Efficient GF(pm) Arithmetic Architectures for Cryptographic Applications

G. Bertoni, Jorge Guajardo Merchan, Sandeep Kumar, G. Orlando, Chris­tof Paar, Thomas Wollinger

In Marc Joye (Ed.): The Cryptographers' Track at the RSA Conference - CT-RSA 2003, volume LNCS 2612, pp. 158-175, San Francisco, CA, USA, April 13-17, 2003.


Abstract

Recently, there has been a lot of interest on cryptographic applications based on ?elds GF(pm ), for p > 2. This contribution presents GF(pm ) multipliers architectures, where p is odd. We present designs which trade area for performance based on the number of coe?cients that the multiplier processes at one time. Families of irreducible polynomials are introduced to reduce the complexity of the modulo reduction operation and, thus, improved the e?ciency of the multiplier. We, then, specialize to ?elds GF(3m ) and provide the ?rst cubing architecture presented in the literature.

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