Cryptology ePrint Archive: Report 2014/134

Kummer strikes back: new DH speed records

Daniel J. Bernstein and Chitchanok Chuengsatiansup and Tanja Lange and Peter Schwabe

Abstract: This paper introduces high-security constant-time variable-base-point Diffie--Hellman software using just 274593 Cortex-A8 cycles, 91460 Sandy Bridge cycles, 90896 Ivy Bridge cycles, or 72220 Haswell cycles. The only higher speed appearing in the literature for any of these platforms is a claim of 60000 Haswell cycles for unpublished software performing arithmetic on a binary elliptic curve.

The new speeds rely on a synergy between (1) state-of-the-art formulas for genus-2 hyperelliptic curves and (2) a modern trend towards vectorization in CPUs. The paper introduces several new techniques for efficient vectorization of Kummer-surface computations.

Category / Keywords: implementation / performance, Diffie--Hellman, hyperelliptic curves, Kummer surfaces, vectorization

Date: received 20 Feb 2014

Contact author: authorcontact-kummer at box cr yp to

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Version: 20140224:033209 (All versions of this report)

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