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

Kimmo Järvinen; Andrea Miele; Reza Azarderakhsh; Patrick Longa

doi:10.1007/978-3-662-53140-2_25

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 proceeding › Conference contribution › Scientific › peer-review

10 Citations (Scopus)

Abstract

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 language	English
Title of host publication	Cryptographic Hardware and Embedded Systems - 18th International Conference, CHES 2016, Proceedings
Publisher	Springer Verlag
Pages	517-537
Number of pages	21
Volume	9813
ISBN (Print)	9783662531396
DOIs	https://doi.org/10.1007/978-3-662-53140-2_25
Publication status	Published - 2016
MoE publication type	A4 Article in a conference publication
Event	International Conference on Cryptographic Hardware and Embedded Systems - Santa Barbara, United States Duration: 17 Aug 2016 → 19 Aug 2016 Conference number: 18

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9813
ISSN (Print)	03029743
ISSN (Electronic)	16113349

Conference

Conference	International Conference on Cryptographic Hardware and Embedded Systems
Abbreviated title	CHES
Country	United States
City	Santa Barbara
Period	17/08/2016 → 19/08/2016

Keywords

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

Access to Document

10.1007/978-3-662-53140-2_25

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Järvinen, K., Miele, A., Azarderakhsh, R., & Longa, P. (2016). Fourq on FPGA: New hardware speed records for elliptic curve cryptography over large prime characteristic fields. In Cryptographic Hardware and Embedded Systems - 18th International Conference, CHES 2016, Proceedings (Vol. 9813, pp. 517-537). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9813). Springer Verlag. https://doi.org/10.1007/978-3-662-53140-2_25

Järvinen, Kimmo ; Miele, Andrea ; Azarderakhsh, Reza ; Longa, Patrick. / Fourq on FPGA : New hardware speed records for elliptic curve cryptography over large prime characteristic fields. Cryptographic Hardware and Embedded Systems - 18th International Conference, CHES 2016, Proceedings. Vol. 9813 Springer Verlag, 2016. pp. 517-537 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "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{\textquoteright}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.",

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Järvinen, K, Miele, A, Azarderakhsh, R & Longa, P 2016, Fourq on FPGA: New hardware speed records for elliptic curve cryptography over large prime characteristic fields. in Cryptographic Hardware and Embedded Systems - 18th International Conference, CHES 2016, Proceedings. vol. 9813, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9813, Springer Verlag, pp. 517-537, International Conference on Cryptographic Hardware and Embedded Systems, Santa Barbara, United States, 17/08/2016. https://doi.org/10.1007/978-3-662-53140-2_25

Fourq on FPGA : New hardware speed records for elliptic curve cryptography over large prime characteristic fields. / Järvinen, Kimmo; Miele, Andrea; Azarderakhsh, Reza; Longa, Patrick.

Cryptographic Hardware and Embedded Systems - 18th International Conference, CHES 2016, Proceedings. Vol. 9813 Springer Verlag, 2016. p. 517-537 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9813).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

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Järvinen K, Miele A, Azarderakhsh R, Longa P. Fourq on FPGA: New hardware speed records for elliptic curve cryptography over large prime characteristic fields. In Cryptographic Hardware and Embedded Systems - 18th International Conference, CHES 2016, Proceedings. Vol. 9813. Springer Verlag. 2016. p. 517-537. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-662-53140-2_25