Polynomial selection in number field sieve for integer factorization
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 describe how we reached a new factoring milestone by completing the first special number field sieve factorization of a number having more than 1024 bits, namely the Mersenne number 2 − 1. Although this factorization is orders of magnitude ‘easier’ than a factorization of a 1024-bit RSA modulus is believed to be, the methods we used to obtain our result shed new light on the feasibility of t...
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ژورنال
عنوان ژورنال: Perspectives in Science
سال: 2016
ISSN: 2213-0209
DOI: 10.1016/j.pisc.2016.04.007