2:30-3:30 pm

Room 8405, CUNY Graduate Center

365 Fifth Avenue at 34th Street

Room Peirce 220, Stevens Institute of Technology

Hoboken, NJ

directions

Security seminars at Stevens

**February 6, Graduate Center**: Antonio Nicolosi (Stevens Institute),
*Average-Case vs. Generic-Case Complexity of Lattice Problems*

**Abstract: ** Lattice problems whose average-case complexity is connected to
worst-case assumptions are appealing foundations for provably secure
cryptosystems. A sharper understanding of their inherent hardness
would enable more precise security analysis, thus resulting in more
efficient cryptographic primitives. In this talk, we review the
landscape of the average-case complexity of lattice problems, sketch
some of the technical tools employed in their analysis, and discuss
our ongoing efforts to assess their generic-case complexity.

**February 20, Graduate Center**: Igor Lysenok (Moscow Steklov Institute
and Stevens Institute), *On complexity of solving equations in free groups*

**March 3, 4, 5, at 1:15 pm, Stevens Institute, room Babbio 203, Peirce 216,
Babbio 210**: Rainer Steinwandt (Florida Atlantic University), *Mini-course on Mathematical Techniques
in Modern Cryptography*

**March 13, Graduate Center**: Marina Pudovkina (Moscow Engineering
Physics Institute), * Group properties of generalized Feistel ciphers*

**April 24, Graduate Center**: Ayan Mahalanobis (Stevens Institute of
Technology), * The MOR cryptosystem*

**Abstract: ** The MOR cryptosystem is an elementary and straightforward generalization of the ElGamal cryptosystem. In this case, the discrete logarithm problem works in the automorphism group of a group G, rather than G itself. This allows us to use almost any group for the MOR cryptosystem.

In this talk we will see the definition of this cryptosystem and one instance of a secure and fast MOR cryptosystem -- using the group of non-singular circulant matrices over a finite field of characteristic 2.

**May 1, Graduate Center**: Alexander Ushakov (Stevens Institute of
Technology), * Strong Law of Large Numbers for Graph(Group)-Valued Random Elements*

**Abstract: ** We introduce the notion of the mean-set (expectation) of a graph-
(group-) valued random element $\xi$ and prove a generalization of the
strong law of large numbers on graphs and groups. Furthermore, we
prove an analogue of the classical Chebyshev's inequality for $\xi$.
We show that our generalized law of large numbers, as a new theoretical
tool, provides a framework for practical applications; namely, it has
implications for cryptanalysis of group-based authentication protocols.
In addition, we prove several results about configurations of mean-sets
in graphs and their applications. In particular, we discuss computational
problems and methods of computing of mean-sets in practice and propose
an algorithm for such computation.

Based on a joint work with Natalia Mosina (Columbia University).

**May 8, Graduate Center**: Vitaly Romankov (Omsk State University),
*The twisted conjugacy problem in solvable groups*

**Abstract: ** We prove that the problem in the title is decidable in every finitely
generated metabelian group M for any endomorphism identical modulo a
normal subgroup N of [M, M], and in every polycyclic group P for any
endomorphism.
Also, it is proved that any free nilpotent group of a big enough class
is in the Reidemeister class R_{\infty }.

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