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Fast FPGA Implementation of Diffie-Hellman on the Kummer Surface of a Genus-2 Curve Philipp Koppermann, Fabrizio De Santis, Johann Heyszl and Georg Sigl History of High-Speed Curve Cryptography over Prime Fields 1 Point Addition on a

  1. Fast FPGA Implementation of Diffie-Hellman on the Kummer Surface of a Genus-2 Curve Philipp Koppermann, Fabrizio De Santis, Johann Heyszl and Georg Sigl

  2. History of High-Speed Curve Cryptography over Prime Fields 1

  3. Point Addition on a Hyperelliptic Genus-2 Curve 2

  4. Point Addition on a Hyperelliptic Genus-2 Curve 3

  5. Kummer: Smaller Field But More Operations 4

  6. Structure of the Kummer-Based Scalar Multiplication 5

  7. Architecture of the Single-Core Implementation 6

  8. Techniques for Designing the Modular Multiplier 7

  9. Modular Multiplication using Mersenne Primes M p = 2 p − 1 8

  10. Regroup the Digit-Products on a Bit-Level 9

  11. Scheduling the Field Operations for a Scalar Multiplication 10

  12. Scheduling the Field Operations for a Scalar Multiplication 11

  13. Single-Core: Performance and Area Results 12

  14. Multi-Core: Performance and Area Results 13

  15. Three Take Home Messages 14

  16. Contact Information Philipp Koppermann Hardware Security Fraunhofer Institute for Applied and Integrated Security (AISEC) Phone: +49 89 3229986-138 E-Mail: philipp.koppermann@aisec.fraunhofer.de 15

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