IJPAM: Volume 69, No. 1 (2011)

GROUP RING CRYPTOGRAPHY

Barry Hurley$^1$, Ted Hurley$^2$
$^{1,2}$School of Mathematics, Statistics and Applied Mathematics
National University of Ireland
University Road, Galway, IRELAND


Abstract. Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the complexity of the discrete logarithm problem to the system.

The method enables encryption and (error-correcting) coding to be combined within one system.

These group ring cryptographic systems may be combined in a neat way with existing cryptographic systems, such as RSA, and a combination has the combined strength of both systems.

Examples are given.

Received: February 25, 2011

AMS Subject Classification: 94A60, 11T71, 14G50, 81P68

Key Words and Phrases: group ring, units, cryptography, public key cryptography, coding

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 1