Fast exponentiation with precomputation

Authors:
Ernest F. Brickell;Daniel M. Gordon;Kevin S. McCurley;David B. Wilson
Affiliations:
Sandia National Laboratories, Albuquerque, NM;Department of Computer Science, University of Georgia, Athens, GA;Sandia National Laboratories, Albuquerque, NM;Department of Mathematics, M.I.T., Cambridge, MA
Venue:
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Year:
1992

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Abstract

In several cryptographic systems, a fixed element g of a group (generally Z/qZ) is repeatedly raised to many different powers. In this paper we present a practical method of speeding up such systems. using precomputed values to reduce the number of multiplications needed. In practice this provides a substantial improvement over the level of performance that can be obtained using addition chains, and allows the computation of gn for n N in O(log N/log log N) group multiplications. We also show how these methods can he parallelized, to compute powers in O(log log N) group multiplications with O(log N/ log log N) processors.