文件名称:
Fast Exponentiation with Precomputation: Algorithms and Lower Bounds
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文件大小: 148kb
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上传时间: 2009-08-15
详细说明： 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 ne eded. 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. ...展开收缩
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