Results 1 to 10 of about 8,170 (257)
The discrete logarithm problem in Bergman's non-representable ring [PDF]
Journal of Mathematical Cryptology, 2012 Bergman's ring , parameterized by a prime number p, is a ring with p5 elements that cannot be embedded in a ring of matrices over any commutative ring. This ring was discovered in 1974.
Banin Matan, Tsaban Boaz
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Discrete logarithm problem in matrix
Lietuvos Matematikos Rinkinys, 2023 In this paper the discrete logarithm problem in matrix in finite fields is formulated, possible ways of solution are given.
Povilas Tvarijonas +2 more
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Quasi-subfield Polynomials and the Elliptic Curve Discrete Logarithm Problem
Journal of Mathematical Cryptology, 2020 We initiate the study of a new class of polynomials which we call quasi-subfield polynomials. First, we show that this class of polynomials could lead to more efficient attacks for the elliptic curve discrete logarithm problem via the index calculus ...
Huang Ming-Deh +4 more
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A deterministic algorithm for the discrete logarithm problem in a semigroup
Journal of Mathematical Cryptology, 2022 The discrete logarithm problem (DLP) in a finite group is the basis for many protocols in cryptography. The best general algorithms which solve this problem have a time complexity of O(NlogN)O\left(\sqrt{N}\log N) and a space complexity of O(N)O\left ...
Tinani Simran, Rosenthal Joachim
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On the Discrete Logarithm Problem on Algebraic Tori [PDF]
Lecture Notes in Computer Science, 2005 Using a recent idea of Gaudry and exploiting rational representations of algebraic tori, we present an index calculus type algorithm for solving the discrete logarithm problem that works directly in these groups. Using a prototype implementation, we obtain practical upper bounds for the difficulty of solving the DLP in the tori $T_2(\mathbb{F}_{p^m ...
Robert Granger, Frederik Vercauteren
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A new method for solving the elliptic curve discrete logarithm problem [PDF]
Groups, Complexity, Cryptology, 2021 The elliptic curve discrete logarithm problem is considered a secure cryptographic primitive. The purpose of this paper is to propose a paradigm shift in attacking the elliptic curve discrete logarithm problem.
Ansari Abdullah +2 more
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Index-calculus algorithm for calculating the discrete logarithms based on index tables
Trudy Odesskogo Politehničeskogo Universiteta, 2014 The complexity of the discrete logarithm problem is the basis of many asymmetric encryption algorithms cryptographic sta-bility, such as the widely used cryptographic algorithm RSA.
Артем Вікторович Соколов +1 more
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On the Discrete Logarithmic Minkowski Problem [PDF]
International Mathematics Research Notices, 2015 If \(K\subset{\mathbb R}^n\) is a convex body (compact and convex set with non-empty interior) containing the origin as an interior point, the cone-volume measure of \(K\) is the Borel measure on the unit sphere \(S^{n-1}\) defined by \[ V_K(\omega)=\frac{1}{n}\int_{x\in\nu_K^{-1}(\omega)}x\cdot\nu_K(x)d\mathcal{H}^{n-1}(x), \quad \text{for each Borel }
Böröczky, Károly (Ifj.) +2 more
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The review on elliptic curves as cryptographic pairing groups [PDF]
Mathematics and Computational Sciences, 2021 Elliptic curve is a set of two variable points on polynomials of degree 3 over a field acted by an addition operation that forms a group structure. The motivation of this study is the mathematics behind that elliptic curve to the applicability within a ...
E Khamseh
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On the Distributed Discrete Logarithm Problem with Preprocessing.
IACR Cryptol. ePrint Arch., 2022 Protocols solving the Distributed Discrete Logarithm (DDLog) problem are a core component of many recent constructions of group-based homomorphic secret sharing schemes. On a high-level, these protocols enable two parties to transform multiplicative shares of a secret into additive share locally without any communication.
Pavel Hubácek +2 more
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