International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Francisco Rodríguez-Henríquez

Publications

Year
Venue
Title
2019
JOFC
Koblitz Curves over Quadratic Fields
Thomaz Oliveira Julio López Daniel Cervantes-Vázquez Francisco Rodríguez-Henríquez
In this work, we retake an old idea that Koblitz presented in his landmark paper (Koblitz, in: Proceedings of CRYPTO 1991. LNCS, vol 576, Springer, Berlin, pp 279–287, 1991 ), where he suggested the possibility of defining anomalous elliptic curves over the base field $${\mathbb {F}}_4$$ F 4 . We present a careful implementation of the base and quadratic field arithmetic required for computing the scalar multiplication operation in such curves. We also introduce two ordinary Koblitz-like elliptic curves defined over $${\mathbb {F}}_4$$ F 4 that are equipped with efficient endomorphisms. To the best of our knowledge, these endomorphisms have not been reported before. In order to achieve a fast reduction procedure, we adopted a redundant trinomial strategy that embeds elements of the field $${\mathbb {F}}_{4^{m}},$$ F 4 m , with m a prime number, into a ring of higher order defined by an almost irreducible trinomial. We also suggest a number of techniques that allow us to take full advantage of the native vector instructions of high-end microprocessors. Our software library achieves the fastest timings reported for the computation of the timing-protected scalar multiplication on Koblitz curves, and competitive timings with respect to the speed records established recently in the computation of the scalar multiplication over binary and prime fields.
2016
CHES
2013
CHES
2011
CHES
2009
CHES

Program Committees

CHES 2022
CHES 2021
Asiacrypt 2021
CHES 2020
CHES 2019
CHES 2009