TY - GEN
T1 - Statistical decoding
AU - Debris-Alazard, Thomas
AU - Tillich, Jean Pierre
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/8/9
Y1 - 2017/8/9
N2 - 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.
AB - 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.
U2 - 10.1109/ISIT.2017.8006839
DO - 10.1109/ISIT.2017.8006839
M3 - Conference contribution
AN - SCOPUS:85034099731
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1798
EP - 1802
BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017
Y2 - 25 June 2017 through 30 June 2017
ER -