Faculty Profile (Math)

Alexander Ushakov

ASSISTANT PROFESSOR
Building: Kidde
Room: 219A
Phone: 201.216.8597
Fax: 201.216.8321
Email: aushakov@stevens.edu
School:  Schaefer School of Engineering & Science
Department:  Mathematical Sciences
Program:  Mathematics
Research
  • combinatorial group theory
  • computational algebra
  • algebraic cryptography
Grants, Contracts & Funds
  • NSA research award ``Taming metabelian groups'', 2014.
  • NSF research award ``Computation with Finitely Presented Groups'', 2013.
  • NSF conference award ``Conference: Groups, geometry and dynamics'', 2013.
  • NSF conference award ``Thematic program semester: Geometric, combinatorial and computational group theory'', 2010.
  • NSF research award ``Collaborative research: Theoretical and experimental approaches to search problems in group theory'', 2009. 
Selected Publications
Journals
  1. P. Morar and A. Ushakov. (2015). "Search problems in groups and branching processes", International Journal of Algebra and Computation. 25 (3), 445-480.  [arxiv]  .
  2. A. G. Miasnikov, A. Nikolaev, A. Ushakov. (2015). "Knapsack problems in groups", Mathematics of Computation. 84 987-1016.  [arxiv]  .
  3. A. G. Myasnikov, A. Nikolaev, A. Ushakov. (2014). "The Post correspondence problem in groups", Journal of Group Theory. 17 (6), 991-1008.  [arxiv]  .
  4. A. Ushakov. (2014). "Algorithmic theory of free solvable groups: randomized computations", Journal of Algebra. 407 178--200.  [arxiv]  .
  5. A. D. Myasnikov and A. Ushakov. (2014). "Quantum algorithm for discrete logarithm problem for matrices over finite group rings", Groups-Complexity-Cryptology. 6 (1), 31--36.  [arxiv]  .
  6. A. D. Myasnikov and A. Ushakov. (2014). "Cryptanalysis of matrix conjugation schemes", Journal of Mathematical Cryptology. 8 (2), 95--114.  [arxiv]  .
  7. A. G. Miasnikov, A. Ushakov, and D. Won. (2012). "Power Circuits, Exponential Algebra, and Time Complexity", International Journal of Algebra and Computation, 22 (6), 51.  arxiv  .
  8. A. G. Miasnikov, A. Ushakov. (2011). "Random van Kampen diagrams and algorithmic problems in groups", Groups - Complexity - Cryptology, 3 (1), 121--185.
  9. N. Mosina and A. Ushakov. (2011). "Strong law of large numbers on graphs and groups", Groups - Complexity - Cryptology, 3 (1), 67-103.  [arxiv]  .
  10. A. G. Miasnikov, A. Ushakov, and D. Won. (2011). "The word problem in the Baumslag group with a non-elementary Dehn function is polynomial time decidable", Journal of Algebra, 345 (1), 324-342.  [arxiv]  .
  11. A. G. Miasnikov, I. Lysenok and A. Ushakov. (2010). "The conjugacy problem in the Grigorchuk group is polynomial time decidable", Groups-Geometry-Dynamics, 4 (4), 813--833.  [arxiv]  .
  12. N. Mosina and A. Ushakov. (2010). "Mean set attack: Cryptanalysis of Sibert et al authentication protocol", Journal of Mathematical Cryptology, 4 (2), 149-174.  [arxiv]  .
  13. A. Miasnikov, V. Roman'kov, A. Ushakov and A. Vershik. (2010). "The Word and Geodesic Problems in Free Solvable Groups", Transactions of AMS, 362 4655-4682.  [arxiv]  .
  14. J. Longrigg and A. Ushakov. (2009). "A Practical Attack on a Certain Braid Group Based Shifted Conjugacy Authentication Protocol", Groups-Complexity-Cryptology, 1 275-286.
