International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Faster Cofactorization with ECM Using Mixed Representations

Authors:
Cyril Bouvier
Laurent Imbert
Download:
DOI: 10.1007/978-3-030-45388-6_17
Search ePrint
Search Google
Presentation: Slides
Abstract: This paper introduces a novel implementation of the elliptic curve factoring method specifically designed for medium-size integers such as those arising by billions in the cofactorization step of the Number Field Sieve. In this context, our algorithm requires fewer modular multiplications than any other publicly available implementation. The main ingredients are: the use of batches of primes, fast point tripling, optimal double-base decompositions and Lucas chains, and a good mix of Edwards and Montgomery representations.
Video from PKC 2020
BibTeX
@article{pkc-2020-30319,
  title={Faster Cofactorization with ECM Using Mixed Representations},
  booktitle={Public-Key Cryptography – PKC 2020},
  series={Public-Key Cryptography – PKC 2020},
  publisher={Springer},
  volume={12111},
  pages={483-504},
  doi={10.1007/978-3-030-45388-6_17},
  author={Cyril Bouvier and Laurent Imbert},
  year=2020
}