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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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The Discrete-Logarithm Problem with Preprocessing
2018This paper studies discrete-log algorithms that use preprocessing. In our model, an adversary may use a very large amount of precomputation to produce an “advice” string about a specific group (e.g., NIST P-256). In a subsequent online phase, the adversary’s task is to use the preprocessed advice to quickly compute discrete logarithms in the group ...
Henry Corrigan-Gibbs, Dmitry Kogan
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Discrete Logarithm Problems with Auxiliary Inputs
Journal of Cryptology, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The discrete logarithmic Minkowski problem for q-capacity
Journal of Mathematical Analysis and Applications, 2022For a compact set \(K\) in the \(n\)-dimensional Euclidean space \(\mathbb{R}^n\) and for \(1 < q < n\), the electrostatic \(q\)-capacity \(C_q(K)\) of \(K\) is defined as the quantity \[ C_q(K) = \inf \left\{ \int_{\mathbb{R}^n} |\nabla u|^{q} dx : u \in C_c^{\infty}(\mathbb{R}^n) \hbox{ and } u \geq \chi_K \right\} \] where \(C_c^{\infty}(\mathbb{R ...
Wei Wang, Rigao He
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An Improved Algorithm for Discrete Logarithm Problem
2009 International Conference on Environmental Science and Information Application Technology, 2009The difficulty in solving the discrete logarithm problem (DLP) is very important to the cryptography since it is widely used in signature schemes, message encryption, authentication, and so on. The baby-step giant-step algorithm is a series of well-defined steps to compute the discrete logarithm, but its gigantic storage cost is an obvious disadvantage.
Jun Zhang, LiQun Chen
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Signature Calculus and Discrete Logarithm Problems
2006Index calculus has been successful in many cases for treating the discrete logarithm problem for the multiplicative group of a finite field, but less so for elliptic curves over a finite field. In this paper we seek to explain why this might be the case from the perspective of arithmetic duality and propose a unified method for treating both problems ...
Ming-Deh A. Huang, Wayne Raskind
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MapReduce for Elliptic Curve Discrete Logarithm Problem
2016 IEEE World Congress on Services (SERVICES), 2016Elliptic curve based cryptography has attracted a lot of attention because these schemes usually require less storage than those based on finite field. It is also used to construct bilinear pairing, which is an essential tool to construct various cryptography schemes.
Zhimin Gao +2 more
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The Discrete Logarithm Problem
1999The public key cryptosystems presented in Chapter 1 rely on the difficulty of solving the discrete logarithm problem in certain groups: An adversary who could efficiently compute discrete logarithms in the group underlying such a cryptosystem would be able to break the system. So to judge the security of the proposed cryptosystems we must have a closer
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Local Duality and the Discrete Logarithm Problem
2011It is shown that the computational complexity of Tate local duality is closely related to that of the discrete logarithm problem over finite fields. Local duality in the multiplicative case and the case of Jacobians of curves over p-adic local fields are considered.
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On the Semidirect Discrete Logarithm Problem in Finite Groups
We present an efficient quantum algorithm for solving the semidirect discrete logarithm problem (SDLP) in any finite group. The believed hardness of the semidirect discrete logarithm problem underlies more than a decade of works constructing candidate post-quantum cryptographic algorithms from non-abelian groups. We use a series of reductionChristopher Battarbee +12 more
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