Computation of a 768-Bit Prime Field Discrete Logarithm

DOI10.1007/978-3-319-56620-7_7zbMath1411.11135OpenAlexW2594578205MaRDI QIDQ5738876

Arjen K. Lenstra, Colin Stahlke, Thorsten Kleinjung, Claus Diem, Christine Priplata

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/10.1007/978-3-319-56620-7_7

zbMATH Keywords

DSAdiscrete logarithmnumber field sieveel-Gamal

Mathematics Subject Classification ID

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

Related Items (8)

The point decomposition problem over hyperelliptic curves, Toward efficient computation of discrete logarithms in even characteristic ⋮ Cocks-Pinch curves of embedding degrees five to eight and optimal ate pairing computation ⋮ Higher-dimensional sieving for the number field sieve algorithms ⋮ Faster individual discrete logarithms in finite fields of composite extension degree ⋮ Updating key size estimations for pairings ⋮ Computation of a 30750-bit binary field discrete logarithm ⋮ Comparing the difficulty of factorization and discrete logarithm: a 240-digit experiment ⋮ A Brief History of Pairings

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The development of the number field sieve
• Modifications to the number field sieve
• Mersenne Factorization Factory
• Improving the Polynomial time Precomputation of Frobenius Representation Discrete Logarithm Algorithms
• A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms
• The Factorization of the Ninth Fermat Number
• Factorization of a 768-Bit RSA Modulus
• Solving sparse linear equations over finite fields
• A method for obtaining digital signatures and public-key cryptosystems
• Solving Homogeneous Linear Equations Over GF(2) via Block Wiedemann Algorithm
• Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the gaussian integer method
• Analysis of Coppersmith's Block Wiedemann Algorithm for the Parallel Solution of Sparse Linear Systems
• Discrete Logarithms in $GF ( P )$ Using the Number Field Sieve
• Algorithmic Number Theory
• Virtual logarithms
• Selecting cryptographic key sizes

This page was built for publication: Computation of a 768-Bit Prime Field Discrete Logarithm