Method and apparatus for elliptic curve cryptography and recording medium therefore

Abstract

A method and an apparatus capable of realizing at a high speed an elliptic curve cryptography in a finite field of characteristic 2, in which the elliptic curve is given by y+xy=x+ax+b (b≠0) and an elliptic curve cryptography method which can protect private key information against leaking from deviation information of processing time to thereby defend a cipher text against a timing attack and a differential power analysis attack are provided. To this end, an arithmetic process for executing scalar multiplication arithmetic d(x, y) a constant number of times per bit of the private key d is adopted. Further, for the scalar multiplication d(x, y), a random number k is generated upon transformation of the affine coordinates (x, y) to the projective coordinates for thereby effectuating the transformation (x, y)→[kx, ky, k] or alternatively (x, y)→[kx, ky, k]. Thus, object for the arithmetic is varied by the random number (k).