Publications

1. Generic case complexity and One-Way functions, Preprint, 2008.
   arXiv:0802.3734v1
2. Cryptanalysis of Anshel-Anshel-Goldfeld-Lemieux key agreement protocol, (with A. Ushakov), 2008.
   arXiv:0801.4786
3. Length Based Attack and Braid Groups: Cryptanalysis of Anshel-Anshel-Goldfeld Key Exchange Protocol, (with A. Ushakov). T. Okamoto and X. Wang (Eds.): PKC 2007, LNCS 4450, 2007, 76–88.
   [PDF 474kb]
4. Report on Generic Case Complexity, (with R. Gilman, A.G.Miasnikov and A.Ushakov), 2007.
   arXiv:0707.1364v1
5. Statistical analysis of the Diffie-Hellman key exchange protocol in a finite group, (with I. Florescu and A. Mahalanobis), 2007.
   arXiv:math/0702155v1
6. A Hybrid Algorithm for Solving the Whitehead Minimzation Problem, (with R.M. Haralick). Journal of Symbolic Computation. Vol. 41, No. 7, July 2006, 818-834.
   [PDF 220kb]
7. Heuristics for Whitehead Minimization Problem, (with R.M. Haralick, A.G. Myasnikov). J. Experimental Mathematics. Vol. 14, No. 1, (2005), 7-14.
   [PDF 174kb]
8. Pattern Recognition and Minimal Words in Free Groups of Rank 2, (with R. M. Haralick, A.G. Myasnikov). J. Group Theory, Vol. 8, No. 4, (2005), 523-538.
9. Recognition of Whitehead-minimal elements in Free Groups of Large Ranks, Artificial Intelligence and Symbolic Computation (Lecture notes in Artificial Intelligence), Vol. 3249, (2004), 211-221.
   [PDF 224kb]
10. Regression analysis and automorphic orbits in free groups of Rank 2, (with R.M. Haralick), 17th International Conference on Pattern Recognition (ICPR'04). Vol. 1, (2004), 180-183.
    [PDF 133kb]
11. A Hierarchical Projection Pursuit Clustering Algorithm, (with J.E.Rome, R.M. Haralick). 17th International Conference on Pattern Recognition (ICPR'04), Vol. 1, (2004), 268-271.
    [PDF 578kb]
12. Pattern Recognition Approaches to Solving Combinatorial Problems in Free Groups, (with R. M. Haralick, A.G. Myasnikov). Contemporary Mathematics, 349:197-213, 2004.
    [PDF 227kb]
13. A Hierarchical Projection Pursuit Clustering Algorithm, (with J.E. Rome, R.M. Haralick). Technical Report TR-2003009, Department Computer Science, Graduate Center of CUNY, 2003.
    [PDF 596kb]
14. Data Modelling and Description: A Guide to Using the SYLModel, (with J.E. Rome, R.M. Haralick). Technical Report TR-2003011, Department Computer Science, Graduate Center of CUNY, 2003.
    [PDF 1.35mb]
15. Whitehead method and Genetic Algorithms, (with A.G.Myasnikov). Contemporary Mathematics, 349:89-114, 2004.
    [PDF 300kb]

16. On the Andrews-Curtis equivalence, ( with A.G.Myasnikov, V.Shpilrain), Contemporary Mathematics, 296:183-198, 2002.
    [PS 123kb]

17. Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture, (with A.G.Myasnikov). In W.Kantor and A.Seress, editors, Groups and Computation III, volume 23, (2001) 257-263, Berlin.
    [PDF 134kb] [PS 123kb]

18. Genetic algorithms and the Andrews-Curtis conjecture, International Journal of Algebra and Computation, Vol. 9 No. 6, (1999) 671-686.
    [PDF 199kb] [PS 236kb]