Smoothness test for polynomials defined over small characteristic finite fields

DOI10.1007/s11786-018-0348-2zbMath1432.11173OpenAlexW2811101801WikidataQ129617802 ScholiaQ129617802MaRDI QIDQ1616168

Luis Rivera-Zamarripa, Gora Adj, Isaac Canales-Martínez, Francisco Rodríguez-Henríquez

Publication date: 1 November 2018

Published in: Mathematics in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11786-018-0348-2

zbMATH Keywords

polynomial ringsindex-calculussmoothness test

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Polynomials over finite fields (11T06) Arithmetic theory of polynomial rings over finite fields (11T55)

Uses Software

• Magma

Cites Work

• Unnamed Item
• The Complete Analysis of a Polynomial Factorization Algorithm over Finite Fields
• Handbook of Finite Fields
• On the Function Field Sieve and the Impact of Higher Splitting Probabilities
• Modern Computer Algebra
• Breaking ‘128-bit Secure’ Supersingular Binary Curves
• Computing Discrete Logarithms in $${\mathbb F}_{3^{6 \cdot 137}}$$ and $${\mathbb F}_{3^{6 \cdot 163}}$$ Using Magma
• A New Index Calculus Algorithm with Complexity $$L(1/4+o(1))$$ in Small Characteristic
• Fast evaluation of logarithms in fields of characteristic two
• Fast Computation of Discrete Logarithms in GF (q)
• Weakness of $\mathbb{F}_{3^{6 \cdot 509}}$ for Discrete Logarithm Cryptography

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