.86266661 2.79399991 ，计算 <math display="block" id="M289"><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415119&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415118&type= 18.62666702 4.48733330 ， <math display="block" id="M290"><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415121&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415120&type= 25.65399933 4.48733330 ， <math display="block" id="M291"><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415123&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415122&type= 26.33133316 4.65666676 ， <math display="block" id="M292"><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415125&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415124&type= 32.93533325 4.48733330 然后把消息 <math id="M293"><msub><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mo>{</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415127&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415126&type= 27.51666832 4.48733330 发送给医疗服务器 <math id="M294"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415129&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415128&type= 2.20133328 2.79399991 。 第2步 服务器 <math id="M295"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415131&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415130&type= 2.20133328 2.79399991 收到消息 <math id="M296"><msub><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415133&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415132&type= 4.57200003 3.72533321 后，计算 <math display="block" id="M297"><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415135&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415134&type= 40.80933380 4.48733330 ， <math display="block" id="M298"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415137&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415136&type= 26.33133316 4.65666676 ， <math display="block" id="M299"><msubsup><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415139&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415138&type= 32.93533325 4.65666676 验证 <math id="M300"><msubsup><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415141&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415140&type= 12.53066635 3.97933340 是否成立，不成立，则会话终止；若成立，服务器成功认证用户的身份。产生 <math id="M301"><mi>v</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415143&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415142&type= 1.86266661 2.79399991 ，计算 <math display="block" id="M302"><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415145&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415144&type= 18.62666702 4.48733330 ， <math display="block" id="M303"><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415147&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415146&type= 25.99266624 4.48733330 ， <math display="block" id="M304"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415149&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415148&type= 28.78666687 4.48733330 ， <math display="block" id="M305"><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow></msub><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415151&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415150&type= 29.04066658 4.48733330 并发送消息 <math id="M306"><msub><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mo>{</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow></msub><mo>}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415153&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415152&type= 21.92866707 4.48733330 给 <math id="M307"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415155&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415154&type= 3.81000018 3.72533321 。 第3步 当 <math id="M308"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415157&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415156&type= 3.81000018 3.72533321 收到消息后，计算 <math display="block" id="M309"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo stretchy="false">)</mo><mo>|</mo><mo>|</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415159&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415158&type= 36.15266418 4.48733330 ， <math display="block" id="M310"><msubsup><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415161&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415160&type= 36.57600021 4.65666676 验证 <math id="M311"><msubsup><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415163&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415162&type= 12.53066635 3.97933340 是否成立，不成立，则会话终止；若成立，用户认定 <math id="M312"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415165&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415164&type= 2.20133328 2.79399991 是合法的服务器。计算 <math id="M313"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mi mathvariant="normal">V</mi><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415167&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415166&type= 36.66066742 4.48733330 ，将 <math id="M314"><msub><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><mo>{</mo><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mi mathvariant="normal">V</mi><mo>}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415169&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415168&type= 20.82799911 4.48733330 发送给服务器 <math id="M315"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415171&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415170&type= 2.20133328 2.79399991 。 第4步 服务器 <math id="M316"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415173&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415172&type= 2.20133328 2.79399991 收到消息 <math id="M317"><msub><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415175&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415174&type= 4.57200003 3.72533321 后，计算 <math id="M318"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mi>V</mi><mi>'</mi><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415177&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415176&type= 37.50733566 4.48733330 并验证 <math id="M319"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mi>V</mi><mi>'</mi><mo>=</mo><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mi mathvariant="normal">V</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415179&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415178&type= 21.25133324 2.87866688 是否成立。