Research And Design On Multivarite Signature

Multivariate signature system security is based on multivariate public key schemewhich relies on the multivariate nonlinear equations NP-C problem instead of numbertheory problem of traditional public key scheme so that it can resist the quantumcomputer attacks. Moreover，compared to traditional cryptosystems, it has significantadvantages both on key space and time efficiency. Therefore it is believed to be analternative security cryptosystem scheme in the post-quantum ages and attracts moreand more attentions in recent years.This thesis provides the research and application designs in multivariate public keycryptosystem and signature system which explain how these schemes are derived andlead schemes analyses. The main gains are summarized as follows:1. A multivariate proxy signature scheme is proposed, in which the proxy key isdesigned and the key system is improved through introducing another secret affinetransformation and combining with the one-way hash function. Therefore, the messagevalue is hidden and the amounts of information obtained by attackers are reduced. Theanalysis shows that the scheme can resist existing attacks, and has both high securityand completeness.2. A multivariate group signature scheme and a conspiracy attack scheme whichcould offer forgery attacks against the group signature system are proposed. Then, thepaper gives a new matrix multiplication definition and prime matrix concept to achievea group signature resisting conspiracy attacks scheme. Analysis shows that the schemewithstands conspiracy and forgery attacks fundamentally and has both high security andcompleteness.3. A multivariate threshold group signature scheme is proposed in which a sharedsecure data recovery method is structured according to the Shamir secret sharingscheme. The security analysis and correctness proof verify the scheme is a completethreshold group signature scheme. Besides, the shared key space and the subkey spaceare the same which means that the scheme is an ideal and complete threshold groupsignature scheme.