A General Polynomial Selection Method and New Asymptotic Complexities for the Tower Number Field Sieve Algorithm

DOI10.1007/978-3-662-53887-6_2zbMath1384.94100OpenAlexW2552494694MaRDI QIDQ2958114

No author found.

Publication date: 1 February 2017

Published in: Advances in Cryptology – ASIACRYPT 2016 (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-662-53887-6_2

Mathematics Subject Classification ID

Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16)

Related Items (11)

Cocks-Pinch curves of embedding degrees five to eight and optimal ate pairing computation ⋮ Individual discrete logarithm with sublattice reduction ⋮ Higher-dimensional sieving for the number field sieve algorithms ⋮ Solving discrete logarithms on a 170-bit MNT curve by pairing reduction ⋮ Faster individual discrete logarithms in finite fields of composite extension degree ⋮ Computing discrete logarithms in \(\mathbb F_{p^6}\) ⋮ Updating key size estimations for pairings ⋮ Indiscreet logarithms in finite fields of small characteristic ⋮ Lattice sieving in three dimensions for discrete log in medium characteristic ⋮ Still wrong use of pairings in cryptography ⋮ Asymptotic complexities of discrete logarithm algorithms in pairing-relevant finite fields

Cites Work

• Unnamed Item
• Unnamed Item
• Bounds for resultants of univariate and bivariate polynomials
• Function field sieve method for discrete logarithms over finite fields
• The Tower Number Field Sieve
• New Complexity Trade-Offs for the (Multiple) Number Field Sieve Algorithm in Non-Prime Fields
• Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case
• The multiple number field sieve for medium- and high-characteristic finite fields
• Improving NFS for the Discrete Logarithm Problem in Non-prime Finite Fields
• The Multiple Number Field Sieve with Conjugation and Generalized Joux-Lercier Methods
• A New Index Calculus Algorithm with Complexity $$L(1/4+o(1))$$ in Small Characteristic
• Fine Tuning the Function Field Sieve Algorithm for the Medium Prime Case
• The Function Field Sieve in the Medium Prime Case
• Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the gaussian integer method
• Faster Index Calculus for the Medium Prime Case Application to 1175-bit and 1425-bit Finite Fields
• Using number fields to compute logarithms in finite fields
• Discrete Logarithms in $GF ( P )$ Using the Number Field Sieve
• A Heuristic Quasi-Polynomial Algorithm for Discrete Logarithm in Finite Fields of Small Characteristic
• The Special Number Field Sieve in $\mathbb{F}_{p^{n}}$
• The Number Field Sieve in the Medium Prime Case

This page was built for publication: A General Polynomial Selection Method and New Asymptotic Complexities for the Tower Number Field Sieve Algorithm