Relation collection using Pollard special-q sieving to solve integer factorization and discrete logarithm problem

Abstract

The strength of many security protocols lies on the computational intractability of the integer factorization and discrete logarithm problems. Currently, the best-known techniques employed are number field sieve (NFS) family of algorithms. They come under the class of sub-exponential time algorithms. This class of algorithms comprises of multiple steps. The relation collection (sieving step) is one of the computationally costly and highly memory-dependent phase of these algorithms. This paper discusses various ways to improve the efficiency of the relation collection phase by using parallelization techniques. Experiments have been carried out by using function field sieve, which is one of the NFS family algorithms, to show the computation efficiency of parallelization techniques along with the suitable sieving techniques and the key parameters. The result of our basic implementation is compared with the parallelized version of it. The result analysis depicts that the relation collection phase can be improved by using parallelization techniques up to fourfold.

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Correspondence to R. Padmavathy.

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Varshney, S., Charpe, P., Padmavathy, R. et al. Relation collection using Pollard special-q sieving to solve integer factorization and discrete logarithm problem. J Supercomput 77, 2734–2769 (2021). https://doi.org/10.1007/s11227-020-03351-6

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Keywords

  • Integer factorization
  • Discrete logarithm
  • Number field sieve (NFS )
  • Function field sieve (FFS)
  • Special-q lattice sieving
  • Bucket sieving
  • Line sieving