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Conference Papers Year : 2020

Faster Cofactorization with ECM Using Mixed Representations

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.
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Dates and versions

lirmm-02613652 , version 1 (20-05-2020)

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Cyril Bouvier, Laurent Imbert. Faster Cofactorization with ECM Using Mixed Representations. PKC 2020 - 23rd IACR International Conference on Practice and Theory of Public-Key Cryptography, Jun 2020, Virtual, United Kingdom. pp.483-504, ⟨10.1007/978-3-030-45388-6_17⟩. ⟨lirmm-02613652⟩
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