Public Key Cryptosystems Constructed Based on Reed-Solomon Codes, K(XV)SE(2)PKC, Realizing Coding Rate of Exactly 1.0
In this paper, the authors present a new class of public-key cryptosystems, K(XV)SE(2)PKC realizing the coding rate of exactly 1.0, based on Reed-Solomon codes(RS codes). They show that K(XV)SE(2)PKC is secure against the various attacks including the attacks based on the Grobner basis calculation (Grobner basis attack, GB attack) and a linear transformation attack. Most of the multivariate PKC are constructed by the simultaneous equations of degree larger than or equal to. All these proposed schemes are very interesting and important. However unfortunately, some of these schemes have been proved not necessarily secure against the conventional attacks such as Patarin's attack, the attack based on the Grobner basis calculation (GB Attack) and Braeken-Wolf-Preneel (BWP) attack.