The multiple number field sieve for medium- and high-characteristic finite fields

DOI10.1112/S1461157014000369zbMath1369.11096OpenAlexW2021384897MaRDI QIDQ2878838

Razvan Barbulescu, Cécile Pierrot

Publication date: 5 September 2014

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s1461157014000369

zbMATH Keywords

discrete logarithm problemvariant of number field sieve

Mathematics Subject Classification ID

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

Related Items (11)

Individual discrete logarithm with sublattice reduction ⋮ 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 BOUNDS FOR BALANCED EMBEDDING DEGREE ⋮ Computing discrete logarithms in \(\mathbb F_{p^6}\) ⋮ Extended Tower Number Field Sieve with Application to Finite Fields of Arbitrary Composite Extension Degree ⋮ Updating key size estimations for pairings ⋮ Refined analysis to the extended tower number field sieve ⋮ Everybody's a target: scalability in public-key encryption ⋮ Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case ⋮ Asymptotic complexities of discrete logarithm algorithms in pairing-relevant finite fields

Uses Software

• SageMath

Cites Work

• On a problem of Oppenheim concerning Factorisatio Numerorum
• Modifications to the number field sieve
• A one round protocol for tripartite Diffie-Hellman
• Modern Computer Algebra
• A public key cryptosystem and a signature scheme based on discrete logarithms
• Solving sparse linear equations over finite fields
• New directions in cryptography
• Identity-Based Encryption from the Weil Pairing
• Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the gaussian integer method
• On asymptotic complexity of computing discrete logarithms over GF(p)
• Pairing the volcano
• Using number fields to compute logarithms in finite fields
• A Heuristic Quasi-Polynomial Algorithm for Discrete Logarithm in Finite Fields of Small Characteristic
• The Number Field Sieve in the Medium Prime Case

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