The Research And Application Of Hyperelliptic Curve Cryptographic Protocol

As a generalization of Elliptic Curve Cryptosystems(ECC),Hyperelliptic Curve Cryptosystems(HCC) was proposed in 1989 by Neal Koblitz.HCC is based on the discrete logarithm problem on the Jacobian of hyperelliptic curves over finite fields. Compared with ECC and other public crypotosystems,HCC has some irreplaceable advantages.It has shorter key size and smaller base field.The DLP of HCC over small genus(g≤4) no longer has exponential complexity.On the same domain field,the bigger the genus(g≤4) is,the more the number of curves is,and the wider the region for the choice of secure curves to be used in cryptography is.Because of these advantages,HCC has gotten more and more attention in recent several years.This paper regards the Hyperelliptic curve based on the binary finite field as the main research object.It carries on deep research to HCC from two aspects which are scalar multiplication and cryptographic protocol.First,the sigle scalar multiplication is optimized. The optimized algorithm of divisor scalar multiplication based on extended double-base chain is proposed in this paper.Then we analyze it in theory and experiment.The result shows that the efficiency of this algorithm is superior to others in this aspect.Then we extend the three basic protocols to Hyperelliptic Curve,give the realization of these protocols on HC and then present the evaluation of the security of them.And then,based on deep research of HCC,a threshold group signature based on HCC is proposed in this paper.The scheme combines the merits of HCC and threshold group signature.Not only does it have high security and small communication traffic,but also it can withstand the conspiracy and trace signers' identities.It is especially suitable for solving security problems existing in some networks with limited resource.Finally,according to the given algrithms,a hyperelliptic curve cryptography system is designed and implemented.Then we apply it into the design of the business document transmission system in order to get high security. The experiment shows that the efficiency and security of the hyperelliptic curve cryptography are improved in a certain extent because of the contribution of this paper. Therefore,the research of this paper has important value to HCC coming into utility.