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Showing 1 to 7 of 7 for “"Discrete logarithm problem"”.
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Algorithms for Solving the Discrete Logarithm Problem
… often many procedures to solve or prove the same problem. The discrete logarithm is one of these problems. The baby step, giant step algorithm and Pollard's kangaroo algorithm are two algorithms that attempt to solve discrete logarithm problems. Explanations on what these two algorithms are will …
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The Elgamal Cryptosystem is better than Th RSA Cryptosystem for Mental Poker
… among the players and the debate between the discrete logarithm problem (DLP) and the factoring problem (FP) for the encryption/decryption schemes. Under these criteria, the comparison results demonstrate that the Elgamal Cryptosystem has better efficiency and effectiveness than RSA for mental …
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Cryptographic Pairings: Efficiency and DLP security
… considered, with a thorough examination of the Discrete Logarithm Problem (DLP) as it occurs in PBC. Results on the relationship between the two instances of the DLP will be presented along with a discussion about the appropriate selection of parameters to ensure particular security level. In …
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Pell Equation - Theory and applications to cryptography
… field, in which case new interesting open problems arise. This work focuses on studying the theoretical and practical potential of the Pell equation in this context. Firstly, the required theoretical results from the state of the art are collected using a new unique and simple notation. …
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Solving Algorithmic Problems in Finitely Presented Groups via Machine Learning
… have been successfully applied to algorithmic problems in free groups. In this dissertation, we seek to extend these techniques to finitely presented non-free groups, in particular to polycyclic and metabelian groups that are of interest to non-commutative cryptography.</p> <p>As a prototypical …
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Order computations in generic groups
We consider the problem of computing the order of an element in a generic group. The two standard algorithms, Pollard's rho method and Shanks' baby-steps giant-steps technique, both use [theta](N^1/2) group operations to compute abs([alpha])=N. A lower bound of [omega](N^1/2) has been conjectured. …
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Security systems based on Gaussian integers : Analysis of basic operations and time complexity of secret transformations
… integers become apparent when they are used with Discrete Logarithm Problem (DLP) based PK algorithms. In order to quantify the complexity of the Gaussian integer DLP, it is reduced to two other well known problems: DLP for Lucas sequences and the real integer DLP. Additionally, a novel …