针对随机延迟防护的安全性评价方法

针对随机延迟防护的安全性评价方法 Safety Evaluation for Random Delay Insertion 1 first-author 罗买兴，男，硕士生，现从事密码学中侧信道分析理论与方法研究. E-mail: lmx2016@whu.edu.cn 罗买兴，男，硕士生，现从事密码学中侧信道分析理论与方法研究. E-mail: lmx2016@whu.edu.cn lmx2016@whu.edu.cn 2 3 4 1 corresp 唐明, E-mail:m.tang@126.com 唐明, E-mail:m.tang@126.com m.tang@126.com 武汉大学 计算机学院，湖北 武汉 430072 武汉大学 计算机学院，湖北 武汉 430072 School of Computer, Wuhan University, Wuhan 430072, Hubei, China School of Computer, Wuhan University, Wuhan 430072, Hubei, China 北京智芯微电子科技有限公司，电力芯片设计分析国家电网公司重点实验室，北京 100080 北京智芯微电子科技有限公司，电力芯片设计分析国家电网公司重点实验室，北京 100080 State Grid Key Laboratory of Power Industrial Chip Design and Analysis Technology, Beijing Smart-Chip Microelectronics Technology Co., Ltd., Beijing 100080, China State Grid Key Laboratory of Power Industrial Chip Design and Analysis Technology, Beijing Smart-Chip Microelectronics Technology Co., Ltd., Beijing 100080, China 北京智芯微电子科技有限公司，北京电力高可靠性集成电路设计工程技术中心，北京 100080 北京智芯微电子科技有限公司，北京电力高可靠性集成电路设计工程技术中心，北京 100080 Beijing Engineering Research Center of High-Reliability IC with Power Industrial Grade, Beijing Smart-Chip Microelectronics Technology Co., Ltd., Beijing 100080, China Beijing Engineering Research Center of High-Reliability IC with Power Industrial Grade, Beijing Smart-Chip Microelectronics Technology Co., Ltd., Beijing 100080, China 国网新疆电力公司检修公司, 新疆 乌鲁木齐 830002 国网新疆电力公司检修公司, 新疆 乌鲁木齐 830002 State Grid Xinjiang Maintenance Company, Urumqi 830002, Xinjiang, China State Grid Xinjiang Maintenance Company, Urumqi 830002, Xinjiang, China 提出了一个针对随机延迟防护的攻击方法的分析评价框架.在这个框架的基础上分析了直接攻击和整合(integration)攻击的攻击效率.同时，提出了一种新的攻击方法WIA(带权重的整合攻击)，分析了其在各种条件下的攻击效率，得出了比现有文献更一般性的结论.试验结果表明，相比于已有的攻击方法，WIA的攻击效率更高，因此WIA的攻击结果更能科学地反映随机延迟防护的安全性强度. An analysis and evaluation framework for analyzing attack methods for random delay insertion is proposed. Then, on the basis of this framework, we analyze the attack efficiency of direct attack and integration attack, our conclusion is more general than the existing literature. At the same time, a new attack method WIA (weighted integration attack) is proposed and its attack efficiency under various conditions is analyzed. The experimental results show that the attack efficiency of WIA is higher than the existing attack methods, so the WIA attack results can scientifically reflect the security strength of random delay insertion in a better way. 侧信道分析 随机延迟 安全性评价 相关功耗分析 side channel analysis random delay safety evaluation correlation power analysis 引言 1 传统密码分析在已知密码算法和明文/密文对的情况下，通过分析密码算法的数学性质来恢复密钥.现在, 标准加密算法如AES(advanced encryption standard)，基本上可以抵抗差分攻击、线性攻击等传统的密码分析技术.但是，这还不足以保证在实际工作中密码芯片是安全的.在实际工作中的密码芯片除了密码算法和明文/密文对外，还有另一类信息可以被利用.这类信息就是密码芯片在加密过程中产生的能量消耗、电磁辐射等物理泄露信息.利用这些物理泄露信息进行攻击的方法统称为侧信道攻击(side channel attack, SCA).1999年Kocher等 [ 1 1 ] 提出了差分功耗分析DPA(differential power analysis)，首次利用密码芯片工作过程中能量消耗与密码算法中数据的相关性成功地恢复出了密钥.随后，Agrawal等 [ 2 2 ] 利用加密过程中的电磁辐射信息成功地恢复出密钥，而早在1996年Kocher等 [ 3 3 ] 曾利用加密算法运行的时间长度信息成功地恢复了密钥.在攻击方法方面，也出现了一大批有效的攻击方法：Chari等 [ 4 4 ] 提出的TA(template attacks)，Brier等 [ 5 5 ] 提出的CPA(correlation power analysis)，Schindler等 [ 6 6 ] 提出的SA(stochastic approach)，以及Gierlichs等 [ 7 7 ] 提出的MIA(mutual information analysis).与此同时，抵抗这些SCA的防护方法也取得了长足的发展.目前防护方法大致分为两类：掩码(masking)和隐藏(hiding).掩码将密码算法中的每个中间值再拆分成两个或多个新的值.这些新的值通常被称为分量(share).每个分量在每次加密过程中都会随机地取值，这样就可以达到抵抗SCA的目的.隐藏可以通过降低信息泄露的程度或是提高噪声水平或是在时间维度上引入随机性来增加SCA的难度. 本文提出的针对随机延迟RDI(random delay insertion)的防护是一种在时间维度上引入随机性的防护方法.RDI使得密码算法中特定操作对应的功耗在功耗曲线上的位置不再固定，这样便可以增加SCA的难度.相比于掩码，RDI是一种简单而又轻量化的防护方法，在实际密码芯片中得到了广泛的应用.在时间维度上引入随机性的防护方法主要包括以下三类：软件实现的RDI，硬件实现的RPI(random process interrupts)以及乱序(shuffing).软件实现的RDI的一种典型方法是在密码算法的汇编代码中加入一些不影响密码算法功能的由随机数控制的循环 [ 8 8 ] .RPI一般通过一些由随机数控制的电路来实现 [ 9 9 , 10 10 ] ，乱序则是通过随机地打乱可以乱序执行的操作(如AES 16个S盒操作可以乱序执行)来实现 [ 11 11 ] . 针对RDI防护的攻击方法主要包括以下四类：直接攻击，整合后进行攻击，对齐(alignment)后进行攻击，通过模式识别的方法消除RDI后进行攻击.相比较而言，前面两类方法更通用，实现起来简单.对齐后进行攻击的方法，只能针对在曲线的开头或结尾插入的随机延迟；基于模式识别的方法实现起来复杂而且需要更多的条件(例如，需要对指令集中的每一条指令都建立模板，这还和处理器的体系架构和实现工艺相关)，而且主要针对通过软件方式插入的随机延迟.Mangard [ 12 12 ] 分析了直接攻击方法的效率，如果目标中间值以概率 p 出现在某一位置，则CPA算出的相关系数约为没有RDI防护的相关系数的 p 倍.Clavier等 [ 9 9 ] 首次提出整合攻击(文中称作SW-DPA)并分析了它的效率.