Cryptology ePrint Archive: Report 2015/745

Faster ECC over F2571 (feat. PMULL)

Hwajeong Seo

Abstract: In this paper, we show efficient elliptic curve cryptography implementations for B-571 over ARMv8. We improve the previous binary field multiplication with finely aligned multiplication and incomplete reduction techniques by taking advantages of advanced 64-bit polynomial multiplication (\texttt{PMULL}) supported by ARMv8. This approach shows performance enhancements by a factor of 1.34 times than previous binary field implementations. For the point addition and doubling, the special types of multiplication, squaring and addition operations are combined together and optimized, where one reduction operation is optimized in each case. The scalar multiplication is implemented in constant-time Montgomery ladder algorithm, which is secure against timing attacks. Finally the proposed implementations achieved 759,630/331,944 clock cycles for random/fixed scalar multiplications for B-571 over ARMv8, respectively.

Category / Keywords: ARMv8, Elliptic Curve Cryptography, Binary Field Multiplication

Date: received 24 Jul 2015, last revised 14 Sep 2016

Contact author: hwajeong84 at gmail com

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Version: 20160914:083637 (All versions of this report)

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