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3,226
Integer Factorization
, 2005
"... Many public key cryptosystems depend on the difficulty of factoring large integers. This thesis serves as a source for the history and development of integer factorization algorithms through time from trial division to the number field sieve. It is the first description of the number field sieve fro ..."
Abstract
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Cited by 123 (8 self)
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Many public key cryptosystems depend on the difficulty of factoring large integers. This thesis serves as a source for the history and development of integer factorization algorithms through time from trial division to the number field sieve. It is the first description of the number field sieve
Integer Factoring
, 2000
"... Using simple examples and informal discussions this article surveys the key ideas and major advances of the last quarter century in integer factorization. ..."
Abstract
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Cited by 2 (0 self)
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Using simple examples and informal discussions this article surveys the key ideas and major advances of the last quarter century in integer factorization.
Integer Factorization
, 1994
"... 6.19> public key cryptosystems (also known as asymmetric cryptosystems and open encryption key cryptosystems) [12, 13]. The security of such systems depends on the (assumed) difficulty of factoring the product of two large primes. This is a practical motivation for the current interest in intege ..."
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Cited by 7 (0 self)
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P processors effectively. However, it is true for many integer factorisation algorithms, provided that P is not too large. Integer factorization algorithms There are many algorithms for finding a nontrivial fac
Integer Factorization
, 2006
"... Factorization problems are the “The problem of distinguishing prime numbers from composite numbers, and of resolving the latter into their prime factors, is known to be one of the most important and useful in arithmetic,” Gauss wrote in his Disquisitiones Arithmeticae in 1801. “The dignity of the sc ..."
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Cited by 10 (1 self)
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Factorization problems are the “The problem of distinguishing prime numbers from composite numbers, and of resolving the latter into their prime factors, is known to be one of the most important and useful in arithmetic,” Gauss wrote in his Disquisitiones Arithmeticae in 1801. “The dignity
Integer Factoring with Extra Information
"... Abstract. In this paper we present an heuristic algorithm and its implementation in C++ program for integer factoring with high-order bits known based on lattice reduction techniques. Our approach is inspired in algorithms for predicting pseudorandom numbers. 1 ..."
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Abstract. In this paper we present an heuristic algorithm and its implementation in C++ program for integer factoring with high-order bits known based on lattice reduction techniques. Our approach is inspired in algorithms for predicting pseudorandom numbers. 1
On the Complexity of Integer Factorization
"... Abstract: This note presents a deterministic integer factorization algorithm based on a system of polynomials equations. This technique exploits a new idea in the construction of irreducible polynomials with parametized roots, and recent advances in polynomial lattices reduction methods. The main re ..."
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Abstract: This note presents a deterministic integer factorization algorithm based on a system of polynomials equations. This technique exploits a new idea in the construction of irreducible polynomials with parametized roots, and recent advances in polynomial lattices reduction methods. The main
Advances in composite integer factorization
"... In this research we propose a new method of integer factorization. Prime numbers are the building blocks of arithmetic. At the moment there are no efficient methods (algorithms) known that will determine whether a given integer is prime or and its prime factors [1]. This fact is the basis behind man ..."
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In this research we propose a new method of integer factorization. Prime numbers are the building blocks of arithmetic. At the moment there are no efficient methods (algorithms) known that will determine whether a given integer is prime or and its prime factors [1]. This fact is the basis behind
SELFSIMILAR TILINGS WITH INTEGER FACTOR
"... Abstract: There are nonperiodic selfsimilar tilings with integer factor, which share many important properties — for example being a projection set or being almost periodic — with the quasiperiodic 1 tilings (e.g. the famous Penrose tilings). Quasiperiodic tilings always have an irrational similarit ..."
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Abstract: There are nonperiodic selfsimilar tilings with integer factor, which share many important properties — for example being a projection set or being almost periodic — with the quasiperiodic 1 tilings (e.g. the famous Penrose tilings). Quasiperiodic tilings always have an irrational
.1 More integer factorization
"... and thus we get a factoring algorithm that runs in time O(N 1=4 ). It is still unknown how to find a general method to generate Q ? p N 's such that Q 2 mod N is significantly smaller than p N . Before we continue let us describe another method for obtaining number Q such that Q 2 mod ..."
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and thus we get a factoring algorithm that runs in time O(N 1=4 ). It is still unknown how to find a general method to generate Q ? p N 's such that Q 2 mod N is significantly smaller than p N . Before we continue let us describe another method for obtaining number Q such that Q 2
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