Use of SIMD-based data parallelism to speed up sieving in integer-factoring algorithms

DOI10.1016/j.amc.2016.08.019zbMath1411.65174OpenAlexW2515909907MaRDI QIDQ1737153

Binanda Sengupta, Abhijit Das

Publication date: 27 March 2019

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

Full work available at URL: https://doi.org/10.1016/j.amc.2016.08.019

zbMATH Keywords

integer factorizationsingle instruction multiple datalattice sieve methodmultiple-polynomial quadratic sieve methodnumber-field sieve method

Mathematics Subject Classification ID

Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Parallel algorithms in computer science (68W10) Parallel numerical computation (65Y05) Mathematical problems of computer architecture (68M07) Factorization (11Y05)

Uses Software

• gmp
• CADO-NFS

Cites Work

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• Factoring integers with elliptic curves
• Discrete logarithms in \(\mathrm{GF}(p)\)
• Function field sieve method for discrete logarithms over finite fields
• SIMD-Based Implementations of Sieving in Integer-Factoring Algorithms
• Factorization of a 768-Bit RSA Modulus
• ECM on Graphics Cards
• The Multiple Polynomial Quadratic Sieve
• Asymptotically Fast Factorization of Integers
• A Method of Factoring and the Factorization of F 7
• On factoring large numbers
• Faster Index Calculus for the Medium Prime Case Application to 1175-bit and 1425-bit Finite Fields
• Factorization Using the Quadratic Sieve Algorithm
• Algorithmic Number Theory

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