若成立，用户和服务器将 <math id="M320"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415181&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415180&type= 4.91066647 2.79399991 当作会话密钥用于将来的通信；否则，会话结束。 4.3　口令更新阶段 2 当用户 <math id="M321"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415183&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415182&type= 3.81000018 3.72533321 想将其口令 <math id="M322"><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415185&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415184&type= 5.41866684 4.57200003 修改为 <math id="M323"><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415187&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415186&type= 8.12800026 4.82599974 时，执行以下过程。用户 <math id="M324"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415189&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415188&type= 3.81000018 3.72533321 将智能卡插入读卡器中，输入 <math id="M325"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415191&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415190&type= 4.82599974 3.72533321 和 <math id="M326"><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415193&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415192&type= 5.41866684 4.57200003 ，并扫描 <math id="M327"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415195&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415194&type= 3.30199981 3.72533321 ，通过模糊识别技术恢复 <math id="M328"><msub><mrow><mi>α</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">R</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">p</mi><mo stretchy="false">(</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415197&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415196&type= 24.97666740 4.82599974 ，然后请求修改口令。收到请求后，智能卡计算 <math id="M329"><mi>b</mi><mi>'</mi><mo>=</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msubsup><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415199&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415198&type= 32.00400162 5.16466665 ， <math id="M330"><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msubsup><mo>|</mo><mo>|</mo><mi>b</mi><mi>'</mi><mo>|</mo><mo>|</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415201&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415200&type= 33.78200150 5.16466665 ， <math id="M331"><msup><mrow><msub><mrow><mi>Q</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi>b</mi><mi>'</mi><mo>|</mo><mo>|</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415203&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415202&type= 20.91266632 4.65666676 并与存储的 <math id="M332"><msub><mrow><mi>Q</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415205&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415204&type= 3.64066648 4.14866638 进行比较。若相等，则用户输入的身份和口令是合法的。否则，智能卡拒绝用户的请求。 接着智能卡计算 <math display="block" id="M333"><msubsup><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup><mo>=</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415207&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415206&type= 58.41999817 5.16466665 ， <math display="block" id="M334"><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup><mo>=</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><mi>b</mi><mo>|</mo><mo>|</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">p</mi><msubsup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup><mo>|</mo><mo>|</mo><mi>b</mi><mo>|</mo><mo>|</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415209&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415208&type= 61.29866791 5.16466665 用 <math id="M335"><msubsup><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415211&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415210&type= 5.92666674 3.97933340 , <math id="M336"><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415213&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415212&type= 6.18066692 3.97933340 替换卡中的 <math id="M337"><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415215&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415214&type= 8.55133343 4.14866638 。 5　 BAN逻辑形式化分析 1 5.1　逻辑符号及含义 2 BAN逻辑的形式化证明中用到的逻辑符号及含义见 表2 表2 。基本的逻辑规则见 表3 表3 。 符号 含义 <math id="M338"><mi>P</mi><mo>|</mo><mo>≡</mo><mi>X</mi></math> <math id="M339"><mi>P</mi></math> 相信 <math id="M340"><mi>X</mi></math> 或相信 <math id="M341"><mi>X</mi></math> 是真的 <math id="M342"><mi>P</mi><mo>⊲</mo><mi>X</mi></math> <math id="M343"><mi>P</mi></math> 看见了 <math id="M344"><mi>X</mi></math> <math id="M345"><mi>P</mi><mo>⇒</mo><mi>X</mi></math> <math id="M346"><mi>P</mi></math> 对 <math id="M347"><mi>X</mi></math> 有裁判权， <math id="M348"><mi>P</mi></math> 有权给出 <math id="M349"><mi>X</mi></math> <math id="M350"><mi>P</mi><mo>|</mo><mo>~</mo><mi>X</mi></math> <math id="M351"><mi>P</mi></math> 说过 <math id="M352"><mi>X</mi></math> <math id="M353"><mi>A</mi><mstyle displaystyle="true"><mover><mrow><mo>↔</mo></mrow><mrow><mi>K</mi></mrow></mover></mstyle><mi>B</mi></math> <math id="M354"><mi>K</mi></math> 是 <math id="M355"><mi>A</mi></math> 和 <math id="M356"><mi>B</mi></math> 的共享密钥 <math id="M357"><mo>#</mo><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">)</mo></math> <math id="M358"><mi>X</mi></math> 是新鲜的 <math id="M359"><msub><mrow><mo stretchy="false">(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo stretchy="false">)</mo></mrow><mrow><mi>K</mi></mrow></msub></math> 用哈希函数作用密钥 <math id="M360"><mi>K</mi></math> 和 <math id="M361"><mo stretchy="false">(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo stretchy="false">)</mo></math> 