Research Of Secret Sharing Scheme Based On Bivariate Polynomial

With the development of information technology and the coming of big data era,information interaction among people through the Internet has become increasingly frequent,information has become an important social resource.In the contemporary society,more attention has been paid to protection of information and privacy.How to ensure the security of information storage and transmission has become one of research hotspot in the field of information security.Secret sharing is an important technology in the field of information security.Its main idea is to divide the shared secret into several shares,which are transmitted to a group of participants to keep,and then stipulate a certain number of participants to recover the secret jointly.Secret sharing technology can protect important privacy and prevent information from being intercepted,damaged or tampered.It also has important applications in key escrowing,electronic transfering,electronic voting and other fields.In this paper,we study the secret sharing scheme from several aspects,such as preventing outside attackers,preventing inside cheaters,asynchronous reconfiguration of multiple secrets,and flexibility of scheme.The research results are described as follows.Firstly,by using bivariate polynomial,paired secure channel is established between participants,which reduces the additional key establishment protocol.Then,combined with the discrete logarithm problem,participants can verify the share they receive,which can effectively prevent the inside cheaters in the secret reconstruction stage.Aiming at the problem that multiple secrets are recovered in one time in most multi-secret sharing schemes,a multi-secret sharing scheme which can satisfy the asynchronous recovery of secret is designed.In addition,the share setting method of the secret sharing scheme based on bivariate polynomial is improved,so that the number of secrets,threshold value and the number of shares are not mutually constrained and the scheme is more flexible.Secondly,combining ElGamal public key cryptosystem and secret sharing scheme based on bivariate polynomials,a cheating-prevention electronic voting scheme for self-voting is proposed.By using the property of binary polynomial,a secure channel can be constructed between voters,which avoids the process of key agreement and the maintenance of secure channel.All voters can verify whether the final result of the election is correct by publishing secret share-related verification information.The security and effectiveness of secret sharing scheme are proved in the scheme analysis.Finally,the research work done in this paper is summarized and the research direction in the next stage is prospected.