Algebraic Cryptography Center

Generic case complexity

1. Robert Gilman, Alexei G. Miasnikov, Alex D. Myasnikov, Alexander Ushakov, Report on Generic Case Complexity, 2007.
2. A.V. Borovik, A.G. Myasnikov, V. Shpilrain, Measuring sets in infinite groups, Computational and statistical group theory (Las Vegas, NV/Hoboken, NJ, 2001), 21--42, Contemp. Math., 298, Amer. Math. Soc., Providence, RI, 2002.
3. A.V. Borovik, A.G. Myasnikov, V.N. Remeslennikov, Multiplicative measures on free groups, Internat. J. Algebra Comput. 13 (2003), no. 6, 705--731.
4. J.D. Hamkins, A. Miasnikov, The halting problem is decidable on a set of asymptotic probability one.
5. I. Kapovich, A. Myasnikov, P. Schupp, V. Shpilrain, Average-case complexity and decision problems in group theory, Adv. Math. 190 (2005), no. 2, 343--359.
6. I. Kapovich, A. Myasnikov, P. Schupp, V. Shpilrain, Generic-case complexity, decision problems in group theory and random walks, J. Algebra 264 (2003), no. 2, 665--694.
7. A.D. Myasnikov, Generic case complexity and One-Way functions, 2008.

Algebraic cryptography

1. J. Longrigg, A. Ushakov, Cryptanalysis of shifted conjugacy authentication protocol.
2. A. Mahalanobis, Diffie-Hellman Key Exchange Protocol, Its Generalization and Nilpotent Groups.
3. A. Mahalanobis, Diffie-Hellman key exchange protocol and non-abelian nilpotent groups.
4. A.D. Myasnikov, A.Ushakov, Cryptanalysis of Anshel-Anshel-Goldfeld-Lemieux key agreement protocol, 2008.
5. A.D. Myasnikov, A.Ushakov. Length Based Attack and Braid Groups: Cryptanalysis of Anshel-Anshel-Goldfeld Key Exchange Protocol. T. Okamoto and X. Wang (Eds.): PKC 2007, LNCS 4450, 2007, 76–88.
6. A. G. Myasnikov, V. Shpilrain and A.Ushakov, A practical attack on some braid group based cryptographic protocols, in CRYPTO 2005, Lecture Notes Comp. Sc. 3621 (2005), 86-96.
7. A. G. Myasnikov, V. Shpilrain and 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.
8. V. Shpilrain and A.Ushakov, Thompson's group and public key cryptography, Lecture Notes Comp. Sc. 3531 (2005), 151-164.
9. V. Shpilrain, A. Ushakov, A new key exchange protocol based on the decomposition problem.
10. V. Shpilrain, Assessing security of some group based cryptosystems, Contemp. Math., 360, Amer. Math. Soc., Providence, RI, 2004.
11. V. Shpilrain, A. Ushakov, The conjugacy search problem in public key cryptography: unnecessary and insufficient.
12. V. Shpilrain, G. Zapata, Combinatorial group theory and public key cryptography.

Experimental algebra

1. A.D. Miasnikov, R.M.Haralick, A Hybrid Algorithm for Solving the Whitehead Minimzation Problem. Journal of Symbolic Computation,Vol. 41, No. 7, 818-834, 2006.
2. R.M.Haralick, A.D. Miasnikov, A.G. Myasnikov, Heuristics for Whitehead Minimization Problem, J. Experimental Mathematics. Vol. 14, No. 1, 7-14, 2005.
3. R.M.Haralick, A.D. Miasnikov, A.G. Myasnikov, Pattern Recognition Approaches to Solving Combinatorial Problems in Free Groups, Contemporary Mathematics, 349:197-213, 2004.

Murray Elder

Robert Gilman

Ayan Mahalanobis

Alexei Miasnikov

Alex Myasnikov

Vladimir Shpilrain

Sasha Ushakov

Rebecca Wright

Susanne Wetzel