Construction of new classes of SE(g)PKC - Along with some notes on K-Matrix·PKC -

摘要

In this paper, a new class of Public-Key Cryptosystem (PKC) based on Simultaneous Equations of de-gree g (SE(g)PKC) is presented. The proposed schemes are based on two classes of SE(g)PKC that are briefly given in the paper [1] by the present author (ISEC, March 17, 2006). In Section 2 of this paper, for the convenience of description, we present 3 new classes of SE(g)PKC, K_I through K_(III)·SE(g)PKC. We show that the finally proposed scheme in Section 2, Km-SE(g)pKG, can be secure against the Grobner Basis Attack (GB Attack) and Patarin's Attack. In Section 3, we present another new class of SE(G)PKC, K-SE(g)PKC, based on K-matrix in Ref. [1]. We show that K·SE(g)PKC can be very secure against Grobner basis attack and Patarin's attack. However, the present author does not feel sufficient confidence on the security of K·SE(g) PKC, as it might be insecure against the similar attacks given in Appendix I in this paper.