得到的数据 〈 <math id="M362"><mi>X</mi><mo>,</mo><mi>Y</mi></math> 〉 <math id="M363"><msub><mrow/><mrow><mi>K</mi></mrow></msub></math> 公式 <math id="M364"><mi>X</mi></math> 和公式 <math id="M365"><mi>Y</mi></math> 相结合 规则名称 符号 消息含义规则（MMR） <math id="M366"><mfrac><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mi>P</mi><mstyle displaystyle="true"><mover><mrow><mo>↔</mo></mrow><mrow><mi>K</mi></mrow></mover></mstyle><mi>Q</mi><mo>,</mo><mi>P</mi><mo>⊲</mo><msub><mrow><mo>{</mo><mi>X</mi><mo>}</mo></mrow><mrow><mi>K</mi></mrow></msub></mrow><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mi>Q</mi><mo>|</mo><mo>~</mo><mi>X</mi><mo>|</mo></mrow></mfrac></math> 随机数验证规则（NVR） <math id="M367"><mfrac><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mo>#</mo><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">)</mo><mo>,</mo><mi>P</mi><mo>|</mo><mo>≡</mo><mi>Q</mi><mo>|</mo><mo>~</mo><mi>X</mi></mrow><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mi>Q</mi><mo>|</mo><mo>≡</mo><mi>X</mi></mrow></mfrac></math> 新鲜串联规则（FCR） <math id="M368"><mfrac><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mo>#</mo><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">)</mo></mrow><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mo>#</mo><mo stretchy="false">(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo stretchy="false">)</mo></mrow></mfrac></math> 裁判权规则（JR） <math id="M369"><mfrac><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mi>Q</mi><mo>⇒</mo><mi>X</mi><mo>,</mo><mi>P</mi><mo>|</mo><mo>≡</mo><mi>Q</mi><mo>|</mo><mo>≡</mo><mi>X</mi></mrow><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mi>X</mi></mrow></mfrac></math> 相信规则（BR） <math id="M370"><mfrac><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mi>X</mi><mo>,</mo><mi>P</mi><mo>|</mo><mo>≡</mo><mi>Y</mi></mrow><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mo stretchy="false">(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo stretchy="false">)</mo></mrow></mfrac></math> ， <math id="M371"><mfrac><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mo stretchy="false">(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo stretchy="false">)</mo></mrow><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mi>X</mi></mrow></mfrac></math> ， <math id="M372"><mfrac><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mi>Q</mi><mo>|</mo><mo>≡</mo><mo stretchy="false">(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo stretchy="false">)</mo></mrow><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mi>Q</mi><mo>|</mo><mo>≡</mo><mi>X</mi></mrow></mfrac></math> ， <math id="M373"><mfrac><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mi>Q</mi><mo>|</mo><mo>~</mo><mo stretchy="false">(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo stretchy="false">)</mo></mrow><mrow><mi>P</mi><mo>|</mo><mo>≡</mo><mi>Q</mi><mo>|</mo><mo>~</mo><mi>X</mi></mrow></mfrac></math> 5.2　安全目标 2 Goal 1: <math id="M374"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>≡</mo><mo stretchy="false">(</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mover accent="false"><mo stretchy="true">↔</mo><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi></mrow></mover><mi>S</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415221&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415220&type= 29.20999908 4.31799984 Goal 2: <math id="M375"><mi>S</mi><mo>|</mo><mo>≡</mo><mo stretchy="false">(</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mover accent="false"><mo stretchy="true">↔</mo><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi></mrow></mover><mi>S</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415223&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415222&type= 27.51666832 4.31799984 5.3　方案的理想化模型 2 消息 1: <math display="block" id="M376"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>→</mo><mi>S</mi><mo>:</mo><mo>{</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>,</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415225&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415224&type= 26.16199875 4.48733330 〈 <math display="block" id="M377"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415227&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415226&type= 4.82599974 3.72533321 〉 <math display="block" id="M378"><msub><mrow/><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow></msub><mo>,</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415229&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415228&type= 10.92199993 4.14866638 〈 <math id="M379"><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415231&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415230&type= 28.70199966 4.48733330 〉 <math id="M380"><msub><mrow/><mrow><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415233&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415232&type= 2.87866688 4.23333359 消息 2: <math display="block" id="M381"><mi>S</mi><mo>→</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>:</mo><mo>{</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>,</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415235&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415234&type= 26.33133316 4.48733330 〈 <math display="block" id="M382"><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>,</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415237&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415236&type= 35.39066696 4.48733330 〉 <math display="block" id="M383"><msub><mrow/><mrow><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415239&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415238&type= 2.87866688 4.23333359 5.4　初始化 2 A1: <math id="M384"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>≡</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415241&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415240&type= 18.96533394 4.48733330 ; A2: <math