Reducible rank codes and their applications to cryptography
EM Gabidulin, AV Ourivski, B Honary… - IEEE Transactions on …, 2003 - ieeexplore.ieee.org
EM Gabidulin, AV Ourivski, B Honary, B Ammar
IEEE Transactions on Information Theory, 2003•ieeexplore.ieee.orgWe present a new family of so-called reducible rank codes which are a generalization of
rank product codes. This family includes maximal rank distance (MRD) codes for lengths n>
N in the field F/sub N/. We give methods for encoding and decoding reducible rank codes. A
public key cryptosystem based on these codes and on the idea of a column scrambler is
proposed. The column scrambler" mixes" columns of a generator (parity-check) matrix of a
code. It makes the system more resistant to structural attacks such as Gibson's attacks …
rank product codes. This family includes maximal rank distance (MRD) codes for lengths n>
N in the field F/sub N/. We give methods for encoding and decoding reducible rank codes. A
public key cryptosystem based on these codes and on the idea of a column scrambler is
proposed. The column scrambler" mixes" columns of a generator (parity-check) matrix of a
code. It makes the system more resistant to structural attacks such as Gibson's attacks …
We present a new family of so-called reducible rank codes which are a generalization of rank product codes . This family includes maximal rank distance (MRD) codes for lengths n>N in the field F/sub N/. We give methods for encoding and decoding reducible rank codes. A public key cryptosystem based on these codes and on the idea of a column scrambler is proposed. The column scrambler "mixes" columns of a generator (parity-check) matrix of a code. It makes the system more resistant to structural attacks such as Gibson's attacks. Possible attacks on the system are thoroughly studied. The system is found to be secure against known attacks for public keys of about 16 kbits and greater.
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