Paper 2017/814

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

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


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.

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Publication info
Published by the IACR in TCHES 2018
Diffie-Hellman key exchangehyperelliptic curve cryptographyKummer surfaceFPGAZynqlow-latencyhigh-throughputfault countermeasure
Contact author(s)
philipp koppermann @ aisec fraunhofer de
2018-01-31: revised
2017-08-31: received
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      author = {Philipp Koppermann and Fabrizio De Santis and Johann Heyszl and Georg Sigl},
      title = {Fast FPGA Implementations of Diffie-Hellman on the Kummer Surface of a Genus-2 Curve},
      howpublished = {Cryptology ePrint Archive, Paper 2017/814},
      year = {2017},
      note = {\url{}},
      url = {}
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