2:30-3:30 pm
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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