Nu har RSA med 768-bitar faktoriserats av ett antal forskare.

Factorization of a 768-bit RSA modulus

Thorsten Kleinjung and Kazumaro Aoki and Jens Franke and Arjen Lenstra and Emmanuel Thomé and Joppe Bos and Pierrick Gaudry and Alexander Kruppa and Peter Montgomery and Dag Arne Osvik and Herman te Riele and Andrey Timofeev and Paul Zimmermann

Abstract: This paper reports on the factorization of the 768-bit number RSA-768 by the number field sieve factoring method and discusses some implications for RSA.

Du hittar deras uppsats här:

http://eprint.iacr.org/2010/006

Intressant är följande citat:

Factoring a 1024-bit RSA modulus would be about a thousand times harder, and a 768-bit RSA modulus is several thousands times harder to factor than a 512-bit one.

Because the first factorization of a 512-bit RSA modulus was reported only a decade ago (cf. [7]) it is not unreasonable to expect that 1024-bit RSA moduli can be factored well within the next decade by an academic effort such as ours or the one in [7]. Thus, it would be prudent to phase out usage of 1024-bit RSA within the next three to four years.