IDS 81650: Non-Commutative Cryptography I

Instructor: Prof. V. Shpilrain

Email: shpil@groups.sci.ccny.cuny.edu

Course description: Until recently, mathematics used in cryptography was "commutative", which means cryptographic primitives were based on commutative rings or commutative (finite) groups. Non-commutative groups were introduced into public-key cryptography by Wagner and Magyarik 20 years ago, but only recently did this direction get serious attention of professional cryptographers worldwide, due to seminal work of Anshel, Anshel, and Goldfeld (1999). Since then, a very active research in non-commutative cryptography is going on, and we are going to study these new promising research avenues, most of which require familiarity with classical as well as modern combinatorial group theory, with a focus on algorithmic problems and their complexity. Previous knowledge of combinatorial group theory is not required for this course; a very basic background in algebra is sufficient.