Towards a Uniform Description of Several Group Based Cryptographic Primitives

Authors:
María Isabel González Vasco;Consuelo Martínez;Rainer Steinwandt
Affiliations:
Departamento de Matemáticas, Facultad de Ciencias, c/Calvo Sotelo, s/n, 33007 Oviedo, Spain;Departamento de Matemáticas, Facultad de Ciencias, c/Calvo Sotelo, s/n, 33007 Oviedo, Spain;Institut für Algorithmen und Kognitive Systeme, Arbeitsgruppen Computeralgebra und Systemsicherheit, Universität Karlsruhe, 76128 Karlsruhe, Germany
Venue:
Designs, Codes and Cryptography
Year:
2004

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Abstract

The public key cryptosystems MST1 and MST2 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 MST2 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.