Applications of non-abelian group theory in cryptography


Delaram Kahrobaei (City Tech and CUNY Graduate Center)

Abstract:

As computers become faster and faster, and with the advent of quantum computers on the horizon, the question of protecting information transmitted over the World Wide Web becomes ever more important. Both academic and industrial establishment are concerned with developing unbreakable cryptosystems. In recent years it has been proposed to use non-commutative groups as a platform on which to build cryptosystems. This work was initiated in 1984 by Wagner et al who proposed an approach to design public-key cryptosystems based on the undecidable word problem for groups and semigroups. In 1999, Anshel-Anshel-Goldfeld proposed a compact algebraic key establishment protocol. The foundation of their method lies in the difficulty of solving equations over algebraic structures, in particular non-commutative groups. In joint work with Eick I proposed a new cryptosystem based on polycyclic groups. In joint work with Khan I proposed non-commutative key-exchange schemes which generalize the classical ElGamal Cipher to polycyclic groups. I will give an overview on the recent development of this field and discuss interesting open problems which arise naturally from this path of research.