Algebra and Cryptography Seminar, Spring 2008

Organizers: Robert Gilman, Alexei Myasnikov, and Vladimir Shpilrain

Fridays:

2:30-3:30 pm
Room 8405, CUNY Graduate Center
365 Fifth Avenue at 34th Street

or

11:00 am-12:00 pm
Room Peirce 220, Stevens Institute of Technology
Hoboken, NJ

directions
Security seminars at Stevens


January 29 (Tuesday!), 4:00, Room Peirce 116, Stevens Institute: Alexander V. Mikhalev (Moscow University), Codes and recurrent sequences over rings and modules
Abstract:


February 29, Graduate Center: Ionut Florescu (Stevens Institute), Looking at the Diffie-Hellman key exchange protocol from a statistical perspective
Abstract: In this talk we will analyze the statistics of the Diffie-Hellman key exchange. More precisely, we will try to answer the question: is the conditional distribution of the key given the information observed uniform on elements of the underlying groups? The study considers small sized groups included in the multiplicative group Z_p. When looked at the ensemble a picture seems to form that relates the security of the exchange with the structure of the underlying group. More empirics are relating some of the ideas here with the Discrete Logarithm problem in the same groups. A drawback of the study is the absence of the analysis using large order groups. This may be subject of a future work. This is joint work with Alex Miasnikov and Ayan Mahalanobis.


March 14, Graduate Center: Ayan Mahalanobis (Stevens Institute), The MOR cryptoystem and special linear groups over finite fields
Abstract: The ElGamal cryptosystem is in the heart of public key cryptography. It is known that the MOR cryptosysetm generalizes it from the cyclic group to the automorphism group of a (non-abelian) group. I will start by describing the MOR cryptosystem and then we will use the special linear group over a finite field as the platform group. It seems likely that this project is competitive with the elliptic curves over finite fields in terms of security. I'll explain why I think so. Then we can talk about challenges in implementation of this cryptosystem.


April 4, Stevens Institute, Room Babbio 219: Ki Hyoung Ko (KAIST, Korea), A polynomial-time solution to the reducibility problem
Abstract: We present an algorithm for deciding whether a given braid is pseudo-Anosov, reducible, or periodic. The algorithm is based on Garside's weighted decomposition and is polynomial-time in both the word-length and the braid index of an input braid. We believe that this algorithm is one of essential steps toward a polynomial solution to the conjugacy problem in the braid groups.
 


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