The Digital Signatures Based On Hyperelliptic Curve Cryptogrophy

During the past few years, ellipse curve cryptography is broadly extended in application. Hyperelliptic curves cryptography (HECC) is one kind surpassing of ellipse curve cryptography (ECC). The based field on which HECC is constructed is less than that of ECC with the same security level, and in same field, HECC could supply more curves so that there are more choice for building the safe cryptography. Because of these virtues HECC is more and more important for scholar of cryptography. But now the research of HECC is mainly in theory because of the difficulty of computing in the Jacobian group. Though there are some simple achievements about kernel computing in recently, there are many great of problem to solve, such as: how to speed the divisor scalar multiplication and how to make the standardization of divisor scalar multiplication hyperelliptic curves cryptography. In this article, we make some research due to some problems of HECC, including the math background of hyperelliptic curves cryptography, the algorithm of divisor scalar multiplication, and providing a kind of general digital signature based on hyperelliptic curves cryptography.Compared to RSA and ECC, the security of HECC is better. Thus the security of HECC is based on the difficulty of computing the discrete logarithm on Jacobian group. How to choose the parameters of HECC plays an important role to make sure the system stabilization and security. There is introduction about how to choose the parameters of HECC in this article. Implement the algorithm of divisor scalar multiplication for the certain curves, which is good for the hyperelliptic curves cryptography in reality.Through the digital signature scheme based on elliptic curves cryptography, introduce a new kind of digital signature scheme based on hyperelliptic curves cryptography. This scheme makes the type of digital signature scheme based on discrete logarithm problem together.