Research On Encrption And Signature Schemes On The Base Of MPKCS

Multivariate public key cryptosystems (MPKCs) stand among the systems thought to have the potential to resist quantum computer attacks. MPKCs are connected to the hardness of solving randomly chosen systems of multivariate polynomial equations over a finite field, a problem which is NP-complete. This paper tries to construct a more secure signature scheme by taking advantage of quadratic multivariable polynomial on finite field on the base of the research of MPKCs. The main contributions are as follows:We propose a new construction of the cubic MI scheme and its variants—projected cubic MI minus scheme and cubic MI internally perturbed plus scheme—on the basis of Matsumoto-Imai scheme. Projected cubic MI minus scheme, which is suggested as a signature scheme, strives to resist the differential attack which has been used recently to achieved a total break of the Sflash signature scheme; while cubic MI internally perturbed plus scheme, which is presented as a encryption scheme, can resist the differential attack by adding a few additional polynomials. Both of the variants can resist the Linearization Equation attack, Rank attack, and XL&Grobner basis attack without much sacrifice in the efficiency of the system.We propose a new construction, which is called the multilayer square-vinegar signature scheme, with the idea of a set of embedded layers and repeated applications of the Square-Vinegar construction such that in the end the signature scheme will be more secure. The combination of the use of odd characteristic, oil-vinegar construction and multi layer construction makes this scheme novel. We also discuss known attacks which could possibly topple such system. Based on the security analysis we give parameter suggestions to our new signature scheme, which is argued to be secure.