整合攻击将多个时刻的功耗累加，通过计算累加功耗和假设功耗之间的相关系数来恢复密钥.Mangard等 [ 13 13 ] 分析了整合方法在CPA攻击下的效率；相比于直接攻击整合攻击可以大大降低攻击所需要的曲线量.在基于对齐的攻击方法方面，Van Woudenberg等 [ 14 14 ] 提出一种基于DTW(dynamic time warping)的对齐方法.文献[ 15 15 , 16 16 ]则通过模式识别的方法试图移除RDI防护插入的伪指令.Strobel等 [ 15 15 ] 首先通过功耗曲线恢复出指令操作码的汉明重，然后通过BMH(Boyer-Moore-Horspool)算法判断并移除伪指令序列.Durvaux等 [ 16 16 ] 使用HMM(hidden Markov model)从功耗曲线恢复出密码算法指令序列，然后移除RDI对应的指令.文献[ 8 8 , 17 17 , 18 18 ]考虑了RDI防护往往需要在多个不同的位置单独地插入随机延迟的情况，这时影响攻击点攻击效率的RDI分布实际上是位于攻击点前面多个RDI随机变量的和分布.他们认为当RDI的分布服从离散均匀分布时防护效果是最好的.但是，多个独立同分布随机变量的和分布趋近于正态分布，不再服从离散均匀分布.文献[ 8 8 ]通过调整单个随机延迟分布的特性来改善和分布，使和分布更加接近离散均匀分布；文献[ 17 17 , 18 18 ]则通过在各个RDI随机变量之间引进相关性来改善和分布. 本文在文献[ 12 12 ]RDI防护分析框架的基础上，提出一种更精细的分析框架.然后用这个框架分析直接攻击和整合攻击的效率，得出比文献[ 12 12 ]和 [ 13 13 ] 更一般性的结论，并分析了文献[ 12 12 ]和 [ 13 13 ] 中结论成立的条件.同时提出一种新的针对RDI防护的方法WIA(weighted integration attack).相比整合攻击，WIA利用了随机延迟的分布信息以及未加防护攻击点附近功耗的特性信息，可以进一步提高攻击效率. RDI防护的分析框架 1 在SCA领域中，芯片的安全性评价方法基本上等同于在最强假设下的攻击方法.最强假设一般是指攻击者知道密码算法的实现细节以及拥有与攻击设备物理泄露特征相同的设备(称为模板设备).模板攻击TA就是一种建立在最强假设基础上的SCA方法.一般认为在实际攻击中知道密码算法的实现细节是可行的，而模板设备是很难得到的.所以像TA这样需要模板设备的SCA方法，在实际攻击中是很难被使用的，但是可以作为一种安全性评价方法.理由如下：一方面，对于密码芯片的设计者而言，模板设备是很容易获取的；另一方面，在对芯片进行安全性评价的时候，往往需要考虑在最坏的情况下芯片的安全性强度.这样，密码芯片设计者在对芯片安全性进行评价的时候，拥有模板设备既是可行的也是合理的.芯片抵抗SCA的安全性强度可以用成功攻击所需要的曲线量来衡量.曲线量越大，安全性强度也就越大.本文就是用曲线量来衡量芯片的安全性强度.由于在CPA攻击场景下曲线量和相关系数有一个直接的函数关系，所以也可以用相关系数的大小来衡量安全性强度的大小，相关系数越小，安全性强度越大. 本文的RDI防护分析框架是建立在Mangard [ 12 12 ] 提出的分析框架的基础上.文献[ 12 12 ]的分析框架用于分析各种硬件防护策略抵抗CPA攻击的效率.下面先给出文献[ 12 12 ]中的分析框架和重要的结论，然后给出本文分析框架. 设攻击点的实测功耗为随机变量 P .它由两部分组成，一部分是和数据相关的部分 Q ，另一部分是和数据无关的加性噪声 N ，即 P = Q + N .假设功耗(假设功耗是通过汉明重、汉明距等功耗模型计算出来的功耗值，也称为预测功耗)为 H .另外，设在RDI防护的情况下攻击点的功耗为 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=middle .它以 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257719&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257719&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257719&type=middle 的概率取到与数据相关的功耗 P ，以(1- http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257719&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257719&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257719&type=middle )的概率取到与数据无关的功耗 O .最终Mangard建立了相关系数 ρ ( H , http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=middle )和信噪比以及概率 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257719&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257719&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257719&type=middle 之间的联系，如下： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257611&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257611&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257611&type=middle 其中, http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257720&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257720&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257720&type=middle . 文献[ 12 12 ]另外一个重要的结果是建立了相关系数(一般取最大值 ρ max )和成功攻击所需要曲线量 S 之间的联系，如下： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257614&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257614&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257614&type=middle 其中, Z α 是标准正态分布的下 α 分位数，用于衡量正确假设密钥相关系数 R ck (均值为 ρ max )分布和错误密钥相关系数 R wk (均值为0)分布之间的距离，满足如下等式： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257618&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257618&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257618&type=middle 当 ρ max 接近于0时，(2)式可进行如下变换 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257622&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257622&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257622&type=middle 本文沿用文献[ 12 12 ]的思路，所有的攻击都使用CPA.因此只需分析相关系数的大小，由相关系数到曲线量的映射由(4)式完成.本文需要如下三条假设：1)攻击者知道插入随机延迟的分布以及攻击点可能出现的位置；2)随机延迟的插入点离攻击点足够远，具体地讲就是两者相距的时钟周期数大于最大延迟数(最多插入的时钟周期数)；3)攻击者知道没有防护情况下，攻击点以及其附近功耗的均值和协方差矩阵.第三条假设对于实际的攻击者是很难满足的，但是对于密码芯片的设计者而言是容易满足的.所以基于以上三条假设的攻击方法并不能作为实际的攻击方法，只能用作芯片安全性评价. 