id="M385"><mi>S</mi><mo>|</mo><mo>≡</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415243&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415242&type= 17.27199936 4.48733330 ; A3: <math id="M386"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>≡</mo><mo>#</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415245&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415244&type= 21.25133324 4.57200003 ； A4: <math id="M387"><mi>S</mi><mo>|</mo><mo>≡</mo><mo>#</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415247&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415246&type= 19.55799866 4.57200003 ; A5: <math id="M388"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>≡</mo><mo stretchy="false">(</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mover accent="false"><mo stretchy="true">↔</mo><mrow><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mover><mi>S</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415249&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415248&type= 28.02466774 5.16466665 ; A6: <math id="M389"><mi>S</mi><mo>|</mo><mo>≡</mo><mo stretchy="false">(</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mover accent="false"><mo stretchy="true">↔</mo><mrow><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mover><mi>S</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415251&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415250&type= 26.24666595 5.16466665 ; A7: <math id="M390"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>≡</mo><mi>S</mi><mo>⇒</mo><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415253&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415252&type= 40.55533218 4.48733330 ; A8: <math id="M391"><mi>S</mi><mo>|</mo><mo>≡</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⇒</mo><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415255&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415254&type= 43.09533310 4.48733330 ; A9: <math id="M392"><mi>S</mi><mo>|</mo><mo>≡</mo><mi>s</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415257&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415256&type= 8.63599968 3.47133350 ； A10: <math id="M393"><mi>S</mi><mo>|</mo><mo>≡</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415259&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415258&type= 16.93333435 4.48733330 ; A11: <math id="M394"><mi>S</mi><mo>|</mo><mo>≡</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415261&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415260&type= 17.27199936 4.48733330 ; A12: <math id="M395"><mi>S</mi><mo>|</mo><mo>≡</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415263&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415262&type= 9.73666668 4.40266657 ； A13: <math id="M396"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>≡</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415265&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415264&type= 13.97000027 4.40266657 。 5.5　协议形式化分析 2 根据消息1,得 <math display="block" id="M397"><mi>S</mi><mo>⊲</mo><mo>{</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>,</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415267&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415266&type= 20.48933411 4.48733330 〈 <math display="block" id="M398"><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415269&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415268&type= 28.70199966 4.48733330 〉 <math display="block" id="M399"><msub><mrow/><mrow><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415271&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415270&type= 2.87866688 4.23333359 根据(S1)，得 <math display="block" id="M400"><mi>S</mi><mo>⊲</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415273&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415272&type= 6.43466663 2.79399991 〈 <math display="block" id="M401"><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415275&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415274&type= 27.09333420 4.48733330 〉 <math display="block" id="M402"><msub><mrow/><mrow><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415277&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415276&type= 1.60866666 4.06400013 根据(S2)，A6和消息含义规则，得 <math display="block" id="M403"><mi>S</mi><mo>|</mo><mo>≡</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>~</mo><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415279&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415278&type= 46.31266785 4.48733330 根据A4和相信规则，得 <math display="block" id="M404"><mi>S</mi><mo>|</mo><mo>≡</mo><mo>#</mo><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mtext> </mtext></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415281&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415280&type= 43.09533310 4.57200003 根据(S3)，(S4)和随机数验证规则，得 <math display="block" id="M405"><mi>S</mi><mo>|</mo><mo>≡</mo><mi>U</mi><mo>|</mo><mo>≡</mo><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415283&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415282&type= 47.66733170 4.48733330 根据(S5)，A8和裁判权规则，得 <math display="block" id="M406"><mi>S</mi><mo>|</mo><mo>≡</mo><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415285&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415284&type= 38.43866730 4.48733330 根据(S6)和相信规则，得 <math display="block" id="M407"><mi>S</mi><mo>|</mo><mo>≡</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>,</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415287&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415286&type= 26.07733345 4.48733330 <math display="block" id="M408"><mi>S</mi><mo>|</mo><mo>≡</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><mtext> </mtext><mi>S</mi><mo>|</mo><mo>≡</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415289&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415288&type= 25.06133270 4.40266657 根据 <math id="M409"><msub><mrow><mi>A</mi></mrow><mrow><mn mathvariant="normal">9</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn