Digital Signature Scheme Based On The Conic Curve

Abstract: With the rapid development of information technology, information security is more and more attractive. The cryptosystem based on algebraic curves has become a hot research. Conic curve cryptography as the representative of algebraic curve cryptography, not only inherits the advantages of elliptic curves, but also is easier than the elliptic curve on the calculation of Order. Conic curve section in the application of cryptography firstly originated from Professor Zhang Mingzhi's decomposition work in large numbers in the Sichuan University, which had been appreciated by C. Pomerance. Then Professor Cao Zhenfu and Professor Sun Qi and others set up a password system, cryptographic protocols and algorithms based on the conic curve. As one of important fields of cryptology, digital signature can ensure the information integrity and the authentication, on-repudiation of sender. Conic curve cryptography will be applied to the concept of digital signature in the field, not only to strengthen the existing security of digital signatures, but also have broader application.This thesis mainly focuses on the conic curve cryptography, its application of sign including the blind signature curve cryptosystem, proxy signature, multiple signatures, and other special signature which based on the Ring Zn, the further application of it on the generalized conic curve and giving the broadcasting multiple digital signature scheme of generalized conic curve which based on the ring Zn as well. First of all, it leads a depth analysis on conic curve, the theory and application of digital signature and then giving a review on the conic curve cryptography. Secondly, it refers to a comprehensive description of classical digital signature scheme based on the difficulty in factorizing large integer and computing discrete logarithm, making a key study on the ring Zn.Such as EIGamal signature, blind signatures, anonymous proxy signature, multiple signatures and etc. Thirdly it discusses the generalized nature and characteristics of generalized conic curve, the further application of signature on the generalized conic curve, and put forward the scheme of broadcasting multiple digital signatures. At last, it gives a brief description of the basic concept of elliptic curve cryptosystem, compareing the conic curve with elliptic curve from the point of order and having the conclusion that the conic curve cryptosystem is better.