Results 1  10
of
169,552
Algorithms for Quantum Computation: Discrete Logarithms and Factoring
, 1994
"... A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a cost in computation time of at most a polynomial factol: It is not clear whether this is still true when quantum mechanics is taken into consider ..."
Abstract

Cited by 1095 (5 self)
 Add to MetaCart
into consideration. Several researchers, starting with David Deutsch, have developed models for quantum mechanical computers and have investigated their computational properties. This paper gives Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number
A public key cryptosystem and a signature scheme based on discrete logarithms
 ADV. IN CRYPTOLOGY, SPRINGERVERLAG
, 1985
"... A new signature scheme is proposed, together with an implementation of the DiffieHellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields. ..."
Abstract

Cited by 1513 (0 self)
 Add to MetaCart
A new signature scheme is proposed, together with an implementation of the DiffieHellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields.
PolynomialTime Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
 SIAM J. on Computing
, 1997
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
Abstract

Cited by 1263 (4 self)
 Add to MetaCart
. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical
Discrete logarithms in free groups
, 2005
"... For the free group on n generators we prove that the discrete logarithm is distributed according to the standard Gaussian when the logarithm is renormalized appropriately. ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
For the free group on n generators we prove that the discrete logarithm is distributed according to the standard Gaussian when the logarithm is renormalized appropriately.
Algebraic Groups and Discrete Logarithm
 IN PUBLICKEY CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY
, 2001
"... We prove two theorems and raise a few questions concerning discrete logarithms and algebraic groups. ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
We prove two theorems and raise a few questions concerning discrete logarithms and algebraic groups.
Kangaroos, Monopoly and Discrete Logarithms
, 2000
"... The kangaroo method computes a discrete logarithm in an arbitrary cyclic group, given that the value is known to lie in a certain interval. A parallel version has been given by van Oorschot and Wiener with “linear speedup”. We improve the analysis of the running time, both for serial and parallel ..."
Abstract

Cited by 53 (1 self)
 Add to MetaCart
The kangaroo method computes a discrete logarithm in an arbitrary cyclic group, given that the value is known to lie in a certain interval. A parallel version has been given by van Oorschot and Wiener with “linear speedup”. We improve the analysis of the running time, both for serial
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 ..."
Abstract
 Add to MetaCart
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
Lower Bounds for Discrete Logarithms and Related Problems
, 1997
"... . This paper considers the computational complexity of the discrete logarithm and related problems in the context of "generic algorithms"that is, algorithms which do not exploit any special properties of the encodings of group elements, other than the property that each group element is ..."
Abstract

Cited by 280 (11 self)
 Add to MetaCart
. This paper considers the computational complexity of the discrete logarithm and related problems in the context of "generic algorithms"that is, algorithms which do not exploit any special properties of the encodings of group elements, other than the property that each group element
Discrete Logarithms in Finite Fields
, 1996
"... Given a finite field F q of order q, and g a primitive element of F q , the discrete logarithm base g of an arbitrary, nonzero y 2 F q is that integer x, 0 x q \Gamma 2, such that g x = y in F q . The security of many realworld cryptographic schemes depends on the difficulty of computing discr ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Given a finite field F q of order q, and g a primitive element of F q , the discrete logarithm base g of an arbitrary, nonzero y 2 F q is that integer x, 0 x q \Gamma 2, such that g x = y in F q . The security of many realworld cryptographic schemes depends on the difficulty of computing
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. ..."
Abstract
 Add to MetaCart
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.
Results 1  10
of
169,552