Higher-dimensional sieving for the number field sieve algorithms

DOI10.2140/obs.2019.2.275WikidataQ128418094 ScholiaQ128418094MaRDI QIDQ6165871

Laurent Grémy

Publication date: 2 August 2023

Published in: The Open Book Series (Search for Journal in Brave)

zbMATH Keywords

finite fieldsdiscrete logarithmsieve algorithmsmedium characteristic

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Number-theoretic algorithms; complexity (11Y16)

Cites Work

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• Bounds for resultants of univariate and bivariate polynomials
• Computing discrete logarithms in \(\mathbb F_{p^6}\)
• Updating key size estimations for pairings
• A taxonomy of pairing-friendly elliptic curves
• Challenges with assessing the impact of NFS advances on the security of pairing-based cryptography
• Better polynomials for GNFS
• The Tower Number Field Sieve
• Computing Individual Discrete Logarithms Faster in $${{\mathrm{GF}}}(p^n)$$ with the NFS-DL Algorithm
• New Complexity Trade-Offs for the (Multiple) Number Field Sieve Algorithm in Non-Prime Fields
• Nearly sparse linear algebra and application to discrete logarithms computations
• Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case
• An Experiment of Number Field Sieve for Discrete Logarithm Problem over GF(p 12)
• Theory and Applications of n-Fold Integer Programming
• Improving NFS for the Discrete Logarithm Problem in Non-prime Finite Fields
• A General Polynomial Selection Method and New Asymptotic Complexities for the Tower Number Field Sieve Algorithm
• Collecting relations for the number field sieve in
• On polynomial selection for the general number field sieve
• On the foundations of linear and integer linear programming I
• Solving Homogeneous Linear Equations Over GF(2) via Block Wiedemann Algorithm
• Discrete logarithms and local units
• Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the gaussian integer method
• Advances in Cryptology - CRYPTO 2003
• Virtual logarithms
• Extended Tower Number Field Sieve with Application to Finite Fields of Arbitrary Composite Extension Degree
• Computation of a 768-Bit Prime Field Discrete Logarithm
• A Kilobit Hidden SNFS Discrete Logarithm Computation
• The Number Field Sieve in the Medium Prime Case
• General Purpose Integer Factoring

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