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.
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).
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Notes
- 1.
We discuss the detailed direct reduction techniques in following section.
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Seo, H. et al. (2016). Faster ECC over \(\mathbb {F}_{2^{521}-1}\) (feat. NEON). In: Kwon, S., Yun, A. (eds) Information Security and Cryptology - ICISC 2015. ICISC 2015. Lecture Notes in Computer Science(), vol 9558. Springer, Cham. https://doi.org/10.1007/978-3-319-30840-1_11
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DOI: https://doi.org/10.1007/978-3-319-30840-1_11
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