Analysis of Information Set Decoding for a Sub-linear Error Weight

International audienceThe security of code-based cryptography is strongly related to the hardness of generic decoding of linear codes. The best knowngeneric decoding algorithms all derive from the Information Set Decoding algorithm proposed by Prange in 1962.When the number of errors w is sub-linear, w = o(n), the cost of all ISD variants has the form 2^{cw(1+o(1))}. We prove here that the constant c only depends of the code rate k=n and is the same for recent known ISD variants, including the fifty years old Prange algorithm.The most promising variants of McEliece encryption scheme use either Goppa codes, with w = O(n/ log(n)), or MDPC codes, with w = O(n^{1/2}).Our result means that, in those cases, when we scale up the system parameters, the improvement of the latest variants of ISD become lessand less signicant