设在攻击点之前插入的随机延迟为随机变量 D (以时钟周期为单位)，并且其分布为： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257626&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257626&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257626&type=middle 其中, d 为可以插入的最大延迟数.如果攻击点之前插入了多个随机延迟 D i ( i =1, 2, …, n )，则(5)式的随机延迟 D 用多个随机延迟的和 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257721&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257721&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257721&type=middle 来代替.在 D =0(也即插入的时钟周期数为0)时，不妨令攻击点的时刻为 t =0，其功耗值为随机变量 P 0 ，前 d 个时刻的功耗值依次为随机变量： P - d , P - d +1 , …, P -2 , P -1 ，后 d 个功耗值为： P 1 , P 2 , …, P d -1 , P d .因为插入的最大延迟数为 D = d ，所以正确功耗 P 0 可能出现的位置为 t =0, 1, …, d .设 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=middle t ( t =0, 1, …, d )为增加了RDI防护的功耗曲线在 t 时刻的功耗值(如 图 1 图 1 所示)，则有： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257628&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257628&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257628&type=middle 针对RDI防护的攻击 1 在本节，我们将分析3种针对RDI防护攻击方法包括直接攻击、整合攻击以及WIA的攻击效率.由(4)式易知，相关系数越大，成功攻击所需要的曲线量就越小，说明对应的攻击方法也就越有效.在密码芯片设计者对芯片进行安全性评价的时候，需要考虑最坏情况下芯片的安全性强度.本文也就是要考虑最有效的攻击方法下相关系数的大小，相关系数越小，芯片抗SCA的能力也就越强. 直接攻击 2 令H为通过中间值计算出的假设功耗，并假设 H 和非攻击点的功耗 P t ( t ≠0)相互独立，则对H与各个时刻的功耗 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=middle t 之间的相关系数 ρ ( H , http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=middle t )有： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257635&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257635&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257635&type=middle http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257637&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257637&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257637&type=middle http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257640&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257640&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257640&type=middle 下面对上面的推导过程作出详细的说明.由 P t ( t ≠0)与 H 相互独立，可以得到Cov( H , P t )=0( t ≠0)，从而由(7)式可以得到(8)式.(7)式的得出需要用到下面引理. 引理1   (重期望公式和条件方差公式)设( X , Y )是二维随机变量，则有： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257642&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257642&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257642&type=middle 以及 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257644&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257644&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257644&type=middle 运用上面引理的推广形式，我们有： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257647&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257647&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257647&type=middle 这样就得到了(7)式. 整合攻击 2 整合攻击先进行如下的预处理：将正确的功耗值可能出现的时间段上的所有功耗值进行累加；然后，按照CPA的一般流程进行攻击.正确功耗值 P 0 可能出现的位置为 t =0, 1, …, d ，所以累加值为随机变量 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257725&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257725&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257725&type=middle ，则其与假设功耗 H 的相关系数为： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257650&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257650&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257650&type=middle http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257652&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257652&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257652&type=middle http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257656&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257656&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257656&type=middle (11) 式直接运用了直接攻击中(8)式的结果，(13)式用到了 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257726&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257726&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257726&type=middle .