Results 11 to 20 of about 762,592 (290)
The Discrete Logarithm Problem [PDF]
, 2016 For large prime numbers p, computing discrete logarithms of elements of the multiplicative group (Z∕pZ)∗ is at present a very difficult problem. The security of certain cryptosystems is based on the difficulty of this computation. In this expository paper we discuss several generalizations of the discrete logarithm problem and we describe various ...
René Schoof +3 more
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Computing Small Discrete Logarithms Faster [PDF]
, 2012 Computations of small discrete logarithms are feasible even in "secure" groups, and are used as subroutines in several cryptographic protocols in the literature. For example, the Boneh–Goh–Nissim degree-2-homomorphic public-key encryption system uses generic square-root discrete-logarithm methods for decryption.
Bernstein, D.J., Lange, T.
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On Search Complexity of Discrete Logarithm [PDF]
CoRR, 2021 In this work, we study the discrete logarithm problem in the context of TFNP - the complexity class of search problems with a syntactically guaranteed existence of a solution for all instances. Our main results establish that suitable variants of the discrete logarithm problem are complete for the complexity class PPP, respectively PWPP, i.e., the ...
Pavel Hubácek, Jan Václavek
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Trace zero varieties in cryptography : optimal representation and index calculus [PDF]
, 2014 The trace zero variety associated to an elliptic or hyperelliptic curve is an abelian variety defined over a finite field F_q. Its F_q-rational points yield a finite group, the trace zero subgroup of the degree zero Picard group of the original curve ...
Massierer, Maike
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Variational Quantum Algorithm for Solving Discrete Logarithms [PDF]
Jisuanji kexueThe discrete logarithm problem is a significant challenge in number theory,and due to the difficulty of solving it,classical computers lack efficient algorithms for this task.As a result,the discrete logarithm problem is widely used in public key ...
ZHANG Xinglan, RONG Xiaojun
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Discrete Logarithm Variants of VSH [PDF]
, 2006 Recent attacks on standardised hash functions such as SHA1 have reawakened interest in design strategies based on techniques common in provable security. In presenting the VSH hash function, a design based on RSA-like modular exponentiation, the authors introduce VSH-DL, a design based on exponentiation in DLP-based groups. In this article we explore a
Lenstra, Arjen +2 more
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IEEE Transactions on Quantum Engineering, 2023 Presents corrections to the article “The Present and Future of Discrete Logarithm Problems on Noisy Quantum Computers”.
Yoshinori Aono +6 more
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Discrete logarithmic energy on the sphere [PDF]
Pacific Journal of Mathematics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dragnev, P. D. +2 more
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DLP in semigroups: Algorithms and lower bounds
Journal of Mathematical Cryptology, 2022 The discrete logarithm problem (DLP) in semigroups has attracted some interests and serves as the foundation of many cryptographic schemes. In this work, we study algorithms and lower bounds for DLP in semigroups.
Han Jiao, Zhuang Jincheng
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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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