Results 31 to 40 of about 1,067,462 (345)
Quasi-subfield Polynomials and the Elliptic Curve Discrete Logarithm Problem
Journal of Mathematical Cryptology, 2020 We initiate the study of a new class of polynomials which we call quasi-subfield polynomials. First, we show that this class of polynomials could lead to more efficient attacks for the elliptic curve discrete logarithm problem via the index calculus ...
Huang Ming-Deh +4 more
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, 2017 The Discrete Logarithm Problem (DLP) is one of the most used mathematical problems in asymmetric cryptography design, the other one being the integer factorization. It is intrinsically related to the Diffie-Hellman problem (DHP). DLP can be stated in various groups. It must be hard in well-chosen groups, so that secure-enough cryptosystems can be built.
Guillevic, Aurore, Morain, François
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On the discrete logarithm problem in finite fields of fixed characteristic [PDF]
IACR Cryptology ePrint Archive, 2015 For $q$ a prime power, the discrete logarithm problem (DLP) in $\mathbb{F}_{q}$ consists in finding, for any $g \in \mathbb{F}_{q}^{\times}$ and $h \in \langle g \rangle$, an integer $x$ such that $g^x = h$. We present an algorithm for computing discrete
R. Granger, T. Kleinjung, J. Zumbrägel
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Cryptanalysis of a Proposal Based on the Discrete Logarithm Problem Inside Sn
Cryptography, 2018 In 2008, Doliskani et al. proposed an ElGamal-style encryption scheme using the symmetric group Sn as mathematical platform. In 2012, an improvement of the cryptosystem’s memory requirements was suggested by Othman. The proposal by Doliskani et al.
María Isabel González Vasco +2 more
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Finite Non-Commutative Associative Algebras as Carriers of Hidden Discrete Logarithm Problem
Bulletin of the South Ural State University Series Mathematical Modelling Programming and Computer Software, 2019 The article introduces new finite algebras attractive as carriers of the discrete logarithm problem in a hidden group. In particular new 4-dimensional and 6-dimensional finite non-commutative algebras with associative multiplication operation and their ...
N. A. Moldovyan, A. Moldovyan
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Picard Groups and Refined Discrete Logarithms [PDF]
LMS Journal of Computation and Mathematics, 2005 AbstractLet K denote a number field, and G a finite abelian group. The ring of algebraic integers in K is denoted in this paper by $/cal{O}_K$, and $/cal{A}$ denotes any $/cal{O}_K$-order in K[G]. The paper describes an algorithm that explicitly computes the Picard group Pic($/cal{A}$), and solves the corresponding (refined) discrete logarithm problem.
Bley, Werner, Endres, Markus
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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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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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Discrete Logarithm Based Protocols [PDF]
, 2007 The Exponential Security System (TESS) developed at the European Institute for System Security is the result of an attempt to increase the security in heterogenous computer networks. In this paper we present the cryptographic protocols in the kernel of TESS.
Horster, Patrick, Knobloch, Hans-Joachim
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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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