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Reducible Rank Codes and Their Applications to Cryptography.

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<mark>Journal publication date</mark>1/01/2004
<mark>Journal</mark>IEEE Transactions on Information Theory
Issue number12
Volume49
Number of pages5
Pages (from-to)3289-3293
Publication StatusPublished
<mark>Original language</mark>English

Abstract

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.

Bibliographic note

This collaborative work with the Moscow Institute of Physics and Technology, Russia, introduces a new class of Combined Coding and Encryption with application to the Public Key Crypto System with short Key size and low Complexity. This novel idea will play a big role in future wireless communication systems, (for example TETRA V2, this can be verified by Dr M. Noori, the Chairman of WG4-TETRA for ETSI). RAE_import_type : Journal article RAE_uoa_type : Electrical and Electronic Engineering