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Appl. Sci. 2018, 8(6), 900; https://doi.org/10.3390/app8060900

Efficient Implementations of Four-Dimensional GLV-GLS Scalar Multiplication on 8-Bit, 16-Bit, and 32-Bit Microcontrollers

1
Center for Information Security Technologies (CIST), Korea University, Seoul 02841, Korea
2
The Affiliated Institute of ETRI, Daejeon 34044, Korea
*
Author to whom correspondence should be addressed.
Received: 16 March 2018 / Revised: 20 May 2018 / Accepted: 22 May 2018 / Published: 31 May 2018
(This article belongs to the Special Issue Security and Privacy for Cyber Physical Systems)
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Abstract

In this paper, we present the first constant-time implementations of four-dimensional Gallant–Lambert–Vanstone and Galbraith–Lin–Scott (GLV-GLS) scalar multiplication using curve Ted 127 - glv 4 on 8-bit AVR, 16-bit MSP430, and 32-bit ARM processors. In Asiacrypt 2012, Longa and Sica introduced the four-dimensional GLV-GLS scalar multiplication, and they reported the implementation results on Intel processors. However, they did not consider efficient implementations on resource-constrained embedded devices. We have optimized the performance of scalar multiplication using curve Ted 127 - glv 4 on 8-bit AVR, 16-bit MSP430, and 32-bit ARM processors. Our implementations compute a variable-base scalar multiplication in 6,856,026, 4,158,453, and 447,836 cycles on AVR, MSP430, and ARM Cortex-M4 processors, respectively. Recently, Four Q -based scalar multiplication has provided the fastest implementation results on AVR, MSP430, and ARM Cortex-M4 processors to date. Compared to Four Q -based scalar multiplication, the proposed implementations require 4.49% more computational cost on AVR, but save 2.85% and 4.61% cycles on MSP430 and ARM, respectively. Our 16-bit and 32-bit implementation results set new speed records for variable-base scalar multiplication. View Full-Text
Keywords: elliptic curves; scalar multiplication; constant-time implementation; twisted Edwards curves; AVR; MSP430; ARM elliptic curves; scalar multiplication; constant-time implementation; twisted Edwards curves; AVR; MSP430; ARM
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Kwon, J.; Seo, S.C.; Hong, S. Efficient Implementations of Four-Dimensional GLV-GLS Scalar Multiplication on 8-Bit, 16-Bit, and 32-Bit Microcontrollers. Appl. Sci. 2018, 8, 900.

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