Algebra and Cryptography Seminar, Spring 2017

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

February 25 (Saturday): NYU Tandon School of Engineering: New York Multidisciplinary Symposium on Security and Privacy

March 3: Ni Lu Yen (CUNY Graduate Center), Cryptosystems using subgroup distortion
Abstract: There has been a great interest in non-commutative cryptography for more than a decade. Various algorithmic problems were studied and used such as: Conjugacy Search Problem, Endomorphism Search Problem, Word Choice Problem, Membership Search Problem and Twisted Conjugacy Problem. However, Geodesic Length Problem or Complexity of Subgroup Distortion has not been discussed in cryptography. Utilizing these problems, we propose cryptosystems based on subgroup distortion, with hyperbolic groups as platform groups, and analyze their security.
This is joint work with Delaram Kahrobaei and Indira Chatterji.

March 31: Quanyan Zhu (New York University), Game-Theoretic Approach to Security and Resilience of Cyber-Physical Systems
Abstract: Game theory is an emerging modeling tool in engineering to capture complex interactions in large-scale intelligent systems such as autonomous systems, smart cities and the Internet of Things. Also, game theory is a quantitative method to understand conflicts and contentions among players or systems. These features make the theory an appropriate tool to model and design secure and resilient cyber-physical and human systems. In this talk, we will first give a short introduction to the theory and its applications. Then, we will present a meta-game approach f the multi-layer and multi-type cyber and physical interactions to provide a holistic analytical framework for assessing cyber risks of CPS under advanced persistent threats. We will leverage the theory as a guideline for developing security-hardening strategies for the network security and designing resilient controllers to respond to failures. We use the Internet of Controlled Things and the autonomous systems as case studies to illustrate the design methodologies.

April 28: Alexander A. Mikhalev (Moscow State University), Combinatorics of Lyndon--Shirshov and Sturmian words
Abstract: Let X be an ordered set, S(X) the free semigroup on X. A word w of S(X) is primitive if w=u^n with a word u and a positive integer n implies n=1. A Lyndon (Shirshov) word is a primitive word which is minimal (maximal) for the lexicographical order in its conjugacy class. Sturmian words are infinite words over the alphabet {0,1} that have exactly n+1 factors (subwords) of length n for each n. In this talk we consider combinatorial properties of Lyndon--Shirshov and Sturmian words with some applications.

May 5: Maggie Habeeb (California University of Pennsylvania), Using Conjugation in an Oblivious Transfer
Abstract: In an oblivious transfer, which was first introduced by Rabin, the sender has a pair of messages and the receiver receives one of them. The sender does not know which message was received, and the receiver obtains exactly one of the messages. We will present some ideas on oblivious transfer protocols using conjugation.

May 12: James Davenport (University of Bath, U.K.), Satisfiability Checking and Symbolic Computation
Abstract: Satisfiability Checking and Symbolic Computation are two research areas, both having their individual scientific focus but with common interests, e.g., in the development, implementation and application of decision procedures for arithmetic theories. Despite their commonalities, the two communities are rather weakly connected. The speaker is leader of the SCSC initiative, aiming to strengthen the connection between these communities. In the area of nonlinear real arithmetic, we will describe and contrast the two different approaches, and discuss some challenges.

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