Structural Attacks for Public Key Cryptosystems based on Gabidulin Codes

Abstract In this paper we look at the Gabidulin version of the McEliece cryptosystem (GPT) and its variants. We give an overview over the existing structural attacks on the basic scheme, and show how to combine them to get an effective attack for every GPT variant. As a consequence, there are no secure parameter sets left for GPT variants, which one would like to use in practice.

[1]  Keith Gibson,et al.  The Security of the Gabidulin Public Key Cryptosystem , 1996, EUROCRYPT.

[2]  Raphael Overbeck,et al.  A New Structural Attack for GPT and Variants , 2005, Mycrypt.

[3]  Bahram Honary,et al.  Reducible rank codes and their applications to cryptography , 2003, IEEE Trans. Inf. Theory.

[4]  Colin Boyd,et al.  Advances in Cryptology - ASIACRYPT 2001 , 2001 .

[5]  Steven R. Finch,et al.  Mathematical constants , 2005, Encyclopedia of mathematics and its applications.

[6]  J. K. Gibson,et al.  Severely denting the Gabidulin version of the McEliece Public Key Cryptosystem , 1995, Des. Codes Cryptogr..

[7]  Matthieu Finiasz,et al.  How to Achieve a McEliece-Based Digital Signature Scheme , 2001, ASIACRYPT.

[8]  P. Loidreau,et al.  Security of the Niderreiter Form of the GPT public-key cryptosystem , 2002, Proceedings IEEE International Symposium on Information Theory,.

[9]  Ernst M. Gabidulin,et al.  Ideals over a Non-Commutative Ring and thier Applications in Cryptology , 1991, EUROCRYPT.

[10]  Pierre Loidreau.  Decoding rank errors beyond the error-correcting capability , 2006 .

[11]  Thierry P. Berger,et al.  How to Mask the Structure of Codes for a Cryptographic Use , 2005, Des. Codes Cryptogr..

[12]  Ernst M. Gabidulin,et al.  Public_Key Cryptosystems Based on Linear Codes , 1995 .

[13]  Raphael Overbeck.  Decoding Interleaved Gabidulin Codes and Ciphertext-Security for GPT variants , 2006, IACR Cryptol. ePrint Arch..

[14]  Robert J. McEliece,et al.  A public key cryptosystem based on algebraic coding theory , 1978 .

[15]  Theresa Migler,et al.  Weight and rank of matrices over finite fields , 2004 .

[16]  Raphael Overbeck.  Extending Gibson's Attacks on the GPT Cryptosystem , 2005, WCC.

[17]  Ernst M. Gabidulin,et al.  Column Scrambler for the GPT Cryptosystem , 2003, Discret. Appl. Math..

[18]  Thomas Johansson,et al.  New Technique for Decoding Codes in the Rank Metric and Its Cryptography Applications , 2002, Probl. Inf. Transm..