The Cryptographic Security of the Syndrome Decoding Problem for Rank Distance Codes on Leave from D El Egation G En Erale De L'armement the Cryptographic Security of the Syndrome Decoding Problem for Rank Distance Codes
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چکیده
We present an algorithm that achieves general syndrome decoding of a (n; k; r) linear rank distance code over GF(q m) in O((nr + m) 3 q (m?r)(r?1)) elementary operations. As a consequence, the cryptographic Al schemes Che94, Che96] which rely on this problem are not secure with the proposed parameters. We also derive from our algorithm a bound on the minimal rank distance of a linear code which shows that the parameters from Che94] are inconsistent. | Abstract. We present an algorithm that achieves general syndrome decoding of a (n; k; r) linear rank distance code over GF(q m) in O((nr + m) 3 q (m?r)(r?1)) elementary operations. As a consequence, the cryptographic Al schemes Che94, Che96] which rely on this problem are not secure with the proposed parameters. We also derive from our algorithm a bound on the minimal rank distance of a linear code which shows that the parameters from Che94] are inconsistent.
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