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Asymmetric cipher protocol using conjugacy and discrete logarithm problem
Lietuvos Matematikos Rinkinys, 2009 The paper proposes asymmetric cipher protocol based on matrix field over some field F. The asymmetric cipher is based on two simultaneous problems: matrix conjugator search problem (MCSP) and matrix discrete logarithm problem (MDLP).
Andrius Raulynaitis +1 more
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On the Complexity of Hyperelliptic Discrete Logarithm Problem [PDF]
, 1991 We give a characterization for the intractability of hyperelliptic discrete logarithm problem from a viewpoint of computational complexity theory. It is shown that the language of which complexity is equivalent to that of the hyperelliptic discrete logarithm problem is in NP ∩ co-AM, and that especially for elliptic curves, the corresponding language ...
Hiroki Shizuya +2 more
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Implications of the Arithmetic Ratio of Prime Numbers for RSA Security
International Journal of Applied Mathematics and Computer Science, 2023 The most commonly used public key cryptographic algorithms are based on the difficulty in solving mathematical problems such as the integer factorization problem (IFP), the discrete logarithm problem (DLP) and the elliptic curve discrete logarithm ...
Ivanov Andrey, Stoianov Nikolai
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The discrete logarithm problem modulo one: cryptanalysing the Ariffin–Abu cryptosystem
Journal of Mathematical Cryptology, 2010 The paper provides a cryptanalysis of the AAβ-cryptosystem recently proposed by Ariffin and Abu. The scheme is in essence a key agreement scheme whose security is based on a discrete logarithm problem in the infinite (additive) group ℝ/ℤ (the reals ...
Blackburn Simon R.
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A new directed signature scheme on a general linear group over a group ring
Journal of Innovative Applied Mathematics and Computational Sciences, 2023 In this work, we propose a new directed digital signature scheme over a group ring whose security relies on the hardness of the discrete logarithm problem and the factorization search problem. This scheme is efficient as it requires very few operations
Sassia MAKHLOUF +2 more
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FHPKE based on multivariate discrete logarithm problem [PDF]
, 2017 Previously I proposed fully homomorphic public-key encryption (FHPKE) based on discrete logarithm problem which is vulnerable to quantum computer attacks. In this paper I propose FHPKE based on multivariate discrete logarithm assumption.
Masahiro Yagisawa
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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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On the discrete logarithm problem for plane curves [PDF]
Journal de théorie des nombres de Bordeaux, 2012 In this article the discrete logarithm problem in degree 0 class groups of curves over finite fields given by plane models is studied. It is proven that the discrete logarithm problem for non-hyperelliptic curves of genus 3 (given by plane models of degree 4) can be solved in an expected time of
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The discrete logarithm problem for exponents of bounded height [PDF]
LMS Journal of Computation and Mathematics, 2014 AbstractLet$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}G$be a cyclic group written multiplicatively (and represented in some concrete way).
Simon R. Blackburn, Sam Scott
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Discrete logarithm problem in cryptography
, 2023 V tem diplomskem delu obravnavamo problem diskretnega logaritma in napade na ta problem. Na začetku razložimo matematično ozadje, ki je potrebno za delovanje algoritmov.
Cajnkar, Nino
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