On lower bounds for information set decoding over &Fopf;<SUB align="right">q and on the effect of partial knowledge

Abstract

Code-based cryptosystems are promising candidates for post-quantum cryptography since they are fast, require only basic arithmetic because their security is well understood. The increasing number of cryptographic schemes based on codes over fields other than F2 presents, however, security issues that are not relevant in the case of binary codes; the security of such constructions, therefore, requires separate assessment. Information set decoding (ISD) is one of the most important generic attacks against code-based cryptosystems. We give lower bounds for ISD over Fq, thereby anticipating future software and