Public Key Cryptosystems Constructed Based on Cyclic Codes, Realizing Coding Rate of Exactly 1.0, K(XI)SE(g)PKC and K(XII)SE(g)PKC

摘要

In this paper, we first present a new class of public-key cryptosystems, K(IX)SE(1)PKC based on error-correcting codes over F_2. The K(IX)SE(1)PKC is constructed by modifying the K(VIII)SE(1)PKC formerly proposed by the author. We second present K(XI)SE(g)PKC by generalizing K(IX)SE(1)PKC. We show that K(IX)SE(1)PKC and K(XI)SE(g)PKC, modified versions of K(IX)SE(1)PKC, realizes the coding rate of exactly 1.0. We finally present a new class of multivariate PKC, K(XII)SE(g)PKC. We discuss on the simplest version, K(XII)_(sim.), in detail. We show that K(XII)_(sim.) is secure against the attacks based on a linear transformation and the Grobner basis calculation (GB attack). "We also show that K(XII)SE(g)PKC realizes the coding rate of exactly 1.0.