An implementation of the number field sieve

The Number Field Sieve (NFS) is the asymptotically fastest known factoring algorithm for large integers. This article describes an implementation of the NFS, including the choice of two quadratic polynomials, both classical and lattice sieving, the block Lanczos method and a new square root algorithm. Finally some data on factorizations obtained with this implementation are listed, including the record factorization of 12^{151-1

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 number

A Dedicated Sieving Hardware

Abstract. We describe a hardware device for supporting the sieving step in integer factoring algorithms like the quadratic sieve or the number field sieve. In analogy to Bernstein’s proposal for speeding up the linear algebra step, we rely on a mesh of very simple processing units. Manufacturing the device at moderate cost with current hardware technology on standard wafers with 200 mm or 300 mm diameter should not provide any major obstacle. A preliminary analysis of the parameters for factoring a 512-bit number with the number field sieve shows that the design considered here might outperform a TWINKLE device