Factorization of a 512-bit RSA Modulus

Stefania Cavallar (1) , Bruce Dodson , Arjen K. Lenstra , Walter Lioen , Peter L. Montgomery , Brian Murphy , Herman Te Riele , Karen Aardal , Jeff Gilchrist , Gérard Guillerm , Paul Leyland , Joël Marchand , François Morain , Alec Muffett , Chris Putnam , Craig Putnam , Paul Zimmermann (2)

1 ST-CROLLES - STMicroelectronics [Crolles]
2 POLKA - Polynomials, Combinatorics, Arithmetic

On August 22, 1999, we completed the factorization of the 512--bit 155--digit number RSA--155 with the help of the Number Field Sieve factoring method (NFS). This is a new record for factoring general numbers. Moreover, 512--bit RSA keys are frequently used for the protection of electronic commerce---at least outside the USA---so this factorization represents a breakthrough in research on RSA--based systems. The previous record, factoring the 140--digit number RSA--140, was established on February 2, 1999, also with the help of NFS, by a subset of the team which factored RSA--155. The amount of computing time spent on RSA--155 was about 8400 MIPS years, roughly four times that needed for RSA--140; this is about half of what could be expected from a straightforward extrapolation of the computing time spent on factoring RSA--140 and about a quarter of what would be expected from a straightforward extrapolation from the computing time spent on RSA--130. The speed-up is due to a new polynomial selection method for NFS of Murphy and Montgomery which was applied for the first time to RSA--140 and now, with improvements, to RSA--155.

Mots clés: number field sieve; factorisation; factorization; integer; rsa; entier; crible algébrique

Domaines: Autre [cs.OH]

Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra, Walter Lioen, Peter L. Montgomery, et al.. Factorization of a 512-bit RSA Modulus. International Conference on the Theory and Application of Cryptographic Techniques - EUROCRYPT 2000, May 2000, Bruges, Belgium. pp.1-18, ⟨10.1007/3-540-45539-6_1⟩. ⟨inria-00099117⟩