The Multiple Number Field Sieve for Medium and High Characteristic Finite Fields

  title={The Multiple Number Field Sieve for Medium and High Characteristic Finite Fields},
  author={R. Barbulescu and C. Pierrot},
  journal={IACR Cryptol. ePrint Arch.},
  • R. Barbulescu, C. Pierrot
  • Published 2014
  • Mathematics, Computer Science, Physics
  • IACR Cryptol. ePrint Arch.
  • In this paper, we study the discrete logarithm problem in medium and high characteristic finite fields. We propose a variant of the Number Field Sieve~(NFS) based on numerous number fields. Our improved algorithm computes discrete logarithms in $\mathbb{F}_{p^n}$ for the whole range of applicability of NFS and lowers the asymptotic complexity from $L_{p^n}(1/3,(128/9)^{1/3})$ to $L_{p^n}(1/3,(2^{13}/3^6)^{1/3})$ in the medium characteristic case, and from $L_{p^n}(1/3,(64/9)^{1/3})$ to $L_{p^n… CONTINUE READING

    Figures and Topics from this paper.

    Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case
    • 139
    • PDF
    A General Polynomial Selection Method and New Asymptotic Complexities for the Tower Number Field Sieve Algorithm
    • 22
    • PDF
    Extended Tower Number Field Sieve with Application to Finite Fields of Arbitrary Composite Extension Degree
    • 39
    • PDF
    Computing Individual Discrete Logarithms Faster in GF(p n ) with the NFS-DL Algorithm
    • 14
    • PDF
    New Complexity Trade-Offs for the (Multiple) Number Field Sieve Algorithm in Non-Prime Fields
    • 27
    • PDF
    The Tower Number Field Sieve
    • 48
    • PDF
    The Multiple Number Field Sieve with Conjugation Method
    • 1
    • PDF


    Publications referenced by this paper.
    The Number Field Sieve in the Medium Prime Case
    • 118
    • PDF
    Using number fields to compute logarithms in finite fields
    • 66
    • PDF
    Solving sparse linear equations over finite fields
    • 588
    • PDF
    On asymptotic complexity of computing discrete logarithms over GF(p)
    • 15