On the Selection of Polynomials for the DLP Quasi-Polynomial Time Algorithm for Finite Fields of Small Characteristic

DOI10.1137/18M1177196zbMath1439.11297arXiv1706.08447WikidataQ127985122 ScholiaQ127985122MaRDI QIDQ5382575

Giacomo Micheli

Publication date: 18 June 2019

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.08447

zbMATH Keywords

finite fieldscryptographyGalois theoryglobal function fieldsirreducible polynomialsDLP

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Polynomials over finite fields (11T06)

Related Items (8)

On construction and (non)existence of \(c\)-(almost) perfect nonlinear functions ⋮ Investigating the exceptionality of scattered polynomials ⋮ Optimal selection for good polynomials of degree up to five ⋮ On complete \(m\)-arcs ⋮ Algebraic constructions of complete \(m\)-arcs ⋮ On a conjecture on irreducible polynomials over finite fields with restricted coefficients ⋮ Exceptional scatteredness in prime degree ⋮ Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic

Cites Work

• Unnamed Item
• Unnamed Item
• On the Function Field Sieve and the Impact of Higher Splitting Probabilities
• A New Index Calculus Algorithm with Complexity $$L(1/4+o(1))$$ in Small Characteristic
• Algebraic Function Fields and Codes
• On the discrete logarithm problem in finite fields of fixed characteristic
• A short proof of a Chebotarev density theorem for function fields
• A Heuristic Quasi-Polynomial Algorithm for Discrete Logarithm in Finite Fields of Small Characteristic
• Exceptional Covers and Bijections on Rational Points
• The distribution of polynomials over finite fields

This page was built for publication: On the Selection of Polynomials for the DLP Quasi-Polynomial Time Algorithm for Finite Fields of Small Characteristic