Efficient Implementations of Four-Dimensional GLV-GLS Scalar Multiplication on 8-Bit, 16-Bit, and 32-Bit Microcontrollers
- Authors
- Kwon, Jihoon; Seo, Seog Chung; Hong, Seokhie
- Issue Date
- 6월-2018
- Publisher
- MDPI
- Keywords
- elliptic curves; scalar multiplication; constant-time implementation; twisted Edwards curves; AVR; MSP430; ARM
- Citation
- APPLIED SCIENCES-BASEL, v.8, no.6
- Indexed
- SCIE
SCOPUS
- Journal Title
- APPLIED SCIENCES-BASEL
- Volume
- 8
- Number
- 6
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/75448
- DOI
- 10.3390/app8060900
- ISSN
- 2076-3417
- 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 Ted127-glv4 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 Ted127-glv4 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.
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