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Improving the performance of {0,1,3}-NAF recoding algorithm for elliptic curve scalar multiplication

Abstract: Although scalar multiplication is highly fundamental to elliptic curve cryptography (ECC), it is the most time-consuming operation. The performance of such scalar multiplication depends on the performance of its scalar recoding which can be measured in terms of the time and memory consumed...

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Main Authors: Abdul Raheem, Waleed K., Md Yasin, Sharifah, Udzir, Nur Izura, Kamel Ariffin, Muhammad Rezal
Format: Article
Language:English
Published: The Science and Information Organization 2019
Online Access:http://psasir.upm.edu.my/id/eprint/80208/1/Improving%20the%20performance%20of%20%7B0%2C1%2C3%7D-NAF%20recoding%20algorithm%20for%20elliptic%20curve%20scalar%20multiplication.pdf
http://psasir.upm.edu.my/id/eprint/80208/
https://www.researchgate.net/publication/332883846_Improving_the_Performance_of_013-NAF_Recoding_Algorithm_for_Elliptic_Curve_Scalar_Multiplication
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spelling my.upm.eprints.802082020-10-02T01:55:14Z http://psasir.upm.edu.my/id/eprint/80208/ Improving the performance of {0,1,3}-NAF recoding algorithm for elliptic curve scalar multiplication Abdul Raheem, Waleed K. Md Yasin, Sharifah Udzir, Nur Izura Kamel Ariffin, Muhammad Rezal Abstract: Although scalar multiplication is highly fundamental to elliptic curve cryptography (ECC), it is the most time-consuming operation. The performance of such scalar multiplication depends on the performance of its scalar recoding which can be measured in terms of the time and memory consumed, as well as its level of security. This paper focuses on the conversion of binary scalar key representation into {0, 1, 3}-NAF non-adjacent form. Thus, we propose an improved {0, 1, 3}-NAF lookup table and mathematical formula algorithm which improves the performance of {0, 1, 3}-NAF algorithm. This is achieved by reducing the number of rows from 15 rows to 6 rows, and reading two (instead of three) digits to produce one. Furthermore, the improved lookup table reduces the recoding time of the algorithm by over 60% with a significant reduction in memory consumption even with an increase in key size. Specifically, the improved lookup table reduces the memory consumption by as much as 75% for the big key, which shows its higher level of resilience to side channel attacks. The Science and Information Organization 2019 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/80208/1/Improving%20the%20performance%20of%20%7B0%2C1%2C3%7D-NAF%20recoding%20algorithm%20for%20elliptic%20curve%20scalar%20multiplication.pdf Abdul Raheem, Waleed K. and Md Yasin, Sharifah and Udzir, Nur Izura and Kamel Ariffin, Muhammad Rezal (2019) Improving the performance of {0,1,3}-NAF recoding algorithm for elliptic curve scalar multiplication. International Journal of Advanced Computer Science and Applications, 10 (4). pp. 275-279. ISSN 2158-107X; ESSN: 2156-5570 https://www.researchgate.net/publication/332883846_Improving_the_Performance_of_013-NAF_Recoding_Algorithm_for_Elliptic_Curve_Scalar_Multiplication 10.14569/IJACSA.2019.0100432
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description Abstract: Although scalar multiplication is highly fundamental to elliptic curve cryptography (ECC), it is the most time-consuming operation. The performance of such scalar multiplication depends on the performance of its scalar recoding which can be measured in terms of the time and memory consumed, as well as its level of security. This paper focuses on the conversion of binary scalar key representation into {0, 1, 3}-NAF non-adjacent form. Thus, we propose an improved {0, 1, 3}-NAF lookup table and mathematical formula algorithm which improves the performance of {0, 1, 3}-NAF algorithm. This is achieved by reducing the number of rows from 15 rows to 6 rows, and reading two (instead of three) digits to produce one. Furthermore, the improved lookup table reduces the recoding time of the algorithm by over 60% with a significant reduction in memory consumption even with an increase in key size. Specifically, the improved lookup table reduces the memory consumption by as much as 75% for the big key, which shows its higher level of resilience to side channel attacks.
format Article
author Abdul Raheem, Waleed K.
Md Yasin, Sharifah
Udzir, Nur Izura
Kamel Ariffin, Muhammad Rezal
spellingShingle Abdul Raheem, Waleed K.
Md Yasin, Sharifah
Udzir, Nur Izura
Kamel Ariffin, Muhammad Rezal
Improving the performance of {0,1,3}-NAF recoding algorithm for elliptic curve scalar multiplication
author_facet Abdul Raheem, Waleed K.
Md Yasin, Sharifah
Udzir, Nur Izura
Kamel Ariffin, Muhammad Rezal
author_sort Abdul Raheem, Waleed K.
title Improving the performance of {0,1,3}-NAF recoding algorithm for elliptic curve scalar multiplication
title_short Improving the performance of {0,1,3}-NAF recoding algorithm for elliptic curve scalar multiplication
title_full Improving the performance of {0,1,3}-NAF recoding algorithm for elliptic curve scalar multiplication
title_fullStr Improving the performance of {0,1,3}-NAF recoding algorithm for elliptic curve scalar multiplication
title_full_unstemmed Improving the performance of {0,1,3}-NAF recoding algorithm for elliptic curve scalar multiplication
title_sort improving the performance of {0,1,3}-naf recoding algorithm for elliptic curve scalar multiplication
publisher The Science and Information Organization
publishDate 2019
url http://psasir.upm.edu.my/id/eprint/80208/1/Improving%20the%20performance%20of%20%7B0%2C1%2C3%7D-NAF%20recoding%20algorithm%20for%20elliptic%20curve%20scalar%20multiplication.pdf
http://psasir.upm.edu.my/id/eprint/80208/
https://www.researchgate.net/publication/332883846_Improving_the_Performance_of_013-NAF_Recoding_Algorithm_for_Elliptic_Curve_Scalar_Multiplication
_version_ 1680322371384246272
score 13.211869

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