Attacking and Defending the McEliece Cryptosystem

• Published in: Post-Quantum Cryptography Vol. 5299; pp. 31 - 46
• Main Authors: Bernstein, Daniel J., Lange, Tanja, Peters, Christiane
• Format: Book Chapter
• Language: English
• Published: Germany Springer Berlin / Heidelberg 2008; Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: list decoding binary Goppa codes; McEliece cryptosystem; minimal weight code word; security analysis; Stern attack
• ISBN: 3540884025; 9783540884026
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-540-88403-3_3

This paper presents several improvements to Stern’s attack on the McEliece cryptosystem and achieves results considerably better than Canteaut et al. This paper shows that the system with the originally proposed parameters can be broken in just 1400 days by a single 2.4GHz Core 2 Quad CPU, or 7 days by a cluster of 200 CPUs. This attack has been implemented and is now in progress. This paper proposes new parameters for the McEliece and Niederreiter cryptosystems achieving standard levels of security against all known attacks. The new parameters take account of the improved attack; the recent introduction of list decoding for binary Goppa codes; and the possibility of choosing code lengths that are not a power of 2. The resulting public-key sizes are considerably smaller than previous parameter choices for the same level of security.