Research On Multivariate Signature Cryptosystem

Cryptography is a solid barrier to ensure modern information security. Represented by RSA, public key cryptosystems have been widely used, but to maintain a high level of security, continuous increase of the length of RS A's public key has led to the reduction of computational efficiency, in addition, the factorization algorithm on quantum computers has been a serious threat to the future security of RSA. Fortunately, Multivariate Public Key Cryptosystems, which emerged only 20 years, make people see the hope for Cryptography security in the future. It has high security and high-performance of computing for a broader field, in particular, the immunity of quantum computers makes it an important candidate to replace RSA.This paper mainly studies Multivariate Public Key Cryptosystems in the three types of branches-MI (Matsumoto-Imai) family, Oil-Vinegar family and HFE (Hidden Field Equations) family which developed by MI, the principal tasks are as follows:Elaborates the development state on Multivariate Public Key Cryptosystems in recent years, and gives a general description of MI, Oil-Vinegar and HFE, a variety of attack techniques they face, as well as the corresponding variants developed for fending off these attacks.According to the thought of perturbation, proposes a new signature scheme based on HFEv and IPHFE. The new scheme makes two kinds of perturbation act on the basic HFE, so the perturbations and the original system are fully mixed, that makes the new cryptosystem more random. and gives security and efficiency analysis, under the premise of no significant increase of the amount of calculations, the security level is lifted.With the minus method, by hiding some secret component, gives a variant of the new scheme, its security is better, and signature verification is more efficient. Then with the thought of further mixing the two perturbed variables, obtain another variant, so its security is enhanced, and the signature generation and verification process without any change, its nature is more excellent.