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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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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 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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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 Huang, Wayne Raskind
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A discrete logarithm problem over composite modulus
Electronics and Communications in Japan (Part III: Fundamental Electronic Science), 1993AbstractRecently, many applications of integer theory to cryptographic techniques have been observed. The discrete logarithm problem is one such case. Usually, the discrete logarithm problem is the determination of the logarithm for the given arbitrary element with a prime number as the modulus.
Yasuyuki Murakami, Masao Kasahara
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Quantum algorithms for the discrete logarithm problem
2021Shor s Algorithmen f r die Primfaktorzerlegung und f r das Problem des diskreten Logarithmus z hlen zu den bahnbrechendsten Entwicklungen im Bereich der Quanteninformatik. Sie l sen Probleme in polynomieller Zeit mithilfe eines Quantencomputers, f r welche keine effizienten klassischen Algorithmen bekannt sind.
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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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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, Lei Xu, Weidong Shi
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