Fourq on FPGA: New hardware speed records for elliptic curve cryptography over large prime characteristic fields

Kimmo Järvinen, Andrea Miele, Reza Azarderakhsh, Patrick Longa*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

10 Citations (Scopus)


We present fast and compact implementations of FourQ (ASIACRYPT 2015) on field-programmable gate arrays (FPGAs), and demonstrate, for the first time, the high efficiency of this new elliptic curve on reconfigurable hardware. By adapting FourQ’s algorithms to hardware, we design FPGA-tailored architectures that are significantly faster than any other ECC alternative over large prime characteristic fields. For example, we show that our single-core and multi-core implementations can compute at a rate of 6389 and 64730 scalar multiplications per second, respectively, on a Xilinx Zynq-7020 FPGA, which represent factor-2.5 and 2 speedups in comparison with the corresponding variants of the fastest Curve25519 implementation on the same device. These results show the potential of deploying FourQ on hardware for high-performance and embedded security applications. All the presented implementations exhibit regular, constant-time execution, protecting against timing and simple side-channel attacks.

Original languageEnglish
Title of host publicationCryptographic Hardware and Embedded Systems - 18th International Conference, CHES 2016, Proceedings
PublisherSpringer Verlag
Number of pages21
ISBN (Print)9783662531396
Publication statusPublished - 2016
MoE publication typeA4 Article in a conference publication
EventInternational Conference on Cryptographic Hardware and Embedded Systems - Santa Barbara, United States
Duration: 17 Aug 201619 Aug 2016
Conference number: 18

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)03029743
ISSN (Electronic)16113349


ConferenceInternational Conference on Cryptographic Hardware and Embedded Systems
Abbreviated titleCHES
CountryUnited States
CitySanta Barbara


  • Constant-time
  • Efficient hardware implementation
  • Elliptic curves
  • FourQ
  • FPGA
  • Simple side-channel attacks

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