mathvariant="normal">10</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn mathvariant="normal">11</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415291&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415290&type= 24.89200020 4.14866638 ，以及 <math id="M410"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415293&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415292&type= 28.61733246 4.48733330 <math id="M411"><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>|</mo><mo>|</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415295&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415294&type= 26.33133316 4.48733330 和(S7)，得 <math id="M412"><mi>S</mi><mo>|</mo><mo>≡</mo><mo stretchy="false">(</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mover accent="false"><mo stretchy="true">↔</mo><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi></mrow></mover><mi>S</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415297&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415296&type= 27.51666832 4.31799984 (Goal 2) 根据消息2，得 <math display="block" id="M413"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊲</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415299&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415298&type= 8.21266651 3.72533321 〈 <math display="block" id="M414"><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>,</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415301&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415300&type= 35.05199814 4.48733330 〉 <math display="block" id="M415"><msub><mrow/><mrow><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415303&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415302&type= 1.60866666 4.06400013 根据（S8），（A5）和消息含义规则，得 <math display="block" id="M416"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>≡</mo><mi>S</mi><mo>|</mo><mo>~</mo><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>,</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415305&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415304&type= 54.69466782 4.48733330 根据A3和相信规则，得 <math display="block" id="M417"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>≡</mo><mo>#</mo><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415307&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415306&type= 32.08866501 4.57200003 根据(S9)，(S10)和随机数验证规则，得 <math display="block" id="M418"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>≡</mo><mi>S</mi><mo>|</mo><mo>≡</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415309&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415308&type= 33.78200150 4.48733330 根据S11，A7和裁判权规则，得 <math display="block" id="M419"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>≡</mo><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415311&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415310&type= 29.12533188 4.48733330 根据(S12)，A13和SK= h ( h (ID <math id="M420"><msub><mrow/><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415313&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415312&type= 0.84666669 4.06400013 <math id="M421"><mo>|</mo><mo>|</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415315&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415314&type= 4.91066647 4.48733330 <math id="M422"><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415317&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415316&type= 18.62666702 4.48733330 <math id="M423"><mo>|</mo><mo>|</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415319&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415318&type= 7.36599970 4.48733330 ，得 <math id="M424"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>≡</mo><mo stretchy="false">(</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mover accent="false"><mo stretchy="true">↔</mo><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi></mrow></mover><mi>S</mi><mo stretchy="false">)</mo><mtext> </mtext></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415321&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415320&type= 29.97199821 4.31799984 (Goal 1) 6　 安全性及性能分析 1 6.1　安全性分析 2 6.1.1 抗口令猜测攻击 3 攻击者无法通过在线口令猜测攻击对用户口令进行验证，因为他不知道用户 <math id="M425"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415323&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415322&type= 3.81000018 3.72533321 的 <math id="M426"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415326&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415325&type= 7.62000036 4.14866638 。另一方面，攻击者也无法通过离线口令猜测攻击获得 <math id="M427"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415328&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415327&type= 3.81000018 3.72533321 的口令 <math id="M428"><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415330&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415329&type= 5.41866684 4.57200003 。因为即使攻击者穷举用户的口令空间，但他不知道用户 <math id="M429"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415332&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415331&type= 3.81000018 3.72533321 的生物特征 <math id="M430"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415334&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415333&type= 3.30199981 3.72533321 。因此，改进的协议可抵抗口令猜测攻击。 6.1.2 抗重放攻击 3 假设攻击者事先窃听到合法用户 <math id="M431"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415336&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415335&type= 3.81000018 3.72533321 登录服务器 <math id="M432"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415338&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415337&type= 2.20133328 2.79399991 的请求消息 <math id="M433"><msub><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mo>{</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415340&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415339&type= 27.51666832 4.48733330 。