Better polynomials for GNFS

Shi Bai 1 Cyril Bouvier 2 Alexander Kruppa 2 Paul Zimmermann 2
1 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
2 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : The general number field sieve (GNFS) is the most efficient algo-rithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the selected polynomials can be modelled in terms of size and root properties. We propose a new kind of polynomials for GNFS: with a new degree of freedom, we further improve the size property. We demonstrate the efficiency of our algorithm by exhibiting a better polynomial than the one used for the factorization of RSA-768, and a polynomial for RSA-1024 that outperforms the best published one.
Document type :
Journal articles
Complete list of metadatas

Cited literature [20 references]  Display  Hide  Download

https://hal.inria.fr/hal-01089507
Contributor : Cyril Bouvier <>
Submitted on : Monday, December 1, 2014 - 8:47:56 PM
Last modification on : Thursday, July 25, 2019 - 9:54:01 AM
Long-term archiving on : Monday, March 2, 2015 - 1:38:18 PM

File

sopt-20140905.pdf
Files produced by the author(s)

Identifiers

Citation

Shi Bai, Cyril Bouvier, Alexander Kruppa, Paul Zimmermann. Better polynomials for GNFS. Mathematics of Computation / Mathematics of Computation, American Mathematical Society, 2016, 85, pp.12. ⟨10.1090/mcom3048⟩. ⟨hal-01089507⟩

Share

Metrics

Record views

1366

Files downloads

719