Research On Scalar Multiplication Fast Algorithm In Hyperelliptic Curve

In the way of public-key encryption, elliptic curve cryptosystem due to the small base domain, the key length is relatively short, etc. become the most popular public key encryption system and has extensive research and attention.Hyperelliptic curve cryptography, whose basic is the discrete logarithm problem, is a generalization of elliptic curve cryptography. It has its unique superiority and has become a hot research field of cryptography, but because the not ideal speed of realization in application, it has not been widely spread. The bottleneck restricting the hyperelliptic curve to the widely used is mainly the calculation complexity of the algorithm on the elliptic curve. In the light of the fast algorithm for hyperelliptic curve, this paper does the following research work:(1) Describes degenerate divisor algorithm, which is a fast algorithm in hyperelliptic curve cryptosystem.Introduces the degenerate divisor algorithm on genus2and3,gives certainty formula on genus3of the addition and multiplication in HEC. Two curves of different genus both compare with the scalar multiplication algorithm which is based on canonical divisor calculation on computation. By the given computational estimation, indicates that the degenerate divisor algorithm can significantly improve the speed of scalar multiplication.(2) Combinates optimizationally and extends the sliding window algorithm and NAF method of the elliptic curve, gets a similar sliding window algorithm over hyperelliptic curves--SWNAF algorithm, so that it can be applied in hyperelliptic cryptosystem, and can improve the operation efficiency of Hyperelliptic Curve Cryptosystem; Uses the idea of shifting in computer to improve the algorithm, compares the improved algorithm with the previous one on operation efficiency, expresses the superiority of the improved algorithm more visually.(3) In the light of the hyperelliptic curve, the genus of which is2, on prime field, analyses the divisor scalar multiplication which is based on double-base chain and given by the literature, combined with the double-chain expression, gets an effective divisor scalar multiplication algorithm.