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

DAGS: Key encapsulation using dyadic GS codes

“…Hamdaoui and Sendrier in [26] provide non-asymptotic complexity estimates for ISD in the binary case. For codes over q , instead, a bound is given in [34], which extends the work of Peters. For a practical evaluation of the ISD running times and corresponding security level, we used Peters's ISDFQ script [46].…”

Polynomial-time plaintext recovery attacks on the IKKR code-based cryptosystems

“…Since then, several improvements of the ISD attack have been proposed for codes over the binary field by Lee-Brickel [11], Leon [13], Stern [20], and more recently by Bernstein et al [5], Becker et al [3], May-Ozerov [14]. Several of these algorithms have been generalized to the case of codes over general finite fields, see [6,7,8,16,17].…”

Encryption scheme based on expanded Reed-Solomon codes

“…Since then several improvements have been proposed for codes over the binary field by Lee-Brickel [27], Leon [28], Stern [44] and more recently by Bernstein et al [13], Becker et al [9], May-Ozerov [30]. Several of these algorithms have been generalized to the case of codes over general finite fields, see [21,22,23,35,38].…”