Calculating optimal addition chains

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An Efficient Algorithm for Optimal Addition Chains

The computational aspects of finding the shortest addition chains for an integer are investigated in this work. Theoretically developed lower and upper bounds for the minimal length of the addition chains for an integer are exploited to construct a subtle pruning function for backtracking algorithm. These techniques are finally combined to build an efficient algorithm for finding the optimal ad...

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On Generalized Addition Chains

Given integers d 1, and g 2, a g-addition chain for d is a sequence of integers a0 = 1, a1, a2, . . . , ar 1, ar = d where ai = aj1 +aj2 + · · ·+ajk , with 2  k  g, and 0  j1  j2  · · ·  jk  i 1. The length of a g-addition chain is r, the number of terms following 1 in the sequence. We denote by lg(d) the length of a shortest addition chain for d. Many results have been established in th...

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Small Finding a shorter addition/subtraction-chain for an integer is an important problem for many cryptographic systems based on number theory. Especially, execution time of multiplication on an elliptic curve cryptosystem is directly proportional to the length of the addition/subtraction-chain. In this paper, we propose an algorithm to find an addition/subtractionchain. The proposed algorithm...

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ژورنال

عنوان ژورنال: Computing

سال: 2010

ISSN: 0010-485X,1436-5057

DOI: 10.1007/s00607-010-0118-8