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Large Integer Multiplication on Hypercubes
"... Previous work has reported on the use of polynomial transforms to compute exact convolution and to perform multiplication of large integers on a massively parallel processor. We now present results of an improved technique, using the Fermat Number Transform. When the Fermat Number Transform was firs ..."
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Cited by 2 (0 self)
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Previous work has reported on the use of polynomial transforms to compute exact convolution and to perform multiplication of large integers on a massively parallel processor. We now present results of an improved technique, using the Fermat Number Transform. When the Fermat Number Transform
More on squaring and multiplying large integers
 INRIA Rocquencourt : Domaine de Voluceau  Rocquencourt  BP 105  78153 Le Chesnay Cedex (France) Unité de recherche INRIA Sophia Antipolis : 2004, route des Lucioles  BP 93  06902 Sophia Antipolis Cedex (France) Éditeur INRIA  Domaine de Voluceau  R
, 1994
"... AbstractMethods of squaring and multiplying large integers are discussed. The obvious O(n”) methods turn out to be best for small numbers. Existing O(nIog 3/10g ”) N O(ni.6*5) methods become better as the numbers get bigger. New methods that O(n’Og 6/U 3) M O(n1.465), O(n’”g 7 /b 4) M O(n1.404), an ..."
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Cited by 25 (0 self)
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AbstractMethods of squaring and multiplying large integers are discussed. The obvious O(n”) methods turn out to be best for small numbers. Existing O(nIog 3/10g ”) N O(ni.6*5) methods become better as the numbers get bigger. New methods that O(n’Og 6/U 3) M O(n1.465), O(n’”g 7 /b 4) M O(n1
The Encyclopedia of Integer Sequences
"... This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs ..."
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Cited by 866 (15 self)
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This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae
An Overview of Factorization of Large Integers Using the GMP Library
"... Many security mechanisms rely on the fact, that factorizing large integers is a very difficult problem[1, 2, 3, 4] and it takes a lot of time to solve it. In this thesis, we analyzed algorithms for factorizing large integers. Our goal was to find optimizations which could improve their performance s ..."
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Many security mechanisms rely on the fact, that factorizing large integers is a very difficult problem[1, 2, 3, 4] and it takes a lot of time to solve it. In this thesis, we analyzed algorithms for factorizing large integers. Our goal was to find optimizations which could improve their performance
Kolmogorov Complexity Conditional to Large Integers
 Theoretical Computer Science
"... this paper the general notion of an algorithmic problem (see [7] for such discussion), as our paper is devoted to very specic problems. The plain Kolmogorov complexity, K(x), is the Kolmogorov complexity of the problem \print x". Likewise the conditional Kolmogorov complexity, dened as K(xjy) ..."
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Cited by 4 (2 self)
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this paper the general notion of an algorithmic problem (see [7] for such discussion), as our paper is devoted to very specic problems. The plain Kolmogorov complexity, K(x), is the Kolmogorov complexity of the problem \print x". Likewise the conditional Kolmogorov complexity, dened as K(xjy) = minfl(p) j p(y) = xg; is the complexity of the problem \given y print x"
Modular multiplication of large integers on fpga
 in Proceedings of the 39th Asilomar Conference on Signals, Systems & Computers. IEEE Signal Processing Society
, 2005
"... Abstract — Public key cryptography often involves modular multiplication of large operands (160 up to 2048 bits). Several researchers have proposed iterative algorithms whose internal data are carrysave numbers. This number system is unfortunately not well suited to today’s Field Programmable Gate ..."
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Cited by 2 (1 self)
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Abstract — Public key cryptography often involves modular multiplication of large operands (160 up to 2048 bits). Several researchers have proposed iterative algorithms whose internal data are carrysave numbers. This number system is unfortunately not well suited to today’s Field Programmable Gate
Large Integer Multiplication on Massively Parallel Processors
, 1990
"... We present results of a technique for multiplying large integers using the Fermat Number Transform. When the Fermat Number Transform was first proposed, word length constraints limited its effectiveness. Despite the development of multidimensional techniques to extend the length of the FNT, the rela ..."
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We present results of a technique for multiplying large integers using the Fermat Number Transform. When the Fermat Number Transform was first proposed, word length constraints limited its effectiveness. Despite the development of multidimensional techniques to extend the length of the FNT
The Omega Test: a fast and practical integer programming algorithm for dependence analysis
 Communications of the ACM
, 1992
"... The Omega testi s ani nteger programmi ng algori thm that can determi ne whether a dependence exi sts between two array references, and i so, under what condi7: ns. Conventi nalwi[A m holds thati nteger programmiB techni:36 are far too expensi e to be used for dependence analysi6 except as a method ..."
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Cited by 521 (15 self)
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The Omega testi s ani nteger programmi ng algori thm that can determi ne whether a dependence exi sts between two array references, and i so, under what condi7: ns. Conventi nalwi[A m holds thati nteger programmiB techni:36 are far too expensi e to be used for dependence analysi6 except as a method of last resort for si:8 ti ns that cannot be deci:A by si[976 methods. We present evi[77B that suggests thiwi sdomi s wrong, and that the Omega testi s competi ti ve wi th approxi mate algori thms usedi n practi ce and sui table for usei n producti on compi lers. Experi ments suggest that, for almost all programs, the average ti me requi red by the Omega test to determi ne the di recti on vectors for an array pai ri s less than 500 secs on a 12 MIPS workstati on. The Omega testi based on an extensi n of Four i0Motzki var i ble eli937 ti n (aliB: r programmiA method) toi nteger programmi ng, and has worstcase exponenti al ti me complexi ty. However, we show that for manysiB7 ti ns i whi h ...
Experience in Factoring Large Integers Using Quadratic Sieve
, 2005
"... GQS is a set of computer programs for factoring “large ” integers. It is based on multiple polynomial quadratic sieve. The current version, 3.0, can factor a 82decimaldigit integer in a PC with AMD 1.8G Hz processor and 512 MB main memory in one day. The largest number I have factored using GQS i ..."
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GQS is a set of computer programs for factoring “large ” integers. It is based on multiple polynomial quadratic sieve. The current version, 3.0, can factor a 82decimaldigit integer in a PC with AMD 1.8G Hz processor and 512 MB main memory in one day. The largest number I have factored using GQS
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