Abstract
We present two new algorithms for decoding an arbitrary (n, k) linear rank distance code over GF(q N). These algorithms correct errors of rank r in O((Nr)3 q (r−1)(k+1)) and O((k + r)3 r 3 q (r−1)(N−r)) operations in GF(q) respectively. The algorithms give one of the most efficient attacks on public-key cryptosystems based on rank codes, as well as on the authentication scheme suggested by Chen.
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Ourivski, A.V., Johansson, T. New Technique for Decoding Codes in the Rank Metric and Its Cryptography Applications. Problems of Information Transmission 38, 237–246 (2002). https://doi.org/10.1023/A:1020369320078
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DOI: https://doi.org/10.1023/A:1020369320078