Modifications to the Number Field Sieve


The Number Field Sieve, due to Lenstra et al. [LLMP] and Buhler et al. [BLP], is a new routine for factoring integers. We present here a modification of that sieve. We use the fact that certain smoothness computations can be reused, and thereby reduce the asymptotic running time of the Number Field Sieve. We also give a way to precompute tables which will be useful for factoring any integers in a large range.


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Communicated by Andrew M. Odlyzko

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Coppersmith, D. Modifications to the Number Field Sieve. J. Cryptology 6, 169–180 (1993).

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Key words

  • Factoring
  • Sieve methods