Study On ECC Digital Signature And Encryption

The security of the Elliptic Curve Cryptography is built upon the difficulty of solving the Elliptic Curve Discrete Problem which in finite field. In addition to its high security, ECC also has many other merits over other public-key cryptosystems such as less computation overheads, shorter key size, considerable handwidth savings, and so on. So more and more people are attracted by this task, and it has become the hotspot of public cryptography.This thesis first analyses and summarizes the status quo and evolution trend of cryptography, and introduces the research status and research significance of ECC. Second, the principle of ECC is discused,including the math foundation of ECC, basic concerption of elliptic curve ,constructing idea of ECC , operation on the elliptic curve and so on. Meanwhile, the security and efficiency of ECC are analyzed. Third , after analysis various typical digital signature algorithm, the variation of Elgamal signature algorithm based on ECC is presented and its validity is proved. Fourth, analyses elliptic curve system, and improve the current elliptic curve system-Menezes Vanstone encryption system to MV1 encryption system. In addition, combine elliptic curves and ElGamal algorithms will be to give the feasibility of ECC-E encryption algorithm and analyses its performance of cryptology, then combined it with AES encryption algorithm, give its digital envelope technology framework. Finally, analyse and summarize the two key technologies of construct elliptic curves: Construction of secure Elliptic Curve and selection of base points, and improve the elliptic curve construct algorithm.