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作者:Qi Wang , Xiubin Fan , Hongyan Zang ...
来源:[J].Theoretical Computer Science(IF 0.489), 2016, Vol.630, pp.76-94
摘要:Abstract(#br)The General Number Sieve is the most efficient algorithm for integer factorization. It consists of polynomial selection, sieving, solving equations and finding square roots. Root lifting of polynomial is discussed in this paper. The p - adic evaluation provided by ea...
作者:Thorsten Kleinjung
来源:[J].mcom(IF 1.366), 2006, Vol.75 (256), pp.2037-2047
摘要: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 b...
作者:Antoine Joux , Reynald Lercier
来源:[J].mcom(IF 1.366), 2002, Vol.72 (242), pp.953-967
摘要:In this paper, we describe many improvements to the number field sieve. Our main contribution consists of a new way to compute individual logarithms with the number field sieve without solving a very large linear system for each logarithm. We show that, with these improvements, t...
来源:[J].Mathematics of Computation(IF 1.366), 2006, Vol.75 (256), pp.2037-2047
摘要: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 b...
作者:Laurence T. Yang , Ying Huang , Jun Feng ...
来源:[J].Information Sciences(IF 3.643), 2017, Vol.379, pp.257-273
摘要:... The security of the RSA algorithm lies in the difficulty of factoring large integers efficiently and the General Number Field Sieve (GNFS) algorithm is the most efficient algorithm for factoring integers greater than 110 digits at present. In this paper, targeted to speed up ...
作者:Antoine Joux , Reynald Lercier
来源:[J].Mathematics of Computation(IF 1.366), 2003, Vol.72 (242), pp.953-967
摘要:In this paper, we describe many improvements to the number field sieve. Our main contribution consists of a new way to compute individual logarithms with the number field sieve without solving a very large linear system for each logarithm. We show that, with these improvements, t...
作者:劉建甫
来源:[C].成功大學數學系應用數學碩博士班學位論文2014
摘要:... In this thesis, we discuss one of these method in the following called general number field sieve, which is also more efficient than others. Since the idea of this method is come from Fermat, we will introduce some history and compare what different between them. Finally, we ...
作者:Gang Zhou
来源:[J].Applied Mechanics and Materials, 2014, Vol.3009, pp.250-256
摘要:This paper analyzes the algorithm of general number field sieve and suggesting some ofits solving in the problem of larger integers factorization. And a design of its implementation via thelibrary GMP for polynomial selection is discussed. Our work has the advantages of easy exte...
来源:[J].Computers, Networks & Communications, 2016
摘要:According to news reporting originating from Beijing, People's Republic of China, by VerticalNews correspondents, research stated, "The General Number Sieve is the most efficient algorithm for integer factorization.

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