A world wide number field sieve factoring record: on to 512 bits

We present data concerning the factorization of the 130-digit number RSA130 which we factored on April 10, 1996, using the number field sieve factoring method. This factorization beats the 129-digit record that was set on April 2, 1994, by the quadratic sieve method. The amount of computer time spent on our new record factorization is only a fraction of what was spent on the previous record. We also discuss a World Wide Web interface to our sieving program that we have developed to facilitate contributing to the sieving stage of future large scale factoring efforts. These developments have a serious impact on the security of RSA public key cryptosystems with small moduli. We present a conservative extrapolation to estimate the difficulty of factoring 512-bit numbers