文件名称：Fast Exponentiation with Precomputation: Algorithms and Lower Bounds
文件大小：148KB
文件格式：PDF
更新时间：2012-09-04 01:47:09
Fast Exponentiation Algorithms
In several cryptographic systems, a fixed element g of a group of order N is repeatedly raised to many diff erent 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 g^n for n < N in O(logN= log logN) multiplicaitons. We show that this method is asymptotically optimal given polynomial storage, and for specific cases, within a small factor of optimal. We also show how these methods can be parallelized, to compute powers in time O(log logN) with O(logN= log2 logN) processors.