Research On Fast Arithmetic Of Hyperelliptic Curves Groups

With the increasing popularity of the Internet, people's lives and production methods, management is changing; the network has acquired a deeper dependence, followed by the network security problem more and more people's attention. Computer network security is the focus of the study, because it for the network e-commerce, electronic government official, military and other important areas ofapplication of the Internet has provided a guarantee.With the development of PKI public key cryptography,RSA,Elliptic curve cryptography (ECC) have become a hot research people. Since 1989, N.Koblitz proposed hyperelliptic curve cryptosystem (HECC) theory since, as with the ECC, and other than the password system has obvious advantages:First, at the same level of security conditions, the use of the base domain smaller; Second, can be simulated based on the multiplicative group on, such as RSA, ElGamal, etc. Almost all the agreements; Third, in the same domain, the genus of a large, curvedand more, select Curve for the security of the password the more. HECC become a newhotspot in recent years.Hyperelliptic curve cryptography key is still in the stage of theoretical research, the main reason is the realization rate of HECC is slower than ECC, because the Jacobian of hyperelliptic curve quotient than the basic operations on theelliptic curve more complicated. In this paper, the research is how to reduce the divisor of hyperelliptic curves and scalar multiplication plus the computation, thereby enhancing the realization of ultra-speed elliptic curve cryptography, the following two specific work:(1) the literature has given genus 3 hyperelliptic curves degenerate divisor deterministic algorithm to improve, the formula from a variety of directions for optimization.First, the inverse using several different techniques for different situations to optimize the formula, which will simplify the process of inversion, and even transform into a low multiplication operations such as computation. Reuse of the nature and structure of the formula, the number of multiplication into a multiplication operation, thus reducing unnecessary operations. Finally, some of the other documents mentioned in the simplified formula for multiplication, and multiplication formula to reduce the amount of deformation. Each method has its limitations, but to improve the formula for adaptation can achieve good results.(2) In addition to the further degradation of sub-algorithm for the extended and improved.the deterministic genus 2 formula and its computation is estimated. Estimation results show that the minimum level of security conditions, d take the big 160-bit integer, then the standard divisor scalar multiplication capacity of 318I+12044 M, than the standard divisor scalar multiplication about 30% faster.Then combined with the dichotomy, parallel algorithms and other algorithms to further improve the degradation of ideological divisor algorithm, respectively, are two smaller computational algorithm. Dichotomy which results improved significantly, a significant reduction in the calculation of the inverse and the multiplication number. The parallel algorithm is computing the major merger in the same round operation, the computation reduction is not obvious, but the processor and the multiplication operation to minimize the number of rounds, so that the overall computation time can be further reduced.