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

• Main Authors: Jihoon Kwon, Seog Chung Seo, Seokhie Hong
• Format: Article
• Language: English
• Published: MDPI AG 2018-05-01
• Series: Applied Sciences
• Subjects: elliptic curves; scalar multiplication; constant-time implementation; twisted Edwards curves; AVR; MSP430; ARM
• Online Access: http://www.mdpi.com/2076-3417/8/6/900

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.