Paper 2002/048

Towards a Uniform Description of Several Group Based Cryptographic Primitives

Maria Isabel Gonzalez Vasco and Consuelo Martinez and Rainer Steinwandt

Abstract

The public key cryptosystems $MST_1$ and $MST_2$ make use of certain kinds of factorizations of finite groups. We show that generalizing such factorizations to infinite groups allows a uniform description of several proposed cryptographic primitives. In particular, a generalization of $MST_2$ can be regarded as a unifying framework for several suggested cryptosystems including the ElGamal public key system, a public key system based on braid groups and the MOR cryptosystem.