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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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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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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
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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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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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
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
SIEVING BY LARGE INTEGERS AND COVERING SYSTEMS OF CONGRUENCES
, 2006
"... An old question of Erdős asks if there exists, for each number N, a finite set S of integers greater than N and residue classes r(n) (mod n) for n ∈ S whose union is Z. We prove that if � n∈S 1/n is bounded for such a covering of the integers, then the least member of S is also bounded, thus confirm ..."
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An old question of Erdős asks if there exists, for each number N, a finite set S of integers greater than N and residue classes r(n) (mod n) for n ∈ S whose union is Z. We prove that if � n∈S 1/n is bounded for such a covering of the integers, then the least member of S is also bounded, thus
Factoring large integers using parallel Quadratic Sieve
, 2000
"... Integer factorization is a well studied topic. Parts of the cryptography we use each day rely on the fact that this problem is di�cult. One method one can use for factorizing a large composite number is the Quadratic Sieve algorithm. This method is among the best known today. We present a parallel i ..."
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Cited by 3 (0 self)
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Integer factorization is a well studied topic. Parts of the cryptography we use each day rely on the fact that this problem is di�cult. One method one can use for factorizing a large composite number is the Quadratic Sieve algorithm. This method is among the best known today. We present a parallel
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