Factorization of RSA-140 Using the Number Field Sieve

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.