Methods of Factoring Large Integers
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Optimization of the MPQS-factoring algorithm on the Cyber 205 and the NEC SX-2
This paper describes the optimization of a program for the factorization of large integers on two large vector processors: a CDC Cyber 205 and a NEC SX-2. The factoring method used is the so-called multiple polynomial version of the quadratic sieve algorithm. Several large integers in the 48–92 decimal digits range have actually been factorized with these two programs. The largest number, the 9...
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This note provides background on the www-factoring project, which was started in the fall of 1995. Factoring a positive integer ri means finding two positive integers u and v such that the product of u and v equals ri, and such that both u a.nd v are greater than 1. Such u and v are called factors (or divisors) of ii, and n = u v is called a factorization of n. Positive integers that ca.n be fa...
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Factoring large integers into primes is one of the most important and most difficult problems of computational number theory (the twin problem is primality testing [13]). Trial division, Fermat's algorithm [1], [3], [8], Pollard's p-\ method [6], Williams' p + \ method [11], Lenstra's elliptic curve method (ECM) [5], Pomerance's quadratic sieve (QS) [7], [10], and Pollard's number field sieve (...
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RSA is one of the most important public key cryptosystems for information security. The security of RSA depends on Integer factorization problem, it relies on the difficulty of factoring large integers. Much research has gone into problem of factoring a large number. Due to advances in factoring algorithms and advances in computing hardware the size of the number that can be factorized increase...
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تاریخ انتشار 2013