Statistical Decoding
Abstract
The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of information set decoding techniques (ISD). A while ago a generic decoding algorithm which does not belong to this family was proposed: statistical decoding. It is a randomized algorithm that requires the computation of a large set of parity-check equations of moderate weight. We solve here several open problems related to this decoding algorithm. We give in particular the asymptotic complexity of this algorithm, give a rather efficient way of computing the parity-check equations needed for it inspired by ISD techniques and give a lower bound on its complexity showing that when it comes to decoding on the Gilbert-Varshamov bound it can never be better than Prange's algorithm.
Keywords
Cite
@article{arxiv.1701.07416,
title = {Statistical Decoding},
author = {Thomas Debris-Alazard and Jean-Pierre Tillich},
journal= {arXiv preprint arXiv:1701.07416},
year = {2017}
}