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Quantum algorithms for computing general discrete logarithms and orders with tradeoffs
Journal of Mathematical Cryptology, 2021 We generalize our earlier works on computing short discrete logarithms with tradeoffs, and bridge them with Seifert's work on computing orders with tradeoffs, and with Shor's groundbreaking works on computing orders and general discrete logarithms.
Martin Ekerå
exaly +2 more sources
Resource analysis and modifications of quantum computing with noisy qubits for elliptic curve discrete logarithms [PDF]
Scientific ReportsWe estimate the number of physical qubits and execution time by decomposing an implementation of Shor’s algorithm for elliptic curve discrete logarithms into universal gate units at the logical level when surface codes are used.
Jinyoung Ha, Jonghyun Lee, Jun Heo
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Application of Partial Discrete Logarithms for Discrete Logarithm Computation
ComputersA novel approach to constructing an algorithm for computing discrete logarithms, which holds significant interest for advancing cryptographic methods and the applied use of multivalued logic, is proposed.
Dina Shaltykova +3 more
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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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Mapping the discrete logarithm [PDF]
Involve, a Journal of Mathematics, 2010 The discrete logarithm is a problem that surfaces frequently in the field of cryptography as a result of using the transformation g^a mod n. This paper focuses on a prime modulus, p, for which it is shown that the basic structure of the functional graph is largely dependent on an interaction between g and p-1.
Holden, Joshua, Cloutier, D.
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Dlog is Practically as Hard (or Easy) as DH – Solving Dlogs via DH Oracles on EC Standards
Transactions on Cryptographic Hardware and Embedded Systems, 2023 Assume that we have a group G of known order q, in which we want to solve discrete logarithms (dlogs). In 1994, Maurer showed how to compute dlogs in G in poly time given a Diffie-Hellman (DH) oracle in G, and an auxiliary elliptic curve ˆÊ (Fq) of ...
Alexander May +1 more
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Computing discrete logarithms in an interval [PDF]
Mathematics of Computation, 2012 The discrete logarithm problem in an interval of size N N in a group
Steven D. Galbraith +2 more
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A Secure and Efficient Image Transmission Scheme Based on Two Chaotic Maps
Complexity, 2021 The application of multimedia sensors is widespread, and people need to transmit images more securely and efficiently. In this paper, an image transmission scheme based on two chaotic maps is proposed.
Wei Feng, Jing Zhang, Zhentao Qin
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An Axiomatic Characterization of Mutual Information
Entropy, 2023 We characterize mutual information as the unique map on ordered pairs of discrete random variables satisfying a set of axioms similar to those of Faddeev’s characterization of the Shannon entropy.
James Fullwood
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Solution to the Problem of Calculating Discrete Logarithms [PDF]
Military Technology and ScienceIn this paper we present two algorithms for computing discrete logarithms. We also introduce theorems that facilitate computing discrete logarithms and show how we break the Diffie-Hellman protocol, which is considered to be very secure.
Łukasz Matysiak
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