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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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Submitted on : Saturday, January 18, 2014 - 6:01:49 PM
Last modification on : Thursday, January 20, 2022 - 4:13:41 PM
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Craig Costello, Huseyin Hisil, Benjamin Smith. Faster Compact Diffie-Hellman: Endomorphisms on the x-line. EUROCRYPT 2014, International Association for Cryptologic Research, May 2014, Copenhagen, Denmark. pp.183-200, ⟨10.1007/978-3-642-55220-5_11⟩. ⟨hal-00932952⟩



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