Improvement of Binary and Non Binary Statistical Decoding Algorithm

Abstract

The security of McEliece’s cryptosystem relies heavily on the hardness of decoding a random linear code. The best known generic decoding algorithms are derived from the Information-Set Decoding (ISD) algorithm. This was first proposed in 1962 by Prange and subsequently improved in 1989 by Stern and later in 1991 by Dumer. In 2001 Al Jabri introduced a new decoding algorithm for general linear block codes which does not belong to this family, called Statistical Decoding (SD). Since then, like for the Information Set Decoding algorithm, there have been numerous work done to improve and generalize the SD algorithm. In this paper, we improve the SD algorithm using the notion of bases lists in binary case. Then, we give a non binary version of this improvement. Finally, we have computed complexity analysis and have made a complexity comparison of our results with that of recent results on SD algorithm and complexity of classic ISD algorithm.