Research Of Generalised Schnorr Identification Schemes And The Analysis And Improvement Of Several Kinds Of ELGAMAL Type Signature Algorithms

In response to the arrival of the information age and the information security requirements.Since the 1970 s,cryptography has made new breakthroughs,resulting in the idea of public key cryptography,which further provides an efficient solution for information security needs,such as key exchange,digital signature and other issues have been well solved.Identification is one of information authentication.It is not only an important research direction of cryptography,but also an important problem in information systems.ELGAMAL cryptographic algorithm is a famous cryptographic scheme based on discrete logarithm problem,its further research has produced many new cryptographic algorithms,such as elliptic curve cryptography.There are many international and national cryptographic standards,which are the cornerstone of cryptography.In this paper,the identification scheme and some variants of ELGAMAL cryptographic algorithm,including the signature scheme with message recovery,are studied.The main work is as follows:Due to the close relationship between cryptography and mathematics,the second chapter of this paper focuses on the basic content of elementary number theory and abstract algebra.The elementary number theory includes some classical concept,the decomposition of integers,congruences,congruence formula,quadratic residue theory,as well as primitive roots and index,and the related concepts of groups,rings and fields are included in modern algebras.In chapter three,we will study the identity protocol,starting with Fiat-Shamir identification scheme,and then focus on Schnorr identification scheme.Inspired by various variants of ELGAMAL cryptosystem,the variants of Schnorr identification protocol are studied,By comparing the signature equations and verification equations of the ELGAMAL signature algorithm with the equations involved in the protocol steps of the Schnorr identification scheme,various variable substitution relations are given,and the variables in the original Schnorr scheme equation are adjusted and permuted,and then many feasible,secure and new identification schemes are proposed.In chapter four,we will focus on the research and analysis of RSA public key cryptography and ELGAMALpublic key cryptography.Various variant schemes of ELGamal signature algorithm are analyzed,Some attack methods on RSA and ELGamal cryptographic scheme are also analyzed,including signature schemes with message recovery.On this basis,several schemes have been proposed by some scholars is studied.Firstly,by replacing the variable r with r mod q,three extended and improved schemes for Zhou Keyuan's signature scheme are proposed,in which the length of signature is shorter than Zhou's scheme.Then,the signature scheme of Zhang Huiying is analyzed,it turned out to be meaningless to add a random number t and find its modulus inverse d as a private key.Finally,a forgery attack is given for Puyan's signature scheme which also attempts to add a random number to enhance the security of cryptographic algorithm.