由(11)式到(12)式，需要 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257727&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257727&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257727&type=middle ，而要使其成立，需要条件 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257728&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257728&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257728&type=middle 成立，展开得： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257657&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257657&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257657&type=middle http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257660&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257660&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257660&type=middle http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257662&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257662&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257662&type=middle Cov( E ( P i - k ), E ( P j - k ))的含义是在功耗曲线上截取两段长度为 d +1的曲线，剔除电子噪声(取均值的效益)的影响，从左到右为每个值指派一个概率 p i ，再求协方差.由于两段曲线的功耗值不存在相互依赖性，所以可暂时假定这个值为0(2.3节将去掉这个条件得出更一般性的结论)，从而得到(12)式. WIA 2 无论是直接攻击还是整合攻击，都可以写成这样的形式 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257729&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257729&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257729&type=middle ，其中 λ i ( i =0, 1, …, d )是一组系数.具体地讲，在整合攻击中所有的系数都为1；而在直接攻击中，这些系数只有一个为1，其他都为0.显然这一组系数还可以取其他任何值，我们并不能保证直接攻击和整合攻击中的系数是最优的.所以，我们可以通过最优化技术，求解使 ρ ( H , P )= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257730&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257730&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257730&type=middle 最大化或最小化(也即绝对值最大化)的一组 λ i ( i =0, 1, …, d ).这就是本文提出的WIA方法. 直接攻击和整合攻击的分析用到了两个条件： ① Cov( H , P t )=0( t ≠0)， ② Cov( http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=middle i , http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=middle j )=0( i ≠ j ). 本节根据这两个条件的成立情况，分三种情况讨论WIA理论上的最优攻击结果，分别在2.3.1节、2.3.2节和2.3.3节给出. 条件①和②都满足时 3 运用2.1节中的一些结论，很容易得出： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257665&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257665&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257665&type=middle http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257666&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257666&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257666&type=middle 下面我们通过对每个 λ i 求偏导数的方法来确定各个待定的 λ i ，令 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257667&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257667&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257667&type=middle 对 λ i 求偏导数得 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257668&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257668&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257668&type=middle 令(13)式等于0，可以得到： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257669&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257669&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257669&type=middle http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257670&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257670&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257670&type=middle 其中， http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257671&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257671&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257671&type=middle 将(22)式代入(19)式，得到一个和 k 无关的结果，所以可以直接令 k =1.最终我们有： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257673&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257673&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257673&type=middle 当 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257733&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257733&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257733&type=middle 时，取得最值. 上面只是找到了一个可能的最大值及其取得的条件，下面给出证明： 要证 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257675&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257675&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257675&type=middle 只要证 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257677&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257677&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257677&type=middle 上式由柯西不等式直接得到，证毕. 