Cryptology ePrint Archive: Report 2017/814

Fast FPGA Implementations of Diffie-Hellman on the Kummer Surface of a Genus-2 Curve

Philipp Koppermann and Fabrizio De Santis and Johann Heyszl and Georg Sigl

Abstract: We present the first hardware implementations of Diffie-Hellman key exchange based on the Kummer surface of Gaudry and Schost’s genus-2 curve targeting a 128-bit security level. We describe a single-core architecture for low-latency applications and a multi-core architecture for high-throughput applications. Synthesized on a Xilinx Zynq-7020 FPGA, our architectures perform a key exchange with lower latency and higher throughput than any other reported implementation using prime-field elliptic curves at the same security level. Our single-core architecture performs a scalar multiplication with a latency of 82 microseconds while our multi-core architecture achieves a throughput of 91,226 scalar multiplications per second. When compared to similar implementations of Microsoft’s FourQ on the same FPGA, this translates to an improvement of 48% in latency and 40% in throughput for the single-core and multi-core architecture, respectively. Both our designs exhibit constant-time execution to thwart timing attacks, use the Montgomery ladder for improved resistance against SPA, and support a countermeasure against fault attacks.

Category / Keywords: implementation / Diffie-Hellman key exchange, hyperelliptic curve cryptography, Kummer surface, FPGA, Zynq, low-latency, high-throughput, fault countermeasure

Original Publication (in the same form): IACR-CHES-2018

Date: received 28 Aug 2017, last revised 31 Jan 2018

Contact author: philipp koppermann at aisec fraunhofer de

Available format(s): PDF | BibTeX Citation

Version: 20180131:212334 (All versions of this report)

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