Factorization of RSA-140 using the Number Field Sieve

Stefania Cavallar , Bruce Dodson , Arjen-K. Lenstra , Paul Leyland , Walter M. Lioen , Peter L. Montgomery , Brian Murphy , Herman Te Riele , Paul Zimmermann (1)

1 POLKA - Polynomials, Combinatorics, Arithmetic

On February 2, 1999, we completed the factorization of the 140--digit number RSA--140 with the help of the Number Field Sieve factoring method (NFS). This is a new general factoring record. The previous record was established on April 10, 1996 by the factorization of the 130--digit number RSA--130, also with the help of NFS. The amount of computing time spent on RSA--140 was roughly twice that needed for RSA--130, about half of what could be expected from a straightforward extrapolation of the computing time spent on factoring RSA--130. The speed-up can be attributed to a new polynomial selection method for NFS which will be sketched in this paper. The implications of the new polynomial selection method for factoring a 512--bit RSA modulus are discussed and it is concluded that 512--bit (= 155--digit) RSA moduli are easily and realistically within reach of factoring efforts similar to the one presented here.

Mots clés: public-key cryptosystems; rsa; factoring; factorisation; crible algèbrique; number field sieve; système à clé publique

Domaines: Autre [cs.OH]

Stefania Cavallar, Bruce Dodson, Arjen-K. Lenstra, Paul Leyland, Walter M. Lioen, et al.. Factorization of RSA-140 using the Number Field Sieve. International Conference on the Theory and Applications of Cryptology and Information Security - ASIACRYPT'99, Nov 1999, Singapore, Singapore. pp.195-207, ⟨10.1007/b72231⟩. ⟨inria-00108061⟩