AVX-512-based Parallelization of Block Sieving and Bucket Sieving for the General Number Field Sieve Method

Pritam Pallab, Abhijit Das

2021

Abstract

The fastest known general-purpose technique for factoring integers is the General Number Field Sieve Method (GNFSM), in which the most time-consuming part is the sieving stage. For both line sieving and lattice sieving, two cache-friendly extensions used in practical implementations are block sieving and bucket sieving. The new AVX-512 instruction set in modern Intel CPUs offers some fast vectorization intrinsics. In this paper, we report our AVX-512 based cache-friendly parallelization of block and bucket sieving for the GNFSM. We use vectorization for both sieve-index calculations and sieve-array updates in block sieving, and for the insertion stage in bucket sieving. Our experiments using Intel Xeon Skylake processors demonstrate a performance boost in both single-core and multi-core environments. The introduction of cache-friendly sieving leads to a speedup of up to 63%. On top of that, vectorization yields a speedup of up to 25%.

Paper Citation

in Harvard Style

Pallab P. and Das A. (2021). AVX-512-based Parallelization of Block Sieving and Bucket Sieving for the General Number Field Sieve Method. In Proceedings of the 18th International Conference on Security and Cryptography - Volume 1: SECRYPT, ISBN 978-989-758-524-1, pages 653-658. DOI: 10.5220/0010515206530658

in Bibtex Style

@conference{secrypt21,
author={Pritam Pallab and Abhijit Das},
title={AVX-512-based Parallelization of Block Sieving and Bucket Sieving for the General Number Field Sieve Method},
booktitle={Proceedings of the 18th International Conference on Security and Cryptography - Volume 1: SECRYPT,},
year={2021},
pages={653-658},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0010515206530658},
isbn={978-989-758-524-1},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 18th International Conference on Security and Cryptography - Volume 1: SECRYPT,
TI - AVX-512-based Parallelization of Block Sieving and Bucket Sieving for the General Number Field Sieve Method
SN - 978-989-758-524-1
AU - Pallab P.
AU - Das A.
PY - 2021
SP - 653
EP - 658
DO - 10.5220/0010515206530658