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 $12^{151-1$.

Department of Numerical Mathematics [NM]

de Jong, M. C. M., Metz, J. A. J., Elkenbracht-Huizing, M., & Diekmann, O. (1995). An implementation of the number field sieve. Department of Numerical Mathematics [NM]. CWI.