A knapsack public-key cryptosystem with cyclic code over $GF(2)$

Abstract

It is required to invent the public-key cryptosystem (PKC) that is based on an {\it NP\/}-hard problem so that the quantum computer might be realized. The knapsack PKC is based on the subset sum problem which is {\it NP\/}-hard. In this paper, we propose a knapsack PKC with a cyclic code over $GF(2)$ using the Chinese remainder theorem. The proposed scheme is secure against Shamir's attack and Adleman's attack and invulnerable to the low-density attack. Furthermore, the proposed scheme can reduce the size of public key by almost $25\% \sim 50\%$ of the conventional scheme using a linear code.