Results 1  10
of
189,700
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 increase in computation time of at most a polynomial factor. It is not clear whether this is still true when quantum mechanics is taken into consi ..."
Abstract

Cited by 1103 (7 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
"... AbstractA 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. I. ..."
Abstract

Cited by 1520 (0 self)
 Add to MetaCart
AbstractA 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. I.
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 1268 (5 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
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
 Add to MetaCart
We prove two theorems and raise a few questions concerning discrete logarithms and algebraic groups.
Discrete logarithms in free groups
"... Abstract. 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. 1. ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
Abstract. 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. 1.
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 279 (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
Discrete Logarithms: Recent Progress
 Proc. International Conference on Coding Theory, Cryptography and Related Areas
, 1998
"... We summarize recent developments on the computation of discrete logarithms in general groups as well as in some specialized settings. More specifically, we consider the following abelian groups: the multiplicative group of finite fields, the group of points of an elliptic curve over a finite field, ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We summarize recent developments on the computation of discrete logarithms in general groups as well as in some specialized settings. More specifically, we consider the following abelian groups: the multiplicative group of finite fields, the group of points of an elliptic curve over a finite field
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
189,700