Fast scalar multiplication algorithm of conic curve over GF(p～m)
Liu Du · Journal of Beijing Jiaotong University · 2013
Until now,all the previous studieson conic curve cryptography have been based on the prime field GF(p).The field with characteristic 2,and the ring Z/ nZ,where n= pq is the product of two primes. In this paper, conic curves defined over the extension field GF(pm)are discussed. The Frobenius map of the pointson the conic curvesoverGF(pm)is defined.Based on this,a new method of computing scalar multiplication of conic curve over GF(pm)is presented. The theoretical analysis and numerical comparison about the new method and traditional methods are given. The results show that the new method is more efficient than the traditional ones on the same memory spaces for precomputed points.