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Reducible rank codes and applications to cryptography. (English) Zbl 1073.94520
Blaum, Mario (ed.) et al., Information, coding and mathematics. Proceedings of workshop honoring Professor Bob McEliece on his 60th birthday, Pasadena, CA, USA, May 24–25, 2002. Boston, MA: Kluwer Academic Publishers (ISBN 1-4020-7079-9/hbk). The Kluwer International Series in Engineering and Computer Science 687, 121-132 (2002).
Summary: A new family of so-called reducible rank codes, which are a generalization of rank product codes [E. M. Gabidulin and P. Loidreau, Proc. 7th Int. Workshop Alg. Comb. Coding Theory, ACCT-7, 151–156 (2000; Zbl 1063.94542)], is introduced. A McEliece type 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 matrix of a code. It makes the system more resistant to structural attacks such as J. Gibson’s attacks [Des. Codes Cryptography 6, 37–45 (1995; Zbl 0837.94018) and Algebraic coded cryptosystems, PhD. Thesis, University of London, Royal Holloway and Bedford New College (1995)]. Possible attacks are studied. The possibility of using the system for combined error protection is investigated. The system is found to be secure against known attacks for public keys of about 10 kbits.
For the entire collection see [Zbl 1054.94001].
94B05 Linear codes, general
94A60 Cryptography