Extended Tower Number Field Sieve with Application to Finite Fields of Arbitrary Composite Extension Degree

DOI10.1007/978-3-662-54365-8_16zbMath1404.11145OpenAlexW2576352420MaRDI QIDQ5738795

Jinhyuck Jeong, Taechan Kim

Publication date: 13 June 2017

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-662-54365-8_16

zbMATH Keywords

finite fieldsdiscrete logarithm problemcryptanalysisnumber field sieve

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16)

Related Items (18)

Efficient hash maps to \(\mathbb{G}_2\) on BLS curves ⋮ Individual discrete logarithm with sublattice reduction ⋮ Fast hashing to \(\mathbb{G}_2\) on pairing-friendly curves with the lack of twists ⋮ Lattice enumeration for tower NFS: a 521-bit discrete logarithm computation ⋮ Higher-dimensional sieving for the number field sieve algorithms ⋮ Lattice enumeration and automorphisms for tower NFS: a 521-bit discrete logarithm computation ⋮ Solving discrete logarithms on a 170-bit MNT curve by pairing reduction ⋮ Faster individual discrete logarithms in finite fields of composite extension degree ⋮ Fast, compact, and expressive attribute-based encryption ⋮ 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 ⋮ Refined analysis to the extended tower number field sieve ⋮ A short-list of pairing-friendly curves resistant to special TNFS at the 128-bit security level ⋮ Still wrong use of pairings in cryptography ⋮ Asymptotic complexities of discrete logarithm algorithms in pairing-relevant finite fields ⋮ Adequate Elliptic Curves for Computing the Product of n Pairings

Cites Work

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• The Tower Number Field Sieve
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• Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case
• Analysis of Optimum Pairing Products at High Security Levels
• 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
• Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field
• Discrete logarithms and local units
• Using number fields to compute logarithms in finite fields
• Discrete Logarithms in $GF ( P )$ Using the Number Field Sieve
• A Kilobit Special Number Field Sieve Factorization
• A Heuristic Quasi-Polynomial Algorithm for Discrete Logarithm in Finite Fields of Small Characteristic
• Pairing-Friendly Elliptic Curves of Prime Order
• The Special Number Field Sieve in $\mathbb{F}_{p^{n}}$
• The Number Field Sieve in the Medium Prime Case

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