Faster Compact Diffie-Hellman: Endomorphisms on the x-line

Abstract : We describe an implementation of fast elliptic curve scalar multiplication, optimized for Diffie--Hellman Key Exchange at the 128-bit security level. The algorithms are compact (using only x-coordinates), run in constant time with uniform execution patterns, and do not distinguish between the curve and its quadratic twist; they thus have a built-in measure of side-channel resistance. The core of our construction is a suite of two-dimensional differential addition chains driven by efficient endomorphism decompositions, built on curves selected from a family of Q-curve reductions over \(\FF_{p^2}\) with \(p = 2^{127}-1\). We include state-of-the-art experimental results for twist-secure, constant-time, x-coordinate-only scalar multiplication.
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Nguyen, Phong Q.; Oswald, Elisabeth. EUROCRYPT 2014, May 2014, Copenhagen, Denmark. Springer, 8441, pp.183-200, 2014, Lecture Notes in Computer Science. 〈10.1007/978-3-642-55220-5_11〉
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Dernière modification le : jeudi 11 janvier 2018 - 06:19:44
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Craig Costello, Huseyin Hisil, Benjamin Smith. Faster Compact Diffie-Hellman: Endomorphisms on the x-line. Nguyen, Phong Q.; Oswald, Elisabeth. EUROCRYPT 2014, May 2014, Copenhagen, Denmark. Springer, 8441, pp.183-200, 2014, Lecture Notes in Computer Science. 〈10.1007/978-3-642-55220-5_11〉. 〈hal-00932952〉

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