Algebra and Cryptography Seminar, Fall 2018

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


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

September 21: Giacomo Micheli (University of Oxford and EPFL, Lausanne), Permutations and codes using a density method
Abstract: The construction of permutation functions over a finite field is a task of great interest in applied areas such as cryptography and coding theory. In this talk I describe a method which combines Chebotarev density theorem with elementary group theory to produce permutation rational functions over a finite field. The method is entirely constructive and as a corollary we get the classification of permutation polynomials up to degree 4 over any finite field of odd characteristic. Time permitting, I briefly explain what is a locally recoverable code (LRC) and describe another application of a similar method which allows to build optimal LRCs by solving a Galois theoretical problem.

September 28: Thomas Koberda (University of Virginia), Graph theory versus algebra of right-angled Artin groups
Abstract: Right-angled Artin groups, due to their tractable algorithmic properties, are a fruitful class of groups to study from the point of view of group-based cryptography. I will discuss some of the ways in which the combinatorics of the underlying graph is reflected on the algebraic structure of the right-angled Artin group, and some algebraic phenomena which are in some sense invisible from the point of view of the combinatorics of the graph. Some of this work is joint with R. Flores and D. Kahrobaei.

October 26: Alexander Treyer (Omsk State Technical University), Universal input for knapsack problem for nilpotent groups
Abstract: Through equivalence between Diophantine problem over integers and knapsack problem (KP) over nilpotent groups, it was proven earlier that KP is undecidable over nilpotent groups. Also, this approach gives us a way to construct a universal input for knapsack type problems over nilpotent groups.

November 2: "The elementary theory of groups and group rings" conference

November 16: Alexander A. Mikhalev (Moscow State University), Nonassociative algebraic structures in coding and cryptography
Abstract: We consider applications of nonassociative algebraic structures to constructing codes and cryptoschemes.

December 7: Manhattan Algebra Day

To subscribe to the seminar mailing list, click here

Spring 2018 talks

Fall 2017 talks

Spring 2017 talks

Fall 2016 talks

Spring 2016 talks

Fall 2015 talks

Spring 2015 talks

Fall 2014 talks

Spring 2014 talks

Fall 2013 talks

Spring 2013 talks

Fall 2012 talks

Spring 2012 talks

Fall 2011 talks

Spring 2011 talks

Fall 2010 talks

Spring 2010 talks

Fall 2009 talks

Spring 2009 talks

Fall 2008 talks

Spring 2008 talks

Fall 2007 talks

Spring 2007 talks

Fall 2006 talks

Spring 2006 talks

Fall 2005 talks