Algebra and Cryptography Seminar, Spring 2016

Organizers: Robert Gilman, Delaram Kahrobaei, Alexei Myasnikov, and Vladimir Shpilrain

Fridays:

2:30-3:30 pm
Room 3307, CUNY Graduate Center
365 Fifth Avenue at 34th Street


February 5: Alexander A. Mikhalev (Moscow State University), Cryptographic algorithms on groups and algebras
Abstract: We analyze algorithms for public key exchange on some noncommutative groups. Algorithms for factorization and decomposition in associative algebras (of small dimension) are considered, too. We also give a survey of applications (in particular, to cryptography) of the so-called ``hidden matrices''.
This talk is based on a joint work with A. S. Kuzmin, V. T. Markov, A.V. Mikhalev, and A. A. Nechaev.


February 19: Bianca Sosnovski (Queensborough Community College and CUNY Graduate Center), Cayley graphs of semigroups and applications to hashing
Abstract: Tillich and Zemor proposed a scheme for a family of hash functions (1994), which uses products of matrices in groups of the form SL_2(F_{2^n}). In 2009, Grassl et al. developed an attack to obtain collisions for palindromic bit strings by exploring a connection between the Tillich-Zemor functions and maximal length chains in the Euclidean algorithm for polynomials over F_2. We propose a new platform to be used in the Tillich-Zemor scheme (1994). The platform consists of the (semi)group of linear functions in one variable over F_p under composition generated by f(x)=2x+1 and g(x)=3x+1. The corresponding hash functions are efficient and a lower bound is provided on the minimum length of bit strings where a collision may occur.
Based on joint work with Vladimir Shpilrain.


April 8: Andrew Sale (Vanderbilt University), TBA



 


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