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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