Two Cubic Polynomials Selection for the Number Field Sieve
نویسندگان
چکیده
منابع مشابه
On Quadratic Polynomials for the Number Field Sieve
The newest, and asymptotically the fastest known integer factorisation algorithm is the number eld sieve. The area in which the number eld sieve has the greatest capacity for improvement is polynomial selection. The best known polynomial selection method nds quadratic polynomials. In this paper we examine the smoothness properties of integer values taken by these polynomials. Given a quadratic ...
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The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some methods to optimize the size property of sextic polynomials.
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The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some algorithms for selecting polynomials with very good root properties. 1...
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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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ژورنال
عنوان ژورنال: The Journal of Korea Information and Communications Society
سال: 2011
ISSN: 1226-4717
DOI: 10.7840/kics.2011.36c.10.614