最终我们得出在条件①和条件②都满足的情况下，WIA的效率： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257678&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257678&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257678&type=middle 条件①满足而条件②不满足时 3 在这一节，我们试图在条件②不满足的情况下，进行更一般意义的分析. 在条件Cov( http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=middle i , http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=middle j )=0( i ≠ j )不成立的情况下，只能得到： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257679&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257679&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257679&type=middle 其中， http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257736&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257736&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257736&type=middle . 在(24)式两边，对 λ i 求偏导数，得： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257680&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257680&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257680&type=middle 展开Var( P )得： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257681&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257681&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257681&type=middle 在(26)式两边，对 λ i 求偏导数，得： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257682&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257682&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257682&type=middle 令(25)式等于0，可以得到： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257683&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257683&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257683&type=middle 其中， http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257737&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257737&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257737&type=middle . 下面证明直接令 K =1时，也可取得最值.易知： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257684&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257684&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257684&type=middle 所以，如果( λ 0 0 , λ 1 0 , …, λ d 0 )是 f ( λ 0 , λ 1 , …, λ d )的最大值点，则对于所有的 k ( k ≠0)，( kλ 0 0 , kλ 1 0 , …, kλ d 0 )也是最大值点.此时， http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257685&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257685&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257685&type=middle 从而可以调整 k ，使得 K =1，同时取得最值. 于是有： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257686&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257686&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257686&type=middle 写成矩阵的形式得： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257687&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257687&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257687&type=middle 令 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257688&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257688&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257688&type=middle 其中 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257689&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257689&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257689&type=middle 于是，(28)式可写成 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257690&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257690&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257690&type=middle 易知，对于所有的 λ ≠ 0 ，Var( P )= λ T Vλ ＞0，所以 V 是一个正定的对称矩阵，一定可逆.从而(29)式一定有解，即 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257691&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257691&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257691&type=middle 另外有 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257692&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257692&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257692&type=middle 最终得到 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257693&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257693&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257693&type=middle 当 λ = V -1 p 时，取得最值. 