An asymmetric cryptography using Gaussian integers

摘要

In this paper, the already strong McEliece cryptosystem is enhanced with a two-dimensional finite Gaussian integer. By substituting the one-dimensional linear code with a two-dimensional code employing a finite Gaussian integer, a new system simultaneously increases the key space and the errors to be correct by syndrome decoding. We compare the proposed system against the classic McEliece system in three aspects: the work factors performing the trial of the attacks, the computational complexity cost, and the empirical running time of the system. Compared to the classic McEliece cryptosystem, the enhanced cryptosystem achieves a higher security level against key recovering and decoding attacks. By carefully selecting parameters, a small code element can improve the key strength without compromising the runtime efficiency.