然后假冒用户 <math id="M434"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415342&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415341&type= 3.81000018 3.72533321 重放窃听到的消息到服务器 <math id="M435"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415344&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415343&type= 2.20133328 2.79399991 。由于用户 <math id="M436"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415346&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415345&type= 3.81000018 3.72533321 每次会话中选取不同的随机数计算认证消息，因此攻击者无法成功实施重放攻击。 6.1.3 抗内部攻击 3 假设服务器 <math id="M437"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415348&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415347&type= 2.20133328 2.79399991 的内部攻击者得到消息 <math id="M438"><mo>{</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi mathvariant="normal">H</mi><mi mathvariant="normal">P</mi><msub><mrow><mi mathvariant="normal">W</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415350&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415349&type= 19.47333336 4.48733330 ，由于攻击者不知道随机数 <math id="M439"><mi>b</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415352&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415351&type= 1.86266661 2.79399991 和生物特征 <math id="M440"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415354&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415353&type= 3.30199981 3.72533321 ，因此无法发起有效的攻击。 6.1.4 抗智能卡丢失攻击 3 智能卡丢失攻击是指攻击者不能根据智能卡中的消息获得用户 <math id="M441"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415356&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415355&type= 3.81000018 3.72533321 的口令或用户 <math id="M442"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415358&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415357&type= 3.81000018 3.72533321 和服务器 <math id="M443"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415360&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415359&type= 2.20133328 2.79399991 之间的会话密钥。若攻击者获得用户 <math id="M444"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415362&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415361&type= 3.81000018 3.72533321 的智能卡，并通过侧信道攻击分析出智能卡中的秘密信息 <math id="M445"><mo stretchy="false">(</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>h</mi><mo stretchy="false">(</mo><mo>⋅</mo><mo stretchy="false">)</mo><mo>,</mo><mi>x</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>,</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">。</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415364&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415363&type= 48.68333054 4.82599974 因为不知 <math id="M446"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415366&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415365&type= 17.27199936 4.57200003 ，无法计算出 <math id="M447"><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415368&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415367&type= 2.45533323 3.72533321 。此外，即使他窃听到用户 <math id="M448"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415370&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415369&type= 3.81000018 3.72533321 和服务器 <math id="M449"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415372&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415371&type= 2.20133328 2.79399991 在公开信道上传递的消息 <math id="M450"><msub><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415374&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415373&type= 17.52599907 4.14866638 ，也无法得到 <math id="M451"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415376&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415375&type= 10.49866676 4.14866638 。因此，攻击者不能恢复出用户 <math id="M452"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415378&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415377&type= 3.81000018 3.72533321 和服务器 <math id="M453"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415380&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415379&type= 2.20133328 2.79399991 之间的会话密钥，也无法伪造有效的登录请求消息。从以上分析可看出，改进协议可抵抗智能卡丢失攻击。 6.1.5 抗假冒攻击 3 假设攻击者试图冒充用户 <math id="M454"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415382&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415381&type= 3.81000018 3.72533321 登录服务器 <math id="M455"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415384&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415383&type= 2.20133328 2.79399991 ，他需要伪造新的合法登录请求消息 <math id="M456"><msub><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mo>{</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>}</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415386&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415385&type= 27.51666832 4.48733330 ，但是攻击者在不知道 <math id="M457"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415388&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415387&type= 4.82599974 3.72533321 和 <math id="M458"><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415390&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415389&type= 2.45533323 3.72533321 的情况下，无法计算出有效的消息 <math id="M459"><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415392&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415391&type= 3.72533321 3.72533321 和 <math id="M460"><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415394&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415393&type= 3.72533321 3.72533321 。另一方面，攻击者也无法伪造出有效的 <math id="M461"><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415396&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415395&type= 3.72533321 3.72533321 和 <math id="M462"><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415398&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415397&type= 3.72533321 3.72533321 。因此，改进的协议可抵抗假冒攻击。 