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www.elsevier.com/locate/jalgor A modular integer GCD algorithm ✩
, 1999
"... This paper describes the first algorithm to compute the greatest common divisor (GCD) of two nbit integers using a modular representation for intermediate values U, V and also for the result. It is based on a reduction step, similar to one used in the accelerated algorithm [T. Jebelean, A gener ..."
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This paper describes the first algorithm to compute the greatest common divisor (GCD) of two nbit integers using a modular representation for intermediate values U, V and also for the result. It is based on a reduction step, similar to one used in the accelerated algorithm [T. Jebelean, A gener
Nbit unsigned division via nbit multiplyadd
 in 17th IEEE Symposium on Computer Arithmetic
, 2005
"... Integer division on modern processors is expensive compared to multiplication. Previous algorithms for performing unsigned division by an invariant divisor, via reciprocal approximation, suffer in the worst case from a common requirement for n+1 bit multiplication, which typically must be synthesize ..."
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Cited by 6 (0 self)
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Integer division on modern processors is expensive compared to multiplication. Previous algorithms for performing unsigned division by an invariant divisor, via reciprocal approximation, suffer in the worst case from a common requirement for n+1 bit multiplication, which typically must
Simulating Physics with Computers
 SIAM Journal on Computing
, 1982
"... 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 of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 601 (1 self)
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. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum
A Digital Signature Scheme Secure Against Adaptive ChosenMessage Attacks
, 1995
"... We present a digital signature scheme based on the computational diculty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosenmessage attack: an adversary who receives signatures for messages of his choice (where each message may be chosen in a ..."
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Cited by 985 (43 self)
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We present a digital signature scheme based on the computational diculty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosenmessage attack: an adversary who receives signatures for messages of his choice (where each message may be chosen
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 ..."
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Cited by 1103 (7 self)
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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
Even faster integer multiplication
, 2015
"... We give a new proof of Fürer’s bound for the cost of multiplying nbit integers in the bit complexity model. Unlike Fürer, our method does not require constructing special coefficient rings with “fast” roots of unity. Moreover, we establish the improved boundO(n lognKlog n) with K = 8. We show that ..."
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We give a new proof of Fürer’s bound for the cost of multiplying nbit integers in the bit complexity model. Unlike Fürer, our method does not require constructing special coefficient rings with “fast” roots of unity. Moreover, we establish the improved boundO(n lognKlog n) with K = 8. We show
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity also carrying over in a similar fashion. Finally we study the significance of these results in a variety of combinatorial optimization problems including the general 01 integer programs, the maximum clique
Efficient Integer Multiplication Overflow Detection Circuits
"... Multiplication of two nbit integers produces a 2nbit product. To allow the result to be stored in the same format as the inputs, many processors return the n least significant bits of the product and an overflow flag. This paper describes methods for integer multiplication with overflow detection ..."
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Cited by 2 (1 self)
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Multiplication of two nbit integers produces a 2nbit product. To allow the result to be stored in the same format as the inputs, many processors return the n least significant bits of the product and an overflow flag. This paper describes methods for integer multiplication with overflow detection
The JPEG still picture compression standard
 Communications of the ACM
, 1991
"... This paper is a revised version of an article by the same title and author which appeared in the April 1991 issue of Communications of the ACM. For the past few years, a joint ISO/CCITT committee known as JPEG (Joint Photographic Experts Group) has been working to establish the first international c ..."
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Cited by 1128 (0 self)
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This paper is a revised version of an article by the same title and author which appeared in the April 1991 issue of Communications of the ACM. For the past few years, a joint ISO/CCITT committee known as JPEG (Joint Photographic Experts Group) has been working to establish the first international compression standard for continuoustone still images, both grayscale and color. JPEG’s proposed standard aims to be generic, to support a wide variety of applications for continuoustone images. To meet the differing needs of many applications, the JPEG standard includes two basic compression methods, each with various modes of operation. A DCTbased method is specified for “lossy’ ’ compression, and a predictive method for “lossless’ ’ compression. JPEG features a simple lossy technique known as the Baseline method, a subset of the other DCTbased modes of operation. The Baseline method has been by far the most widely implemented JPEG method to date, and is sufficient in its own right for a large number of applications. This article provides an overview of the JPEG standard, and focuses in detail on the Baseline method. 1
A Fast Quantum Mechanical Algorithm for Database Search
 ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1996
"... Imagine a phone directory containing N names arranged in completely random order. In order to find someone's phone number with a probability of , any classical algorithm (whether deterministic or probabilistic)
will need to look at a minimum of names. Quantum mechanical systems can be in a supe ..."
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Cited by 1126 (10 self)
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Imagine a phone directory containing N names arranged in completely random order. In order to find someone's phone number with a probability of , any classical algorithm (whether deterministic or probabilistic)
will need to look at a minimum of names. Quantum mechanical systems can be in a
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