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

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; Park, Taehwan; Choi, Jongseok; Zhou, Lu; Kim, Howon.

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)). https://doi.org/10.1007/978-3-319-30840-1_11

Seo, Hwajeong ; Liu, Zhe ; Nogami, Yasuyuki ; Park, Taehwan ; Choi, Jongseok ; Zhou, Lu ; Kim, Howon. / 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)).

@inproceedings{51a8c33a443b4b7b83908eba9a707ee8,

title = "Faster ECC over F2521−1 (feat. NEON)",

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{\textquoteright}s (and SECG{\textquoteright}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{\textquoteright}s ECDH speed test for curve P-521 requires 23.8/18.7M cycles for ARM Cortex-A9/A15, respectively.",

keywords = "Elliptic curve cryptography, Karatsuba, NEON, P-521, SIMD",

author = "Hwajeong Seo and Zhe Liu and Yasuyuki Nogami and Taehwan Park and Jongseok Choi and Lu Zhou and Howon Kim",

note = "Funding Information: This work was partly supported by Institute for Information & communications Technology Promotion (IITP) grant funded by the Korea government (MSIP) (No. 10043907, Development of high performance IoT device and Open Platform with Intelligent Software) and the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the ITRC(Information Technology Research Center) support program (IITP-2015-H8501-15-1017) supervised by the IITP(Institute for Information & communications Technology Promotion). Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.; 18th International Conference on Information Security and Cryptology, ICISC 2015 ; Conference date: 25-11-2015 Through 27-11-2015",

year = "2016",

doi = "10.1007/978-3-319-30840-1_11",

language = "English",

isbn = "9783319308395",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "169--181",

editor = "Aaram Yun and Soonhak Kwon",

booktitle = "Information Security and Cryptology - ICISC 2015 - 18th International Conference, Revised Selected Papers",

}

TY - GEN

T1 - Faster ECC over F2521−1 (feat. NEON)

AU - Seo, Hwajeong

AU - Liu, Zhe

AU - Nogami, Yasuyuki

AU - Park, Taehwan

AU - Choi, Jongseok

AU - Zhou, Lu

AU - Kim, Howon

N1 - Funding Information: This work was partly supported by Institute for Information & communications Technology Promotion (IITP) grant funded by the Korea government (MSIP) (No. 10043907, Development of high performance IoT device and Open Platform with Intelligent Software) and the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the ITRC(Information Technology Research Center) support program (IITP-2015-H8501-15-1017) supervised by the IITP(Institute for Information & communications Technology Promotion). Publisher Copyright: © Springer International Publishing Switzerland 2016.

PY - 2016

Y1 - 2016

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.

AB - 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.

KW - Elliptic curve cryptography

KW - Karatsuba

KW - NEON

KW - P-521

KW - SIMD

UR - http://www.scopus.com/inward/record.url?scp=84961184682&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961184682&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-30840-1_11

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

M3 - Conference contribution

AN - SCOPUS:84961184682

SN - 9783319308395

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 169

EP - 181

BT - Information Security and Cryptology - ICISC 2015 - 18th International Conference, Revised Selected Papers

A2 - Yun, Aaram

A2 - Kwon, Soonhak

PB - Springer Verlag

T2 - 18th International Conference on Information Security and Cryptology, ICISC 2015

Y2 - 25 November 2015 through 27 November 2015

ER -