  15. J. Longrigg and A. Ushakov. (2008). "Cryptanalysis of shifted conjugacy authentication protocol", Journal of Mathematical Cryptology, 2 (2), 107-114.  [arxiv]  .
  16. A. D. Myasnikov and A. Ushakov. (2008). "Cryptanalysis of Anshel-Anshel-Goldfeld-Lemieux key agreement protocol", Groups-Complexity-Cryptology, 1 (1), 63-75.  [arxiv]  .
  17. A. G. Miasnikov and A. Ushakov. (2008). "Random subgroups and analysis of the length-based and quotient attacks", Journal of Mathematical Cryptology, 2 (1), 29-61.  [arxiv]  .
  18. R. Gilman, A. D. Myasnikov, A. G. Miasnikov and A. Ushakov. (2007). "A Report on Generic Complexity", Herald of Omsk State University,  [arxiv]  .
  19. V. Shpilrain, A. Ushakov. (2006). "The Conjugacy search problem in public key cryptography: unnecessary and insufficient", Applicable Algebra in Engineering, Communication and Computing (17), 285--289.  [IACR]  .
Conference Proceedings
  1. M. Kreuzer, A. D. Myasnikov, and A. Ushakov. (2014). "A Linear Algebra Attack to Group-Ring-Based Key Exchange Protocols", Applied Cryptography and Network Security. LNCS 8479 37--43.
  2. V. Diekert, J. Laun, A. Ushakov. (2012). "Efficient algorithms for highly compressed data: The Word Problem in Higman's group is in P", STACS-2012. Proceedings of the 29th Symposium on Theoretical Aspects of Computer Science, 218-229.  [arxiv]  .
  3. R. Gilman, A. D. Myasnikov, A. G. Miasnikov and A. Ushakov. (2008). "New developments in Commutator Key Exchange", Proceedings of the First International Conference on Symbolic Computation and Cryptography. 146--150.
  4. V. Shpilrain and A. Ushakov. (2008). "An authentication scheme based on the twisted conjugacy problem", Applied Cryptography and Network Security (ACNS) 2008. LNCS 5037 366--372.  [arxiv]  .
  5. A. D. Miasnikov and A. Ushakov. (2007). "Length Based Attack and Braid Groups: Cryptanalysis of Anshel- Anshel-Godlfeld Key Exchange Protocol", Theory and Practice of Public-Key Cryptography (PKC) 2007. LNCS 4450 76--88.
  6. M. Kreuzer, A. G. Miasnikov, G. Rosenberger and A. Ushakov. (2006). "Quotient Tests and Grobner Bases", Combinatorial Group Theory, Discrete Groups and Number Theory. 187-200.  [link]  .
  7. V. Shpilrain and A. Ushakov. (2006). "A New Key Exchange Protocol Based on the Decomposition Problem", International Workshop on Algebraic Methods in Cryptography. 161--167.  [arxiv]  .
  8. A. Miasnikov, V. Shpilrain, and A. Ushakov. (2006). "Random subgroups of braid groups: cryptanalysis of a braid group based cryptographic protocol", Theory and Practice of Public-Key Cryptography (PKC) 2006. LNCS 3958 302-314.  [IACR]  .
  9. A. Miasnikov, V. Shpilrain, and A. Ushakov. (2005). "A Practical Attack on a Braid Group Based Cryptographic Protocol", Crypto 2005. LNCS 3621 86--96.  [IACR]  .
  10. V. Shpilrain and A. Ushakov. (2005). "Thompson's Group and Public Key Cryptography", Applied Cryptography and Network Security (ACNS) 2005. LNCS 3531 151-164.  [arxiv]  .
Books
  1. Alexei Myasnikov, Vladimir Shpilrain, Alexander Ushakov. (Dec 2011). Non-Commutative Cryptography and Complexity of Group-Theoretic Problems, American Mathematical Society.
  2. Alexei Myasnikov, Vladimir Shpilrain, Alexander Ushakov. (Aug 2008). Group-based Cryptography, Birkhauser Basel.