A Kilobit Special Number Field Sieve Factorization

DOI10.1007/978-3-540-76900-2_1zbMath1153.11344OpenAlexW2095980625MaRDI QIDQ5387089

Dag Arne Osvik, Arjen K. Lenstra, Jens Franke, Thorsten Kleinjung, Kazumaro Aoki

Publication date: 15 May 2008

Published in: Advances in Cryptology – ASIACRYPT 2007 (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-76900-2_1

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Factorization (11Y05)

Related Items (10)

Cocks-Pinch curves of embedding degrees five to eight and optimal ate pairing computation ⋮ Faster Multiplication in GF(2)[x] ⋮ Predicting the Sieving Effort for the Number Field Sieve ⋮ Computational hardness of IFP and ECDLP ⋮ Extended Tower Number Field Sieve with Application to Finite Fields of Arbitrary Composite Extension Degree ⋮ A Kilobit Hidden SNFS Discrete Logarithm Computation ⋮ Updating key size estimations for pairings ⋮ ECM on Graphics Cards ⋮ Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case ⋮ Comparing the difficulty of factorization and discrete logarithm: a 240-digit experiment

Cites Work

• The development of the number field sieve
• Subquadratic computation of vector generating polynomials and improvement of the block Wiedemann algorithm
• Factoring integers with elliptic curves
• Solving linear equations over GF(2): Block Lanczos algorithm
• Solving Homogeneous Linear Equations Over GF(2) via Block Wiedemann Algorithm
• Selecting cryptographic key sizes
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