New Code-Based Cryptosystem Based on Binary Image of Generalized Reed-Solomon Code

Abstract

McEliece cryptosystem represents a smart open key system based on the hardness of the decoding of an arbitrary linear code, which is believed to be able to resist the advent of quantum computers. But the original McEliece cryptosystem, based on Goppa codes, has just very limited interest in practice, partly because it requires a very large public key. In this paper we propose a new instance of McEliece cryptosystem that reduces a public key size. This cryptosystem is based on images of Generalized Reed-Solomon (GRS) codes. It was shown that in order to break the proposed system, intruder has to solve a decoding problem for a code that is not equivalent to private GRS code.