On Multi-Scalar Multiplication Algorithms for Register-Constrained Environments
A basic but expensive operation in the implementations of several famous public-key cryptosystems is the computation of the multi-scalar multiplication in a certain finite additive group defined by an elliptic curve. We propose an adaptive window method for the multi-scalar multiplication, which aim...
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doaj-cc1ed8e12adf496c92a2f7a892907e5a2021-03-06T00:04:20ZengMDPI AGElectronics2079-92922021-03-011060560510.3390/electronics10050605On Multi-Scalar Multiplication Algorithms for Register-Constrained EnvironmentsDa-Zhi Sun0Ji-Dong Zhong1Hong-De Zhang2Xiang-Yu Guo3China Tianjin Key Laboratory of Advanced Networking (TANK), College of Intelligence and Computing, Tianjin University, Tianjin 300350, ChinaDepartment of Computer Science and Engineering, Tongji University, No. 1239 Siping Road, Hongkou District, Shanghai 201804, ChinaChina Tianjin Key Laboratory of Advanced Networking (TANK), College of Intelligence and Computing, Tianjin University, Tianjin 300350, ChinaChina Tianjin Key Laboratory of Advanced Networking (TANK), College of Intelligence and Computing, Tianjin University, Tianjin 300350, ChinaA basic but expensive operation in the implementations of several famous public-key cryptosystems is the computation of the multi-scalar multiplication in a certain finite additive group defined by an elliptic curve. We propose an adaptive window method for the multi-scalar multiplication, which aims to balance the computation cost and the memory cost under register-constrained environments. That is, our method can maximize the computation efficiency of multi-scalar multiplication according to any small, fixed number of registers provided by electronic devices. We further demonstrate that our method is efficient when five registers are available. Our method is further studied in detail in the case where it is combined with the non-adjacent form (NAF) representation and the joint sparse form (JSF) representation. One efficiency result is that our method with the proposed improved NAF <em>n</em>-bit representation on average requires 209<em>n</em>/432<em> </em>point additions. To the best of our knowledge, this efficiency result is optimal compared with those of similar methods using five registers. Unlike the previous window methods, which store all possible values in the window, our method stores those with comparatively high probabilities to reduce the number of required registers.https://www.mdpi.com/2079-9292/10/5/605public-key cryptosystemmulti-scalar multiplicationadaptive window methodnon-adjacent form (NAF)joint sparse form (JSF)register-constrained environment |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Da-Zhi Sun Ji-Dong Zhong Hong-De Zhang Xiang-Yu Guo |
spellingShingle |
Da-Zhi Sun Ji-Dong Zhong Hong-De Zhang Xiang-Yu Guo On Multi-Scalar Multiplication Algorithms for Register-Constrained Environments Electronics public-key cryptosystem multi-scalar multiplication adaptive window method non-adjacent form (NAF) joint sparse form (JSF) register-constrained environment |
author_facet |
Da-Zhi Sun Ji-Dong Zhong Hong-De Zhang Xiang-Yu Guo |
author_sort |
Da-Zhi Sun |
title |
On Multi-Scalar Multiplication Algorithms for Register-Constrained Environments |
title_short |
On Multi-Scalar Multiplication Algorithms for Register-Constrained Environments |
title_full |
On Multi-Scalar Multiplication Algorithms for Register-Constrained Environments |
title_fullStr |
On Multi-Scalar Multiplication Algorithms for Register-Constrained Environments |
title_full_unstemmed |
On Multi-Scalar Multiplication Algorithms for Register-Constrained Environments |
title_sort |
on multi-scalar multiplication algorithms for register-constrained environments |
publisher |
MDPI AG |
series |
Electronics |
issn |
2079-9292 |
publishDate |
2021-03-01 |
description |
A basic but expensive operation in the implementations of several famous public-key cryptosystems is the computation of the multi-scalar multiplication in a certain finite additive group defined by an elliptic curve. We propose an adaptive window method for the multi-scalar multiplication, which aims to balance the computation cost and the memory cost under register-constrained environments. That is, our method can maximize the computation efficiency of multi-scalar multiplication according to any small, fixed number of registers provided by electronic devices. We further demonstrate that our method is efficient when five registers are available. Our method is further studied in detail in the case where it is combined with the non-adjacent form (NAF) representation and the joint sparse form (JSF) representation. One efficiency result is that our method with the proposed improved NAF <em>n</em>-bit representation on average requires 209<em>n</em>/432<em> </em>point additions. To the best of our knowledge, this efficiency result is optimal compared with those of similar methods using five registers. Unlike the previous window methods, which store all possible values in the window, our method stores those with comparatively high probabilities to reduce the number of required registers. |
topic |
public-key cryptosystem multi-scalar multiplication adaptive window method non-adjacent form (NAF) joint sparse form (JSF) register-constrained environment |
url |
https://www.mdpi.com/2079-9292/10/5/605 |
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