The sliding window method is a general purpose algorithm to determine the exponentiation g**e in a general group. Let s_(nk) (e) and m_(nk) (e) denote, respectively, the number of squarings and multiplications required by the sliding window method when g**e is computed using k-bit windows, and e is a uniformly distributed n-bit exponent. In this paper we prove that E[ s_(nk) (e) ] = n - k +O(1) and E[ m_(nk) (e) ] = 2**k-1 + n/(k+1) +O(1), and further that both distributions are concentrated around their respective means.
By: L. O'Connor
Published in: RZ3162 in 1999
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