"Secret- and Public-key Cryptosystems from Group Factorizations"

Abstract

We describe two possible approaches to the construction of new, secret- and public-key cryptosystems with message space a large finite group G. These schemes utilize certain factorization bases for G, called "logarithmic signatures", and their generalizations. The first scheme relies on the fact that the permutations on G induced by transversal logarithmic signatures almost always generate the full symmetric group on G. The second approach is based on trap-door, one-way functions, induced by objects we call "meshes" which cover G uniformly. This approach could potentially lead to new, general, ElGamal-like, systems.

Position

Spyros Magliveras is "Henson Professor Emeritus" at the University of Nebraska - Lincoln, and Professor of Mathematical Sciences at Florida Atlantic University. He is Coordinator of the Applied Mathematics Program, and Director of the "Cryptology and Computer Security Initiative" at Florida Atlantic University.