Faster ECC over F2521−1 (feat. NEON)

Hwajeong Seo; Zhe Liu; Yasuyuki Nogami; Taehwan Park; Jongseok Choi; Lu Zhou; Howon Kim

doi:10.1007/978-3-319-30840-1_11

Faster ECC over F₂⁵²¹−1 (feat. NEON)

Hwajeong Seo, Zhe Liu, Yasuyuki Nogami, Taehwan Park, Jongseok Choi, Lu Zhou, Howon Kim

School of Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

10 Citations (Scopus)

Abstract

In this paper, we present high speed parallel multiplication and squaring algorithms for the Mersenne prime 2⁵²¹ − 1. We exploit 1- level Karatsuba method in order to provide asymptotically faster integer multiplication and fast reduction algorithms. With these optimization techniques, ECDH on NIST’s (and SECG’s) curve P-521 requires 8.1/4M cycles on an ARM Cortex-A9/A15, respectively. As a comparison, on the same architecture, the latest OpenSSL 1.0.2d’s ECDH speed test for curve P-521 requires 23.8/18.7M cycles for ARM Cortex-A9/A15, respectively.

Original language	English
Title of host publication	Information Security and Cryptology - ICISC 2015 - 18th International Conference, Revised Selected Papers
Editors	Aaram Yun, Soonhak Kwon
Publisher	Springer Verlag
Pages	169-181
Number of pages	13
ISBN (Print)	9783319308395
DOIs	https://doi.org/10.1007/978-3-319-30840-1_11
Publication status	Published - 2016
Event	18th International Conference on Information Security and Cryptology, ICISC 2015 - Seoul, Korea, Republic of Duration: Nov 25 2015 → Nov 27 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9558
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	18th International Conference on Information Security and Cryptology, ICISC 2015
Country/Territory	Korea, Republic of
City	Seoul
Period	11/25/15 → 11/27/15

Keywords

Elliptic curve cryptography
Karatsuba
NEON
P-521
SIMD

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-319-30840-1_11

Cite this

Seo, H., Liu, Z., Nogami, Y., Park, T., Choi, J., Zhou, L., & Kim, H. (2016). Faster ECC over F₂⁵²¹−1 (feat. NEON). In A. Yun, & S. Kwon (Eds.), Information Security and Cryptology - ICISC 2015 - 18th International Conference, Revised Selected Papers (pp. 169-181). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9558). Springer Verlag. https://doi.org/10.1007/978-3-319-30840-1_11

Faster ECC over F₂⁵²¹−1 (feat. NEON). / Seo, Hwajeong; Liu, Zhe; Nogami, Yasuyuki et al.
Information Security and Cryptology - ICISC 2015 - 18th International Conference, Revised Selected Papers. ed. / Aaram Yun; Soonhak Kwon. Springer Verlag, 2016. p. 169-181 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9558).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Seo, H, Liu, Z, Nogami, Y, Park, T, Choi, J, Zhou, L & Kim, H 2016, Faster ECC over F₂⁵²¹−1 (feat. NEON). in A Yun & S Kwon (eds), Information Security and Cryptology - ICISC 2015 - 18th International Conference, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9558, Springer Verlag, pp. 169-181, 18th International Conference on Information Security and Cryptology, ICISC 2015, Seoul, Korea, Republic of, 11/25/15. https://doi.org/10.1007/978-3-319-30840-1_11

Seo H, Liu Z, Nogami Y, Park T, Choi J, Zhou L et al. Faster ECC over F₂⁵²¹−1 (feat. NEON). In Yun A, Kwon S, editors, Information Security and Cryptology - ICISC 2015 - 18th International Conference, Revised Selected Papers. Springer Verlag. 2016. p. 169-181. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-30840-1_11

Seo, Hwajeong ; Liu, Zhe ; Nogami, Yasuyuki et al. / Faster ECC over F₂⁵²¹−1 (feat. NEON). Information Security and Cryptology - ICISC 2015 - 18th International Conference, Revised Selected Papers. editor / Aaram Yun ; Soonhak Kwon. Springer Verlag, 2016. pp. 169-181 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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N2 - In this paper, we present high speed parallel multiplication and squaring algorithms for the Mersenne prime 2521 − 1. We exploit 1- level Karatsuba method in order to provide asymptotically faster integer multiplication and fast reduction algorithms. With these optimization techniques, ECDH on NIST’s (and SECG’s) curve P-521 requires 8.1/4M cycles on an ARM Cortex-A9/A15, respectively. As a comparison, on the same architecture, the latest OpenSSL 1.0.2d’s ECDH speed test for curve P-521 requires 23.8/18.7M cycles for ARM Cortex-A9/A15, respectively.

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