6.1.6 相互认证 3 在登录和认证阶段的第2步，服务器 <math id="M463"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415400&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415399&type= 2.20133328 2.79399991 计算 <math id="M464"><msubsup><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>|</mo><mo>|</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415402&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415401&type= 32.93533325 4.65666676 ，与用户 <math id="M465"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415404&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415403&type= 3.81000018 3.72533321 发送登录消息中的 <math id="M466"><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415406&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415405&type= 3.72533321 3.72533321 比较。若二者相等，服务器 <math id="M467"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415408&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415407&type= 2.20133328 2.79399991 认证用户 <math id="M468"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415410&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415409&type= 3.81000018 3.72533321 身份的合法性；否则，终止会话。另一方面，在登录和认证阶段的第3步，用户计算 <math id="M469"><msubsup><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415412&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415411&type= 29.04066658 4.65666676 ，通过验证 <math id="M470"><msubsup><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415414&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415413&type= 12.53066635 3.97933340 是否成立来实现对服务器 <math id="M471"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415416&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415415&type= 2.20133328 2.79399991 的认证。若等式成立，用户 <math id="M472"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415419&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415417&type= 3.81000018 3.72533321 认证服务器 <math id="M473"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415423&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415421&type= 2.20133328 2.79399991 的合法性。最后，双方协商会话密钥 <math id="M474"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>|</mo><mo>|</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415427&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415425&type= 42.58733368 4.48733330 用于将来的通信。 6.1.7 抗中间人攻击 3 根据6.1.5和6.1.6的分析可知，攻击者不知道 <math id="M475"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415430&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415429&type= 4.82599974 3.72533321 和 <math id="M476"><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415434&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415432&type= 2.45533323 3.72533321 无法成功实施中间人攻击。 6.1.8 提供匿名性 3 用户 <math id="M477"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415438&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415437&type= 3.81000018 3.72533321 的真实身份信息 <math id="M478"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415442&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415440&type= 4.82599974 3.72533321 隐藏在 <math id="M479"><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415447&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415445&type= 5.24933338 4.14866638 <math id="M480"><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>,</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415450&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415448&type= 5.24933338 4.14866638 <math id="M481"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mi mathvariant="normal">V</mi><mo>,</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415454&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415452&type= 9.56733322 3.21733332 只有服务器 <math id="M482"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415458&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415456&type= 2.20133328 2.79399991 能通过公式 <math id="M483"><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>⊕</mo><mi>h</mi><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415462&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415460&type= 39.79333496 4.65666676 恢复出用户的身份。此外，攻击者无法通过公开信息中的消息 <math id="M484"><msub><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415466&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415464&type= 17.52599907 4.14866638 追踪用户 <math id="M485"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415470&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415468&type= 3.81000018 3.72533321 。因为这些消息都与随机数 <math id="M486"><mi>u</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415472&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415471&type= 1.86266661 2.79399991 和 <math id="M487"><mi>v</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415474&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415473&type= 1.86266661 2.79399991 有关。因此，改进协议实现了用户行为的不可追踪性。 6.1.9 提供前向安全性 3 假设用户 <math id="M488"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415476&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415475&type= 3.81000018 3.72533321 的口令 <math id="M489"><mi mathvariant="normal">p</mi><msub><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415478&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415477&type= 5.41866684 4.57200003 和服务器 <math id="M490"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415480&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415479&type= 2.20133328 2.79399991 长期的私钥 <math id="M491"><mi>s</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415482&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415481&type= 1.26999998 2.79399991 泄露给了攻击者，且攻击者也获得了用户 <math id="M492"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415484&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415483&type= 3.81000018 3.72533321 和服务器 <math id="M493"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415486&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415485&type= 2.20133328 2.79399991 之间在公开信道上传输的消息。