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MSc thesis of Christos Pilichos

Algorithms in Group Theory

Supervisor: Evangelos Raptis

A modern branch of Mathematics is Non-Commutative Cryptography, which is based on the algorithmic hardness of solving some Group Theory based problems. Since 1911, Max Dehn announced that a part of his interest were the word, conjugacy and group-isomorphism problems. The former two accompanied with the analysis problem consist the fundamental problems on which all the protocols of the current Thesis are based on. The tour in the world of Non-Commutative Cryptography begins from the protocols of Wagner-Magyarik (using free groups) and Garzon-Zalcstein (using Grigorchyk's groups) and via Anshel-Anshel-Goldfeld and Ko-Lee et al. (both using braid groups) is over at protocols of Shpilrain-Ushakov (using Thompson's group F), Stickel anf Kurt. Cryptanalysis and the tries of making the above cryptosystems more secure creates some interesting byproducts (like a protocol based on circuits, dynamic version of Stickel's protoocol, using monoids in Wagner-Magyarik protocol, the generalised version of Anshel-Anshel-Goldfeld and Ko-Lee et al. protocols, etc).

Work in progress.

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