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The Discrete Logarithm Problem
"... 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 ..."
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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
Integer factorization and discrete logarithm problems
, 2014
"... Pierrick Gaudry. Integer factorization and discrete logarithm problems. Notes d’un cours donné ..."
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Pierrick Gaudry. Integer factorization and discrete logarithm problems. Notes d’un cours donné
Index Term — Discrete logarithm problem
"... Abstract — Huhnlein et al showed that for totally nonaximal imaginary quadratic orders, the discrete logarithm problem can be reduced to the discrete logarithm problem in some finite fields. In previous work we showed that for twisted anomalous elliptic curves, the logarithm problem can also be re ..."
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Abstract — Huhnlein et al showed that for totally nonaximal imaginary quadratic orders, the discrete logarithm problem can be reduced to the discrete logarithm problem in some finite fields. In previous work we showed that for twisted anomalous elliptic curves, the logarithm problem can also
ON THE DISCRETE LOGARITHM PROBLEM
, 811
"... Abstract. Let p> 2 be prime and g a primitive root modulo p. We present an argument for the fact that discrete logarithms of the numbers in any arithmetic progression are uniformly distributed in [1, p] and raise some questions on the subject. 1. ..."
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Abstract. Let p> 2 be prime and g a primitive root modulo p. We present an argument for the fact that discrete logarithms of the numbers in any arithmetic progression are uniformly distributed in [1, p] and raise some questions on the subject. 1.
Signature calculus and discrete logarithm problems
 In Proc. ANTS VII, LNCS 4076
, 2006
"... This is the third in a series of papers in which we develop a unified method for treating the discrete logarithm problem (DLP) in various contexts. In [HR1], we described a formalism using global duality for a unified approach to the DLP for the multiplicative group and for elliptic ..."
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Cited by 5 (1 self)
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This is the third in a series of papers in which we develop a unified method for treating the discrete logarithm problem (DLP) in various contexts. In [HR1], we described a formalism using global duality for a unified approach to the DLP for the multiplicative group and for elliptic
On the Discrete Logarithm Problem on Algebraic Tori
 In Advances in Cryptology (CRYPTO 2005), Springer LNCS 3621, 66–85
, 2005
"... Abstract. Using a recent idea of Gaudry and exploiting rational representations of algebraic tori, we present an index calculus type algorithm for solving the discrete logarithm problem that works directly in these groups. Using a prototype implementation, we obtain practical upper bounds for the di ..."
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Cited by 20 (3 self)
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Abstract. Using a recent idea of Gaudry and exploiting rational representations of algebraic tori, we present an index calculus type algorithm for solving the discrete logarithm problem that works directly in these groups. Using a prototype implementation, we obtain practical upper bounds
The Discrete Logarithm Problem in GL(n; q)
"... Abstract This paper presents a probabilistic polynomialtime reduction of the discrete logarithm problem in the general linear group GL(n; q) to the discrete logarithm problem in some small extension fields of Fq. ..."
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Abstract This paper presents a probabilistic polynomialtime reduction of the discrete logarithm problem in the general linear group GL(n; q) to the discrete logarithm problem in some small extension fields of Fq.
Discrete Logarithm Problem Assumption in PDAs?)
"... Personal Digital Assistants (PDAs) are the miniature of normal size PCs, with a very limited computational power. In this paper, we investigate the security of PDAs when they are used to perform some cryptographic applications. In our context, we investigate the computation y = g ' (mod p), for ..."
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), for a prime p, which is believed to be secure in the sense of the Discrete Logarithm Problem (DLP) assumption. To be more precise, knowing only p, g and y, it is hard to derive x. We note that this computation is the most important operation in most cryptographic algorithms. However, due to the limited
The Discrete Logarithm Problem On Elliptic Curves Of Trace One
 Journal of Cryptology
, 1999
"... In this short note we describe an elementary technique which leads to a linear algorithm for solving the discrete logarithm problem on elliptic curves of trace one. In practice the method described means that when choosing elliptic curves to use in cryptography one has to eliminate all curves who ..."
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Cited by 114 (2 self)
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In this short note we describe an elementary technique which leads to a linear algorithm for solving the discrete logarithm problem on elliptic curves of trace one. In practice the method described means that when choosing elliptic curves to use in cryptography one has to eliminate all curves
Results 1  10
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1,341,105