Combinatorial Group Theory and Public Key Cryptography

Anshel I., Anshel M., Goldfeld D. (1999) An algebraic method for public-key cryptography. Math. Res. Lett. 6, 287–291

Appel K., Schupp P. (1983) Artin groups and infinite Coxeter groups. Invent. Math. 72, 201–220

Cryptography and braid groups, http://www.cs.ut.ee/~lipmaa/crypto/link/public/braid/

Dehornoy, P. Braid-based cryptography. In: Group theory, statistics, and cryptography, vol. 360, pp. 5–33, Contemp. Math., Providence, Am. Math. Soc. (2004)

Garber, D., Kaplan, S., Teicher, M., Tsaban, B., Vishne, U. Length-based conjugacy search in the braid group, preprint. http://www.arXiv.org/abs/math.GR/0209267

Garrett P. (2001) Making, breaking codes: an introduction to cryptology. Prentice Hall, Englewood Cliifs

Hofheinz, D., Steinwandt, R. A practical attack on some braid group based cryptographic primitives. In: Y. G. Desmedt (ed.) Public Key Cryptography, 6th International Workshop on Practice and Theory in Public Key Cryptography, PKC 2003 Proceedings, vol. 2567, pp. 187–198, Lecture Notes Comp. Sc., Springer, Berlin Heidelberg New York Tokyo: (2002)

Howie J.M. (1995) Fundamentals of Semigroup Theory, vol. 12. London Mathematical Society Monographs Clarendon Press, Oxford

Hughes, J., Tannenbaum, A. Length-based attacks for certain group based encryption rewriting systems. In: Workshop SECI02 Securitè de la Communication sur Intenet, September, Tunis, Tunisia (2002). http://www.network.com/~hughes/

Kapovich I., Myasnikov A., Schupp P., Shpilrain V. (2003) Generic-case complexity, decision problems in group theory and random walks. J. Algebra 264, 665–694

Kapovich I., Myasnikov A., Schupp P., Shpilrain V. (2005) Average-case complexity and decision problems in group theory. Adv. Math. 190, 343–359

Ko, K. H. Conjugacy problem in braid groups and applications, I. Overview: Conjugacy problems, their variations, and their applications, preprint. http://www.kyokan.ms.u-tokyo.ac.jp/~topology/files/KS03a.pdf

Ko, K. H., Lee, S.J., Cheon, J.H., Han, J.W., Kang, J., Park, C. New public-key cryptosystem using braid groups. In: Advances in cryptology – CRYPTO 2000 (Santa Barbara, CA), vol. 1880, pp. 166–183, Lecture Notes Comp. Sc. Springer, Berlin Heidelberg New York Tokyo: (2000)

Lyndon, R.C., Schupp, P.E. Combinatorial Group Theory, Ergebnisse der Mathematik, band 89, Springer 1977. Reprinted in the Springer Classics in Mathematics series (2000)

Myasnikov, A.D., Myasnikov, A.G., Shpilrain V. On the Andrews-Curtis equivalence. In: Combinatorial and geometric group theory, vol. 296, pp. 183–198, Contemp. Math. Providence, Am. Math. Soc. (2002)

Myasnikov, A.G., Ushakov, A. Random van Kampen diagrams, preprint

Peifer D. (1996) Artin groups of extra-large type are automatic. J. Pure Appl. Alg. 110, 15–56

Shpilrain, V. Assessing security of some group based cryptosystems. In: Group theory, statistics, and cryptography, vol. 360, pp. 167–177, Contemp. Math. Providence, Am. Math. Soc. (2004)