- Volume 53 Issue 1
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ON NONLINEAR POLYNOMIAL SELECTION AND GEOMETRIC PROGRESSION (MOD N) FOR NUMBER FIELD SIEVE
- Cho, Gook Hwa (Institute for Mathematical Sciences Ewha Womans University) ;
- Koo, Namhun (Division of Mathematical Models National Institute for Mathematical Sciences) ;
- Kwon, Soonhak (Department of Mathematics Sungkyunkwan University)
- Received : 2013.08.27
- Published : 2016.01.31
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 nonlinear method which selects two polynomials of the same degree greater than one. In this paper, we generalize Montgomery's method  using geometric progression (GP) (mod N) to construct a pair of nonlinear polynomials. We also introduce GP of length d + k with
polynomial selection;number field sieve;geometric progression;LLL algorithm
Grant : BK21플러스
Supported by : 성균관대학교
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