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
  • computational group theory
  • generic complexity
  • 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. A. Ushakov. (2014). "Algorithmic theory of free solvable groups: randomized computations", Journal of Algebra. 407 178--200.  [arxiv]  .
  2. 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]  .
  3. A. D. Myasnikov and A. Ushakov. (2014). "Cryptanalysis of matrix conjugation schemes", Journal of Mathematical Cryptology. 8 (2), 95--114.  [arxiv]  .
  4. 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  .
  5. A. G. Miasnikov, A. Ushakov. (2011). "Random van Kampen diagrams and algorithmic problems in groups", Groups - Complexity - Cryptology, 3 (1), 121--185.
  6. N. Mosina and A. Ushakov. (2011). "Strong law of large numbers on graphs and groups", Groups - Complexity - Cryptology, 3 (1), 67-103.  [arxiv]  .
  7. 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]  .
  8. 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]  .
  9. 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]  .
  10. 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]  .
  11. 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.
  12. J. Longrigg and A. Ushakov. (2008). "Cryptanalysis of shifted conjugacy authentication protocol", Journal of Mathematical Cryptology, 2 (2), 107-114.  [arxiv]  .
  13. A. D. Myasnikov and A. Ushakov. (2008). "Cryptanalysis of Anshel-Anshel-Goldfeld-Lemieux key agreement protocol", Groups-Complexity-Cryptology, 1 (1), 63-75.  [arxiv]  .
  14. 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]  .
  15. R. Gilman, A. D. Myasnikov, A. G. Miasnikov and A. Ushakov. (2007). "A Report on Generic Complexity", Herald of Omsk State University,  [arxiv]  .
  16. 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.