On polynomial selection for the general number field sieve
نویسندگان
چکیده
منابع مشابه
On polynomial selection for the general number field sieve
The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends on a good choice of a polynomial pair. In this article we present an improvement of the polynomial selection method of Montgomery and Murphy which has been used in recent GNFS records. 1. The polynomial selection method of Montgomery and Murphy In this section we brief...
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The number field sieve is the most efficient known algorithm for factoring large integers that are free of small prime factors. For the polynomial selection stage of the algorithm, Montgomery proposed a method of generating polynomials which relies on the construction of small modular geometric progressions. Montgomery’s method is analysed in this paper and the existence of suitable geometric p...
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We present an algorithm to find two non-linear polynomials for the Number Field Sieve integer factorization method. This algorithm extends Montgomery’s “two quadratics” method; for degree 3, it gives two skewed polynomials with resultant O(N5/4), which improves on Williams O(N4/3) result [12].
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In a recent work, Kim and Barbulescu had extended the tower number field sieve algorithm to obtain improved asymptotic complexities in the medium prime case for the discrete logarithm problem on Fpn where n is not a prime power. Their method does not work when n is a composite prime power. For this case, we obtain new asymptotic complexities, e.g., Lpn(1/3, (64/9) ) (resp. Lpn(1/3, 1.88) for th...
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The general number field sieve (GNFS) is asymptotically the fastest known factoring algorithm. One of the most important steps of GNFS is to select a good polynomial pair. A standard way of polynomial selection (being used in factoring RSA challenge numbers) is to select a nonlinear polynomial for algebraic sieving and a linear polynomial for rational sieving. There is another method called a n...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2006
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-06-01870-9