Length based attack and braid groups: Cryptanalysis of Anshel-Anshel- Goldfeld key exchange protocol

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4450 LNCS, Issue , 2007, Pages 76-88

  Myasnikov, Alex D ^a   Ushakov, Alexander ^a  

^a Stevens Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC COMMUTATORS; ONLINE SEARCHING; PARAMETER ESTIMATION; PROBLEM SOLVING;

BRAID GROUPS; CONJUGACY SEARCH PROBLEMS; CRYPTANALYSIS; PRIVATE INFORMATION; PUBLIC INFORMATION;

CRYPTOGRAPHY;

EID: 38049061060     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-71677-8_6     Document Type: Conference Paper

References (17)

1. I. Anshel, M. Anshel, D. Goldfeld, An algebraic method for public-key cryptography, Math. Res. Lett. 6 (1999), 287-291.
2. J. S. Birman, Braids, links and mapping class groups, Ann. Math. Studies 82, Princeton Univ. Press, 1974.
3. CRyptography And Groups (CRAG), C++ and Python Library for computations in groups and group based cryptography, available at http://www.sicc.stevens. edu/downloads.php.
4. P.Dehornoy, A fast method for comparing braids, Advances in math. 125, (1997), 200-235.
5. D. B. A. Epstein, J. W. Cannon, D. F. Holt, S. V. F. Levy, M. S. Paterson, W. P. Thurston, Word processing in groups. Jones and Bartlett Publishers, Boston, MA, 1992.
6. D. Garber, S. Kaplan, M. Teicher, B. Tsaban, U. Vishne, "Length-based conjugacy search in the Braid group", http://arxiv.org/abs/math.GR/0209267.
7. D. Hofheinz, R. Steinwandt. A Practical Attack on Some Braid Group Based Cryptographic Primitives. In Public Key Cryptography, 6th International Workshop on Practice and Theory in Public Key Cryptography, PKC 2003 Proceedings, Y.G. Desmedt, ed., vol. 2567 of Lecture Notes in Computer Science, pp. 187-198, Springer, 2002.
8. J. Hughes, "A Linear Algebraic Attack on the AAFG1 Braid Group Cryptosystem", ACISP 2002, Lecture Notes in Computer Science, vol. 2384, (2002), 176-189.
9. J. Hughes, A. Tannenbaum, Length-based attacks for certain group based encryption rewriting systems. In: Workshop SECI02 Sécurité de la Communication sur Intenet, September 2002, Tunis, Tunisia.
10. K. H. Ko, S. J. Lee, J. H. Cheon, J. W. Han, J. Kang, C. Park, New public-key cryptosystem using braid groups. In: Advances in cryptology - CRYPTO 2000 (Santa Barbara, CA), 166-183 (Lecture Notes Comp. Sc., vol. 1880) Berlin Heidelberg New York Tokyo: Springer 2000.
11. S. J. Lee, E. Lee, Potential Weaknesses of the Commutator Key Agreement protocol Based on Braid Groups. In: Advances in cryptology - Eurocrypt 2002, 14-28 (Lecture Notes Comp. Sc., vol. 2332) Berlin Heidelberg New York Tokyo: Springer 2002.
12. K. A. Mihailova, "The occurrence problem for free products of groups", Math USSR-Sbornik 70, (1966), 241-251.
13. A. G. Myasnikov, V. Shpilrain, A. Ushakov. A practical attack on some braid group based cryptographic protocols. In CRYPTO 2005, Lecture Notes Comp. Sc. 3621 (2005), 86-96.
14. A. G. Myasnikov, V. Shpilrain, A. Ushakov. Random subgroups of braid groups: an approach to cryptanalysis of a braid group based cryptographic protocol. In PKC 2006, Lecture Notes Comp. Sc. 3958 (2006), 302-314.
15. M. Paterson, A. Razborov, The set of minimal braids in co-NP-complete J. Algorithms, 12 (1991), 393-408.
16. V. Shpilrain and A. Ushakov, The conjugacy search problem in public key cryptography: unnecessary and insufficient, Applicable Algebra in Engineering, Communication and Computing, to appear. http://eprint.iacr.org/ 2004/321/
17. A. Vershik, S. Nechaev, R. Bikbov. Statistical properties of braid groups in locally free approximation. In Communications in Mathematical Physics, vol. 212, 2000, pp. 469-501.