Berstein Seminar, Spring 2006
Group Theory and Cryptography
MT 230, Mondays and Wednesdays 2:55-4:10

Most of the links lead to pages that give bibliographical information and allow you to download the papers

Background / Survey
Learning About Cryptography, web page by T.Ritter
Lecture Notes on Cryptography, S.Goldwasser and M.Bellare
Handbook of Applied Cryptography, A.J.Menezes, P.C. van Oorschot and A.A.Vanstone
M. Anshel's web page
Combinatorial group theory and public key cryptography, V.Shpilrain and G.Zapata
An overview of public key cryptography, M.E.Hellman
Non-Abelian Groups as Candidate Platform for Cryptographic Schemes: Strengths and Weaknesses, R. Steinwandt

Security and complexity
Assessing security of some group based cryptosystems, V. Shpilrain
Generic-case complexity, decision problems in group theory and random walks, I. Kapovich, A. G. Myasnikov, P. Schupp, V.Shpilrain
Average-case complexity and decision problems in group theory, I. Kapovich, A. G. Myasnikov, P. Schupp, V.Shpilrain
Random van Kampen diagrams, preprint, A.G.Myasnikov and A.Ushakov
Complexity of computations and cryptography, slides from a talk, A.G.Myasnikov

Group theoretic problems for potential use in public key systems
A public-key cryptosystem based on the word problem, N.R. Wagner and M.R. Magyarik
An algebraic method for public-key cryptography , I.Anshel, M.Anshel, D.Goldfeld, Math. Res. Lett. 6, 287-291 (1999)
A reaction attack on a public key cryptosystem based on the word problem, M.I. Gonzalez Vasoc and R. Steinwandt
On public-key cryptosystems based on combinatorial group theory, J.-C. Birget, S.S. Mgliveras, M. Sramka
Using the subgroup membership search problem in public key cryptography , V. Shpilrain and G.Zapata
Using decision problems in public key cryptography, V. Shpilrain and G.Zapata, (not yet available)
The conjugacy search problem in public key cryptography: unnecessary and insufficient, V. Shpilrain and A. Ushakov
A new key exchange protocol based on the decomposition problem, V. Shpilrain and A. Ushakov
Trap doors from subgroup chains and recombinant bilateral transversals, RECSI VII(2002), Asturjas - Spain, pages 31-48, J.-C. Birget, S. S. Magliveras and W. Wei (see also M.I. Gonzalez Vasco, D. Hofheinz, C. Martinez and R. Steinwandt listed below)

Braid Groups
H. Lipmaa's pages on Cryptography and Braid Groups
Braid-based cryptography, P. Dehornoy
A new approach to the word and conjugacy problems in the braid groups, J.S.Birman, K.H.Ko and J.S.Lee
Braids: a survey, J.S.Birman and T.E.Brendle
Undeniable signature schemes using braid groups, T.Thomas and A.K.Lal

Thompson's Group
Thompson's group and public key cryptography, V. Shpilrain and A. Ushakov

Grigorchuk Groups
The complexity of Grigorchuk groups with application to cryptography, Theoretical Computer Science, Vol. 88, No. 1 (1991) pp. 83�98, M. Garzon and Y. Zalcstein - see also:
On the security of two public key cryptosystems using non-abelian groups. Designs, Codes and Cryptography, 32(1--3):207--216, 2004, M.I. Gonzalez Vasco, D. Hofheinz, C. Martinez and R. Steinwandt

Polycyclic Groups
Polycyclic groups: A new platform for cryptology?, B. Eick and D. Kahrobaei

Aut(F_n)
Using the subgroup membership search problem in public key cryptography, V. Shpilrain and G.Zapata

Matrix Groups
Constructions in public-key cryptography over matrix groups, (number 109), D.Grigoriev and I.Ponomarenko -- also here on the ArXiv.

Expanders and hashing
Hashing with SL 2, J.-P. Tillich and G. Zemor, in Advances in Cryptology -- CRYPTO 1994, Y. Desmedt, Ed., vol. 839 of Lecture Notes in Computer Science, Springer-Verlag, pp. 40--49.
Weaknesses in the SL2(F2n) Hashing Scheme, R.Steinwandt, M.Grassl, W.Geiselmann, and Th.Beth, in Advances in Cryptology - CRYPTO 2000 Proceedings, M. Bellare, ed., vol. 1880 of Lecture Notes in Computer Science, Springer, pp. 287-299, 2000.
Cryptology and graph theory, slides for a talk given by J.-J.Quisquater, 2005
Cryptographic hash functions from expander graphs, D.X.Charles, E.Z.Goren, K.E.Lauter, 2005

Open Problems
The World of Groups, Open Problems - in particular see this page

Other
Bochum Workshop 2005 talks
Algebraic Cryptography Center at Stevens