下面给出证明，首先，由于 V 是正定矩阵，所以它可以分解为 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257694&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257694&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257694&type=middle 其中 Q 可逆，且 Q -1 = Q T ， W 为对角矩阵，且其对角元素都大于0(因为 V 是正定矩阵)，记其对角元素为 w j ( j =0, 1, …, d ). 要证 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257695&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257695&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257695&type=middle 只要证 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257696&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257696&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257696&type=middle 记 p ′= Qp ，其分量为 p ′ j ； λ ′= Qλ ，其分量为 λ ′ j , j =0, 1, 2, …, d ，首先有 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257697&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257697&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257697&type=middle 另外，由柯西不等式有 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257698&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257698&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257698&type=middle 即 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257699&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257699&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257699&type=middle 综上(31)~(34)式，可得 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257700&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257700&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257700&type=middle 证毕. 条件①和②都不满足时 3 在这一小节，我们去除前面所有的关于独立性和不相关性的假设，给出更一般性的结论. http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257701&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257701&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257701&type=middle 令 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257702&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257702&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257702&type=middle 则(36)式可以写成如下形式(其他矩阵符号同2.3.2节) http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257703&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257703&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257703&type=middle 我们有如下结论 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257704&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257704&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257704&type=middle 当 λ = V -1 Gp 时，取得最值.证明同2.3.2节，只需在(30)式中，令 p = Gp 便可得到(38)式. 基于WIA的安全性评价 2 虽然WIA是一种针对随机延迟防护的有效的攻击方法, 但是，对于攻击者而言，一般情况下进行WIA所需要的条件是很难被满足的，所以WIA更适合芯片设计者对芯片进行安全性评价.下面我们直接以相关系数作为评价安全性强度的指标.相关系数越小，成功恢复出密钥所需要的曲线量就越大，芯片安全性强度就越大.我们将从一般情况出发，慢慢加入新的条件，得出在不同条件下WIA的效率. a) 由2.3.3节中的结论知，一般情况下有： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257705&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257705&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257705&type=middle 当 λ = V -1 Gp 时，可取得最值. b) 进一步，如果条件Cov( H , P t )=0( t ≠0)成立，即假设功耗与非攻击点功耗不相关，此时有 G =Cov( H , P 0 ) I ( I 为单位矩阵)，代入(39)式得： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257706&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257706&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257706&type=middle 当 λ = V -1 p 时，可取得最值. c) 进一步，如果条件Cov( http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=middle i , http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=middle j )=0( i ≠ j )成立，则 V 为对角矩阵，此时可以将(40)式写成如下形式： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257707&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257707&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257707&type=middle 当 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257740&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257740&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257740&type=middle 