Addition chains, vector chains, and efficient computation
نویسندگان
چکیده
منابع مشابه
Efficient computation of addition-subtraction chains using generalized continued Fractions
The aim of this paper is to present a new way of computing short addition-subtraction chains using the generalized continued fractions where subtraction is allowed. We will recover the most used ways of getting addition-subtraction chains. This method is not always optimal but gives minimal chains that are easy to compute.
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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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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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Differential addition chains (also known as strong addition chains, Lucas chains, and Chebyshev chains) are addition chains in which every sum is already accompanied by a difference. Low-cost differential addition chains are used to efficiently exponentiate in groups where the operation a, b, a/b 7→ ab is fast: in particular, to perform x-coordinate scalar multiplication P 7→ mP on an elliptic ...
متن کاملFinding Shorter Addition/Subtraction-Chains
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: Discrete Mathematics
سال: 2021
ISSN: 0012-365X
DOI: 10.1016/j.disc.2020.112200