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

Authors:
Philipp Koppermann , Fraunhofer Research Institution AISEC, Munich
Fabrizio De Santis , Siemens AG, Corporate Technology, Munich
Johann Heyszl , Fraunhofer Research Institution AISEC, Munich
Georg Sigl , Fraunhofer Research Institution AISEC, Munich; Technische Universität München, EI SEC, Munich
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DOI: 10.13154/tches.v2018.i1.1-17
URL: https://tches.iacr.org/index.php/TCHES/article/view/830
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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 lowlatency 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 multicore 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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BibTeX
@article{tches-2018-28957,
  title={Fast FPGA Implementations of Diffie-Hellman on the Kummer Surface of a Genus-2 Curve},
  journal={Transactions on Cryptographic Hardware and Embedded Systems},
  publisher={Ruhr-Universität Bochum},
  volume={2018, Issue 1},
  pages={1-17},
  url={https://tches.iacr.org/index.php/TCHES/article/view/830},
  doi={10.13154/tches.v2018.i1.1-17},
  author={Philipp Koppermann and Fabrizio De Santis and Johann Heyszl and Georg Sigl},
  year=2018
}