The Research And Application On Equivalent Relationship In Multivariate Public Key Cryptosystem

Cryptography technology is crucial to the security of modern social communications.However,with the deepening of research on quantum cryptography algorithms and quantum computers,the security of the traditional public key cryptography system has been severely challenged.As an alternative to traditional public key cryptosystems,multi-variable public key cryptosystems can promote the application research of anti-quantum attack cryptographic algorithms.The application of equivalence relationships to multivariate cryptosystems can can effectively reduce the computational complexity of the Gr(?)bner basis method and has significant implications for the research and development of multivariate public key cryptosystems.The main works and contributions of this thesis are as follows:1.This thesis analyzes the security of the novel extended multivariable public key cryptosystem,which is used to improve a defective multivariable public key cryptosystem.If there is a linear equation in the original system,then there must be a quadratic equation in the the novel extended multivariate public key cryptography.Finding all the quadratic equations that satisfy the conditions and combining the Gr(?)bner method to find the corresponding plaintext of the legitimate ciphertext.2.This thesis proposes a new digital signature scheme that can resist equivalence relationship or equivalence relationship equation attacks.In this scheme,the central map draws on the design method of the central map of the l-Invertible Cycles cryptosystem.At the same time,the method of polynomial disturbances and vinegar variables is combined collectively to avoid the occurrence of equivalence relationship in center maps.By setting suitable parameters,the new scheme can be protected against direct attacks,differential attacks and all known isometric relations attacks.3.The above security analysis and design of the novel system are conducted on the Magma simulation experiments,which indicate the correctness of the theoretical analysis.