Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms
نویسندگان
چکیده
منابع مشابه
Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms
We prove collision bounds for the Pollard rho algorithm to solve the discrete logarithm problem in a general cyclic group G. Unlike the setting studied by Kim et al., we consider additive walks: the setting used in practice to solve the elliptic curve discrete logarithm problem. Our bounds differ from the birthday bound O. p jGj/ by a factor of p log jGj and are based on mixing time estimates f...
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15 صفحه اولA Birthday Paradox for Markov Chains, with an Optimal Bound for Collision in the Pollard Rho Algorithm for Discrete Logarithm
We show a Birthday Paradox for self-intersections of Markov chains with uniform stationary distribution. As an application, we analyze Pollard’s Rho algorithm for finding the discrete logarithm in a cyclic group G and find that, if the partition in the algorithm is given by a random oracle, then with high probability a collision occurs in Θ( √ |G|) steps. Moreover, for the parallelized distingu...
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Pollard’s rho method and its parallelized variant are at present known as the best generic algorithms for computing discrete logarithms. However, when we compute discrete logarithms in cyclic groups of large orders using Pollard’s rho method, collision detection is always a high time and space consumer. In this paper, we present a new efficient collision detection algorithm for Pollard’s rho me...
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Pollard’s rho method is a randomized algorithm for computing discrete logarithms. It works by defining a pseudo-random sequence and then detecting a match in the sequence. Many improvements have been proposed, while few evaluation results and efficiency suggestions have been reported. This paper is devoted to a detailed study of the efficiency issues in Pollard’s rho method. We describe an empi...
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ژورنال
عنوان ژورنال: Journal of Mathematical Cryptology
سال: 2014
ISSN: 1862-2976,1862-2984
DOI: 10.1515/jmc-2012-0032