The Analysis Of Elliptic Curve Cryptosystem

This dissertation discusses the analysis of elliptic curve cryptosystem .The main results obtained are as follows:1. We analyze the principle of Pollard rho-method and parallel collision search method using graph theory and algebra, and obtain important principle of directing the design of algorithms directed by this principle, we redesign the two algorithms, and achieve more efficient effect.2.We study the Index calculus algorithm, discusses the selection way of factor base about cyclic group Z*p, and then ascertains the formulasof the generated relation: Inthe Discrete Logarithm Cryptosystem , the way is very good at the Index calculus Algorithm which computes the discrete logarithm. We test it by many examples.We hope that our work will benefit the development and application of elliptic curve cryptographic technology.