منابع مشابه
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...
متن کاملFinding Optimal Addition Chains Using a Genetic Algorithm Approach
Since most public key cryptosystem primitives require the computation of modular exponentiation as their main building block, the problem of performing modular exponentiation efficiently has received considerable attention over the years. It is known that optimal (shortest) addition chains are the key mathematical concept for accomplishing modular exponentiations optimally. However, finding an ...
متن کاملOn 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...
متن کاملDifferential addition chains
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: Computing
سال: 2010
ISSN: 0010-485X,1436-5057
DOI: 10.1007/s00607-010-0118-8