Using Lucas Sequences to Factor Large Integers near Group Orders
نویسنده
چکیده
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 (NFS) [4] are commonly used methods for factorization, Trial division and Fermat's method are two of the oldest systematic methods of factoring integers. Although, in general, both methods are not very efficient, it is worthwhile attempting them before other methods. Trial division consists of making trial divisions of the integer N by the small primes; it.succeeds when
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