The development of the number field sieve

Volume 1554 of the series Lecture Notes in Mathematics pp 103-126


A general number field sieve implementation

  • Daniel J. BernsteinAffiliated with
  • , A. K. LenstraAffiliated with

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The general number field sieve is the asymptotically fastest—and by far most complex—factoring algorithm known. We have implemented this algorithm, including five practical improvements: projective polynomials, the lattice sieve, the large prime variation, character columns, and the positive square root method. In this paper we describe our implementation and list some factorizations we obtained, including the record factorization of 2523 − 1.