International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Laurent Imbert

Publications

Year
Venue
Title
2021
PKC
An Alternative Approach for SIDH Arithmetic
Cyril Bouvier Laurent Imbert
In this paper, we present new algorithms for the field arithmetic layers of supersingular isogeny Diffie-Hellman; one of the fifteen remaining candidates in the NIST post-quantum standardization process. Our approach uses a polynomial representation of the field elements together with mechanisms to keep the coefficients within bounds during the arithmetic operations. We present timings and comparisons for SIKEp503 and suggest a novel 736-bit prime that offers a 1.17x speedup compared to SIKEp751 for a similar level of security.
2020
PKC
Faster Cofactorization with ECM Using Mixed Representations 📺
Cyril Bouvier Laurent Imbert
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.
2017
CRYPTO
2005
ASIACRYPT
2004
CHES