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A General Framework for Redactable Signatures and New Constructions Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Faster ECC over \(\mathbb {F}_{2^{521}-1}\) (feat. NEON)

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

Published in: Information Security and Cryptology - ICISC 2015

Publisher: Springer International Publishing

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Abstract

In this paper, we present high speed parallel multiplication and squaring algorithms for the Mersenne prime \(2^{521}-1\). 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 8.1/4 M 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 23.8/18.7 M cycles for ARM Cortex-A9/A15, respectively.

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previous chapter Point Decomposition Problem in Binary Elliptic Curves
next chapter On the (In)Efficiency of Non-Interactive Secure Multiparty Computation
Footnotes
1
We discuss the detailed direct reduction techniques in following section.
 
Literature
1.
Bernstein, D.J., Chuengsatiansup, C., Lange, T.: Curve41417: karatsuba revisited. In: Batina, L., Robshaw, M. (eds.) CHES 2014. LNCS, vol. 8731, pp. 316–334. Springer, Heidelberg (2014)
2.
Bos, J.W., Kaihara, M.E.: Montgomery multiplication on the cell. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds.) PPAM 2009, Part I. LNCS, vol. 6067, pp. 477–485. Springer, Heidelberg (2010)CrossRef
3.
Standard for Efficient Cryptography Group: Recommended elliptic curve domain parameters (2000)
4.
Granger, R., Scott, M.: Faster ECC over \(\mathbb{F}_{2^{521}-1}\). In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 539–553. Springer, Heidelberg (2015)
5.
Hamburg, M.: Ed448-goldilocks, a new elliptic curve
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U.D. of Commerce/N.I.S.T. Federal information processing standards publication 186–2 fipps 186–2 digital signature standard
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Pabbuleti, K.C., Mane, D.H., Desai, A., Albert, C., Schaumont, P.: SIMD acceleration of modular arithmetic on contemporary embedded platforms. In: High Performance Extreme Computing Conference (HPEC), pp. 1–6. IEEE (2013)
Metadata
Title
Faster ECC over (feat. NEON)
Authors
Hwajeong Seo
Zhe Liu
Yasuyuki Nogami
Taehwan Park
Jongseok Choi
Lu Zhou
Howon Kim
Copyright Year
2016
Book
Information Security and Cryptology - ICISC 2015

Print ISBN: 978-3-319-30839-5

Electronic ISBN: 978-3-319-30840-1

Copyright Year: 2016

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

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