时，可取得最值. d) 进一步，如果Var( http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=middle k )= σ 2 ( k =0, 1, …, d )( σ 2 为一个常量)，代入(41)式得： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257708&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257708&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257708&type=middle 当 λ i = p k ( k =0, 1, 2, …, d )时，可取得最值. e) 进一步，如果插入的随机延迟 D 的分布是离散均匀分布，即 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257709&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257709&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257709&type=middle 将(43)式代入(42)式得： http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257710&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257710&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257710&type=middle http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257711&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257711&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257711&type=middle 当 λ i =1( i =0, 1, 2, …, d )时，可取得最值，此时WIA同整合攻击相同，也就是说整合攻击是在极其苛刻的条件下的WIA.而这些条件在实际中基本不可能满足，从而WIA总是优于整合攻击.(45)式既是整合攻击的结论，也是文献[ 13 13 ]中的结论.由于(45)式需要满足一系列的条件，这就注定了这个结论的适用面比较窄，不能科学地反映现实中各种RDI防护的安全性强度.所以，在对芯片进行安全性评价时，一般性的结论(39)式比(45)式更精确更科学. 实验 1 为了比较2.4节中a)~e)中5组参数 λ i ( i =0, 1, 2, …, d )的有效性专门进行了实验.实验使用了在SASEBO-W(专门用于SCA评估的一个电路板)上做AES加密的ATMega-163卡，时钟频率为3.571 2 MHz；功耗信号要经过一个PA303放大器；使用Agilent DSO-X3034A示波器(采样率为50MSa/s)采集了未加防护AES设计的10万条曲线.一个时钟周期有 T =50/3.571 2=14个点，实验通过在未加RDI防护的曲线第一个点前面随机插入 D × T 个0(插入值的大小对实验没有影响)来模拟加了RDI防护的曲线，其中 D 是随机变量.实验中， D 是一个服从二项分布的随机变量，即 D ~ B (19, 0.5).实验通过以下三个步骤进行： 第1步   通过CPA得到与第一个 S 盒输出的汉明重取得最大相关性的点 t 0 =7 345(每条曲线上的点从0开始编号)作为目标攻击点.该点的相关系数达到0.608 3，如 图 2 图 2 所示. 黑线对应正确子密钥的相关系数，灰线对应错误子密钥的相关系数 第2步   取6 000条实测曲线，每条曲线选取以下位置 t = t 0 + T × i ( i =0, ±1, ±2, …, ±19)的39个点，代表前面理论部分 P i ( i =0, ±1, …, ±19)的观测值.结合真实子密钥假设功耗 H ，就可以对2.4节中a)~e)中5组参数 λ i ( i =0, 1, 2, …, d )进行估计.结果如 图 3 图 3 所示，这几组权重都做了归一化处理，即每组数据的每个数据都除以本组数据的和，使得和为1. 第3步   用第2步中得到的权重进行攻击.首先在没有加RDI防护的10万条曲线前面插入满足二项分布的随机延迟，然后从每条曲线中选取以下位置 t = t 0 + T × i ( i =0, 1, 2, …, 19)的20个点用来代表理论部分的 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257742&type=middle i ( i =0, 1, 2, …, 19)的观测值.用第2步中的每一组权重计算 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257743&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257743&type=small http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=4257743&type=middle ，再计算其 P 和所有256个可能子密钥对应的假设功耗 H k ( k =0, 1, 2, …, 255)之间的相关系数，这5组结果对应 图 4 图 4 中横坐标取值21，22，…，25的情况，具体数值见 表 1 表 1 . 图 4 图 4 中, 横坐标1~20表示直接攻击场景.在11，12，19，20等点处，正确子密钥和错误子密钥可以区分开来，其中在横坐标等于11的位置取得直接攻击下的最大相关系数0.033 6.横坐标21代表e组权重，也即传统整合攻击，在这个实验中未能恢复出正确子密钥.横坐标22、23、24、25分别表示d、c、b、a组权重下的攻击结果.a组如理论预期, 是最好的; b组是假设攻击点以外的功耗和正确子密钥假设功耗相互独立的情况下的最优结果，也取得了较高的相关系数.相比于a组，它对应的参数可以在不知道正确密钥的情况下，通过实测曲线估计出来，可以用于实际的攻击.c组和d组可以作为b组的一种近似，也取得了比较好的效果.相对而言，d组直接以随机延迟的概率为权重，在实际攻击中操作更容易. 横坐标值 权重组合 相关系数 1~20 直接攻击 0.033 6 21 e组权重 0.005 2 22 d组权重 0.144 7 23 c组权重 0.137 0 24 b组权重 0.232 9 25 a组权重 0.235 4 从 表 1 表 1 可以得出以下结论：1)WIA的攻击效率最高，攻击结果更能反映RDI防护的安全性强度，因为a组相关系数最大；2)在随机延迟分布不是离散均匀分布的情况下，整合攻击不一定比直接攻击更有效，因为直接攻击对应的相关系数比e组的大；3)假设攻击点以外的实测功耗和假设功耗不相关是合理的，因为a组和b组的相关系数差不多. 结论 1 针对RDI防护，本文提出了一种精细的分析框架.在这个框架的基础上分析了已有文献中的直接攻击和整合攻击的效率，得出了比已有文献更一般性的结论.同时提出了一种WIA方法，它是直接攻击和整合攻击的推广，并给出了在各种条件下的理论最优结果.对于RDI防护，WIA是一种有效的攻击方法.相比于传统的直接攻击和整合攻击，它可以进一步提高假设功耗和实测功耗之间的相关系数，从而减少成功攻击所需要的曲线量.但是，另一方面它需要更多的信息——随机延迟的分布以及未加防护攻击点附近的功耗特征.WIA正是利用了这些信息才提高了攻击效率.因此，WIA的攻击结果能更科学地反映RDI防护的安全性强度. 参考文献 KOCHER P, JAFFE J, JUN B. 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DOI: 10.1007/978-3-642-15031-9_7 http://dx.doi.org/10.1007/978-3-642-15031-9_7 . 10.14188/j.1671-8836.2018.06.003 TP309 whdxxblxb-64-6-491 国家自然科学基金(61202386，61472292，61332019)；国家重点基础研究发展计划(973)(2014CB340601)；国家高技术研究发展(863)计划(2015AA016002)；面向智能电网新一代高速高等级安全芯片关键技术研究项目(526816160015) 2017-04-07 2018-12-24 2020-11-30 版权所有© 2018 《武汉大学学报(理学版)》编辑部 Copyright © 2018 Journal of Wuhan University(Natural Science Edition). All rights reserved. 2018 武汉大学学报(理学版) 6 64