Analysis of Sliding Window Techniques for Exponentiation
نویسنده
چکیده
The m-ary method for computing x E partitions the bits of the integer E into words of constant length, and then performs as many multiplications as there are nonzero words. Variable length partitioning strategies have been suggested to reduce the number of nonzero words, and thus, the total numb e r o f m ultiplications. Algorithms for exponentiation using such partitioning strategies are termed sliding window techniques. In this paper, we give algorithmic descriptions of two recently proposed sliding window techniques, and calculate the average numberofmultiplications by modeling the partitioning process as a Markov chain. We tabulate the optimal values of the partitioning parameters, and show that the sliding window algorithms require up to 8 fewer multiplications than the m-ary method.
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