Quadratic Sieve - Factoring Records

Factoring Records

Until the discovery of the number field sieve (NFS), QS was the asymptotically-fastest known general-purpose factoring algorithm. Now, Lenstra elliptic curve factorization has the same asymptotic running time as QS (in the case where n has exactly two prime factors of equal size), but in practice, QS is faster since it uses single-precision operations instead of the multi-precision operations used by the elliptic curve method.

On April 2, 1994, the factorization of RSA-129 was completed using QS. It was a 129-digit number, the product of two large primes, one of 64 digits and the other of 65. The factor base for this factorization contained 524339 primes. The data collection phase took 5000 MIPS-years, done in distributed fashion over the Internet. The data collected totaled 2GB. The data processing phase took 45 hours on Bellcore's (now Telcordia Technologies) MasPar (massively parallel) supercomputer. This was the largest published factorization by a general-purpose algorithm, until NFS was used to factor RSA-130, completed April 10, 1996. All RSA numbers factored since then have been factored using NFS.

The current QS record is a 135-digit cofactor of, itself an Aurifeuillian factor of, which was split into 66-digit and 69-digit prime factors in 2001.