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MODIFICATION OF POLLARD RHO ALGORITHM USING NEGATION MAPPING
Barekeng, 2022 El Gamal encryption was introduced in 1985 and is still commonly used today. Its hardness is based on a discrete logarithm problem defined over the finite abelian cyclic group group chosen in the original paper was but later it was proven that using the
Sa'aadah Sajjana Carita, Herman Kabetta
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The formal solutions of Diophantine equation agy = bx + c
HeliyonWe develop a novel method to completely solve the 3-term partial exponential Diophantine equation that represents a generalization of the standard discrete logarithm problem.
Xiazhou Yang
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Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms
Journal of Mathematical Cryptology, 2014 We prove collision bounds for the Pollard rho algorithm to solve the discrete logarithm problem in a general cyclic group 𝐆$\mathbf {G}$. Unlike the setting studied by Kim et al., we consider additive walks: the setting used in practice to solve the ...
Bos Joppe W. +2 more
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An ECDLP-Based Verifiable Multi-Secret Sharing Scheme [PDF]
Mathematics Interdisciplinary Research, 2020 Secret sharing is an important issue in cryptography which has many applications. In a secret sharing scheme, a secret is shared by a dealer among several participants in such a way that any authorized subset of participants can recover the secret ...
Khadijeh Eslami, Mojtaba Bahramian
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Journal of Telecommunications and Information TechnologyThis paper investigates how to reduce the elliptic curve discrete logarithm problem over prime fields to the quadratic unconstrained binary optimization (QUBO) problem in order to obtain as few logical qubits as possible. In the best case scenario, if n
Michał Wroński +3 more
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Finite fields and cryptology [PDF]
Computer Science Journal of Moldova, 2003 The problem of a computationally feasible method of finding the discrete logarithm in a (large) finite field is discussed, presenting the main algorithms in this direction.
Ennio Cortellini
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Publicly-Verifiable Proofs of Storage Based on the Discrete Logarithm Problem
IEEE Access, 2019 With the rapid development of cloud computing platforms, cloud storage services are becoming widespread in recent years. Based on these services, clients are able to store data on remote cloud servers and thereby saving their local storage.
Miaomiao Tian +5 more
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Cryptanalysis of the cryptosystems based on the generalized hidden discrete logarithm problem [PDF]
Computer Science Journal of MoldovaIn this paper, we will solve an important form of hidden discrete logarithm problem (HDLP) and a generalized form of HDLP (GHDLP) over non-commutative associative algebras (FNAAs). We will reduce them to discrete logarithm problem (DLP) in a finite field
Yanlong Ma
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Fusion Discrete Logarithm Problems
, 2010 The Discrete Logarithm Problem is well-known among cryptographers, for its computational hardness that grants security to some of the most commonly used cryptosystems these days. Still, many of these are limited to a small number of candidate algebraic structures which permit implementing the algorithms. In order to extend the applicability of discrete-
Schaffer, Martin, Rass, Stefan
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Cryptanalysing the critical group: efficiently solving Biggs's discrete logarithm problem
Journal of Mathematical Cryptology, 2009 Biggs has recently proposed the critical group of a certain class of finite graphs as a platform group for cryptosystems relying on the difficulty of the discrete log problem. The paper uses techniques from the theory of Picard groups on finite graphs to
Blackburn Simon R.
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