Geodesic
On a strategy in the sieving procedure for the factorization of large natural numbers
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 1, pp. 231-239
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

This work describes a sieving strategy applied for the efficient algorithms of the quadratic sieve and the number field sieve integer factorization. A modification of the quadratic sieve method (Zhang's method) is also considered. Examples and theoretical estimations are given which show practicability of this approach for improving integer factorization procedures.
Keywords: factorization, quadratic sieve, number field sieve. 
@article{UZKU_2011_153_1_a18,
     author = {D. B. Ziyatdinov and G. G. Rubtsova},
     title = {On a~strategy in the sieving procedure for the factorization of large natural numbers},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {231--239},
     year = {2011},
     volume = {153},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2011_153_1_a18/}
}
TY  - JOUR
AU  - D. B. Ziyatdinov
AU  - G. G. Rubtsova
TI  - On a strategy in the sieving procedure for the factorization of large natural numbers
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2011
SP  - 231
EP  - 239
VL  - 153
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UZKU_2011_153_1_a18/
LA  - ru
ID  - UZKU_2011_153_1_a18
ER  - 
%0 Journal Article
%A D. B. Ziyatdinov
%A G. G. Rubtsova
%T On a strategy in the sieving procedure for the factorization of large natural numbers
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2011
%P 231-239
%V 153
%N 1
%U http://geodesic.mathdoc.fr/item/UZKU_2011_153_1_a18/
%G ru
%F UZKU_2011_153_1_a18
D. B. Ziyatdinov; G. G. Rubtsova. On a strategy in the sieving procedure for the factorization of large natural numbers. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 1, pp. 231-239. http://geodesic.mathdoc.fr/item/UZKU_2011_153_1_a18/

[1] Pomerance C., “Smooth Numbers and the Quadratic Sieve”, Algorithmic Number Theory. MSRI Publications, 44 (2008), 69–81 | MR | Zbl

[2] Briggs M., An Introduction to the General Number Field Sieve, Master's Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 1998, 84 pp., svobodnyi http://scholar.lib.vt.edu/theses/available/etd-32298-93111/unrestricted/etd.pdf

[3] Boiko A. A., Ziyatdinov D. B., Ishmukhametov Sh. T., “Ob odnom podkhode k probleme faktorizatsii naturalnykh chisel”, Izv. vuzov. Matem., 2011, no. 4, 15–22 | MR | Zbl

[4] Cohen H., A Course in Computational Algebraic Number Theory, Springer, Berlin, 1993, 545 pp. | MR

[5] Niven I., Zuckrman H., Mongomery H., An introduction to the number theory, Willey Publ., 1991, 541 pp. | Zbl

[6] Zhang M., “Factorization of the Numbers of the Form $\mathbf{m^3+c_2m^2+c_1m+c_0}$”, Proc. 5th Int. Symposium on Algorithmic Number Theory, Lecture Notes in Computer Science, 1423, Springer-Verlag, Berlin, 1998, 131–136 | DOI | MR | Zbl