In this paper

we submit the key characters of the curves

namly vertices and rock bottom

and introduce a new curve similarity definition based on the discrete Fréchet distance.We present a new mathematical model for the discrete curve similarity judgment

which does not need to carry on translation and stretching to the curves.Because the model solution is one kind of NP difficult problem

we propose a new multinomial solution algorithm

and finally take online handwriting signature verification as example to confirm the mathematical model.For 150 test signatures that we choose randomly

the successful matching rate is 91.33%

the wrong reacceptance is 6% and the wrong reject rate is 2.67%.