攻击者仍然无法计算出用户 <math id="M494"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415488&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415487&type= 3.81000018 3.72533321 和服务器 <math id="M495"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415490&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415489&type= 2.20133328 2.79399991 之间的会话密钥 <math id="M496"><mi mathvariant="normal">S</mi><mi mathvariant="normal">K</mi><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><mo>|</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>u</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>|</mo><mo>|</mo><mi mathvariant="normal">I</mi><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415493&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415491&type= 42.58733368 4.48733330 。因为他将面临扩展切比雪夫多项式的CDHP困难问题。因此，改进的协议实现了前向安全性。 6.2　性能分析 2 本节分别从安全属性和计算量两方面来分析改进协议的性能。 表4 表4 给出了现有的协议与本文提出的协议安全属性的比较结果，从中可看出本文给出的改进协议满足所有的安全属性（与文献[ 2 2 ]比较是因为文献[ 2 2 ]中的协议也是基于扩展混沌映射的三因子身份认证协议）。 安全属性 Lu等 [ 2 2 ] Sutrala等 [ 18 18 ] 本文协议 相互认证 否 是 是 匿名性 否 是 是 抗口令猜测攻击 否 是 是 抗重放攻击 是 是 是 抗中间人攻击 是 否 是 抗内部攻击 是 是 是 抗智能卡丢失攻击 否 否 是 抗假冒攻击 否 否 是 提供前向安全性 是 否 是 表5 表5 列出了改进协议与现有一些方案的计算开销的对比，主要比较提出的协议和其他相关协议在登录阶段和认证阶段的计算时间。为了方便讨论，用 <math id="M497"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">h</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415497&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415496&type= 3.72533321 3.72533321 表示单向哈希函数的时间（ <math id="M498"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">h</mi></mrow></msub><mo>≈</mo><mn mathvariant="normal">0.000</mn><mtext> </mtext><mn mathvariant="normal">32</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415500&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415499&type= 21.67466736 3.72533321 s）， <math id="M499"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">C</mi><mi mathvariant="normal">C</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415503&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415502&type= 6.77333355 3.72533321 表示计算一次椭圆曲线点乘的时间（ <math id="M500"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">C</mi><mi mathvariant="normal">C</mi></mrow></msub><mo>≈</mo><mn mathvariant="normal">0.017</mn><mtext> </mtext><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415505&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415504&type= 22.77533340 3.72533321 s）， <math id="M501"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">M</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415508&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415506&type= 5.92666674 3.72533321 表示计算一次切比雪夫混沌映射的时间（ <math id="M502"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">M</mi></mrow></msub><mo>≈</mo><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">C</mi><mi mathvariant="normal">C</mi></mrow></msub><mo>≈</mo><mn mathvariant="normal">0.017</mn><mtext> </mtext><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415511&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415510&type= 33.69733429 3.72533321 s）， <math id="M503"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415513&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415512&type= 3.64066648 3.72533321 表示RSA加密和RSA解密的时间（ <math id="M504"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub><mo>≈</mo><mn mathvariant="normal">0.019</mn><mtext> </mtext><mn mathvariant="normal">2</mn><mtext> </mtext></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415515&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415514&type= 20.23533440 3.72533321 s），上述 <math id="M505"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">h</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415517&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415516&type= 3.72533321 3.72533321 ， <math id="M506"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">C</mi><mi mathvariant="normal">C</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415519&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415518&type= 6.77333355 3.72533321 ， <math id="M507"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">M</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415521&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415520&type= 5.92666674 3.72533321 ， <math id="M508"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415523&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415522&type= 3.64066648 3.72533321 这些操作运行所花费的时间参考文献[ 22 22 ]，异或 <math id="M509"><mo>⊕</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415525&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415524&type= 3.72533321 3.47133350 运算和 <math id="M510"><mo>|</mo><mo>|</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415527&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=3415526&type= 1.43933344 3.47133350 运算的计算量很小，通常忽略不计。从 表4 表4 和 表5 表5 中可看出本方案耗时比文献[ 2 2 ]和文献[ 18 18 ]多，但是安全性优于它们。 协议 执行时间/s Lu等 [ 2 2 ] <math id="M511"><mn>14</mn><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">h</mi></mrow></msub><mo>+</mo><mn>4</mn><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">C</mi><mi mathvariant="normal">C</mi></mrow></msub><mo>≈</mo><mn>0.072</mn><mtext> </mtext><mn>88</mn></math> Sutrala等 [ 18 18 ] <math id="M512"><mn>16</mn><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">h</mi></mrow></msub><mo>+</mo><mn>2</mn><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub><mo>≈</mo><mn>0.043</mn><mtext> </mtext><mn>52</mn></math> 本文协议 <math id="M513"><mn>18</mn><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">h</mi></mrow></msub><mo>+</mo><mn>6</mn><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">M</mi></mrow></msub><mo>≈</mo><mn>0.108</mn><mtext> </mtext><mn>36</mn></math> 7　 结 语 1 本文首先回顾了Sutrala等的基于口令的用户匿名认证和密钥协商协议，指出其不能抵抗口令猜测攻击、中间人攻击，不具备前向安全性。为了克服以上安全漏洞，基于扩展混沌映射提出了一个三因子的匿名用户身份认证协议，形式化证明和安全分析表明本文提出的方案是安全的。此外，与现有的协议相比，本文更适用于远程医疗信息系统环境。 参考文献 WEI J , HU X , LIU W . 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DOI:10.14188/j.1671-8836.2019.0507(Ch). 屈娟,李艳平.适用于远程医疗信息系统的身份认证协议[J].武汉大学学报（理学版）,2020,66(2):117-125. DOI:10.14188/j.1671-8836.2019.0507. 屈娟,李艳平.适用于远程医疗信息系统的身份认证协议[J].武汉大学学报（理学版）,2020,66(2):117-125. DOI:10.14188/j.1671-8836.2019.0507. 国家自然科学基金 (61802243); 陕西省重点研发计划(2019GY-013); 中央高校基本科研业务费专项资金 (GK201803005) 2019-09-10 2020-04-24 2020-09-30 武汉大学学报（理学版） 2 66