Research And Application Of Multivariate Public Key Cryptosystems

The appearance of the quantum computer is a threat to the security of traditional cryptosystems, so the multivariable cryptography was born, and attracted more and more attentions recently. The multivariate public key cryptosystems are connected to the hardness of solving randomly chosen systems of multivariate polynomial equations over a finite field, and it has better performance both in memory space and time efficiency than the traditional cryptosystems.This paper does some study and research on the MPKCs, sums up the development history and research situation, does a brief introduction to the implementation of trapdoor functions, and presents the main attacks. On this basis, the main contributions are as follows.(1) A new multivariate public key cryptographic schemes proposed by Dr. Yuan Feng is analyzed, which is realized by Magma computational algebra system. A proposed parameter with proficiency and security is given based on experimental data from multiple tests.(2) Proposes a new mixed multivariate public key cryptographic scheme over finite field that uses odd characteristic and an embedding in its construction. The scheme can not only resist all known attacks, but also keep advantages in being realized, etc.