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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 d ..."
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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
On the discrete logarithm problem for plane curves
, 2010
"... 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 in degree 0 class groups of nonhyperelliptic curves of genus 3 (given by plane models of degree 4) can be solved in ..."
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Cited by 4 (2 self)
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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 in degree 0 class groups of nonhyperelliptic curves of genus 3 (given by plane models of degree 4) can be solved
ON THE DISCRETE LOGARITHM PROBLEM
, 2008
"... 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. ..."
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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.
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 6 (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
"... 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 difficulty ..."
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Cited by 19 (3 self)
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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 difficulty
The Discrete Logarithm Problem in GL(n, q)
"... 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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Cited by 7 (0 self)
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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.
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 117 (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
On partial lifting and the elliptic curve discrete logarithm problem
 PROCEEDING OF THE 15TH ANNUAL INTERNATIONAL SYMPOSIUM ON ALGORITHMS AND COMPUTATION, 342–351, LNCS 3341
"... It has been suggested that a major obstacle in finding an index calculus attack on the elliptic curve discrete logarithm problem lies in the difficulty of lifting points from elliptic curves over finite fields to global fields. We explore the possibility of circumventing the problem of explicitly ..."
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Cited by 1 (0 self)
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It has been suggested that a major obstacle in finding an index calculus attack on the elliptic curve discrete logarithm problem lies in the difficulty of lifting points from elliptic curves over finite fields to global fields. We explore the possibility of circumventing the problem of explicitly
On the discrete logarithm problem in elliptic curves II
 ACCEPTED FOR PUBLICATION AT COMPOSITIO MATHEMATICA
, 2010
"... We continue our study on the elliptic curve discrete logarithm problem over finite extension fields. We show, among other results, the following two results: For sequences of prime powers (qi)i∈N and natural numbers (ni)i∈N ni with ni − → ∞ and log(qi) 2 − → 0 for i − → ∞, the discrete logarithm pr ..."
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Cited by 27 (0 self)
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We continue our study on the elliptic curve discrete logarithm problem over finite extension fields. We show, among other results, the following two results: For sequences of prime powers (qi)i∈N and natural numbers (ni)i∈N ni with ni − → ∞ and log(qi) 2 − → 0 for i − → ∞, the discrete logarithm
Generalized Jacobian and Discrete Logarithm Problem on Elliptic Curves
"... Abstract. Let E be an elliptic curve over the finite field Fq, P a point in E(Fq) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logari ..."
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Abstract. Let E be an elliptic curve over the finite field Fq, P a point in E(Fq) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete
Results 1  10
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31,747