Pollard’s Rho Algorithm for Elliptic Curves
نویسنده
چکیده
Elliptic curve cryptographic protocols often make use of the inherent hardness of the discrete logarithm problem, which is to solve kG = P for k. There is an abundance of evidence suggesting that elliptic curve cryptography is more secure than the classical case. One reason for this is the best known general-purpose algorithm to solve the elliptic curve discrete logarithm problem is Pollard’s Rho algorithm, which has exponential time complexity O( √ n), where n is the order of the elliptic curve. In this paper, we explore Pollard’s Rho algorithm. In particular, we show that it only requires O(1) space complexity. This is an astronomical improvement over the related Baby-Step Giant-Step algorithm, which requires O( √ n) time and space complexity. We also investigate different methods of defining the sequence of points used in Pollard’s Rho algorithm and discuss their effects on efficiency.
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New Collisions to Improve Pollardâs Rho Method of Solving the Discrete Logarithm Problem on Elliptic Curves
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