Seminar: Group-theoretic cryptography
Dr. Spyros Magliveras of Florida Atlantic University, USA, will be speaking on "Group-theoretic cryptography" as part of the Cryptography in a Quantum World seminar series. The seminar will be presented by CACR and held in MC 5158 at the University of Waterloo.
Dr. Magliveras is the Director of the Center for Cryptology and Information Security and a professor in the Department of Mathematical Sciences at the Florida Atlantic University. He works on cutting-edge research in cryptology and information security. He is also interested in algebraic combinatorics, coding theory, algorithms, and algorithmic complexity.
Some 10 years ago, Phong Q. Nguyen wrote: “...Due to Shor’s algorithms for computing prime factorizations and discrete logarithms on quantum computers, most of present day public key cryptosystems must be considered insecure, if sufficiently large quantum computers became available... ”, he further added: “ ...One interesting line of research in this direction is the use of computational problems in non-abelian groups.” In this talk we present some fundamental objects in the context of non-abelian groups. We also present associated problems which we believe to be (classically) hard, and can serve as a new foundation in the design of cryptographic primitives. We will discuss “group covers”, “logarithmic signatures” of groups and the mappings they induce, as well as the closely related problem of discrete logarithms in non-abelian groups. These ideas deal with factorizations in groups and of groups. We discuss some progress in designing primitives based on these ideas, some persisting difficulties, open problems, and ask whether these problems could have efficient quantum solutions. If time permits we will demonstrate an elementary application of log signatures.