AN ADAPTIVE EXPONENTIATION METHOD

Exponentiation of large positive integer with a 512-bit exponent is th e basis of several well-known cryptographic algorithms. In this paper, an adaptive method for improving the performance of the m-ary method is proposed and analyzed. Due to the efficient utilization of partial results, it is useful for systems with varied exponent and base. This method is based on two ideas. Firstly, for base x, a few of the expone ntiations with smaller exponents are precomputed on-line, that is, x(2 ), x(3),... x((2w-1)) are precomputed, where w is an optimization para meter. Secondly, a number of used partial results will be determined a nd stored in a look-lip table during the computation. Assume that squa ring is Jj-ee as compared with multiplication, depending on the number s of precomputations and partial results, the proposed method on avera ge gives a 26-40% time reduction as compared with the m-ary method. On the other hand, it does require little temporary storage for the used partial results. (C) 1998 Elsevier Science Inc. All rights reserved.