Addition chain heuristics in application to elliptic curve cryptosystems
The idea of an addition chain can be applied to scalar multiplication involving huge number operations in elliptic curve cryptosystems. In this article, initially, we study the taxonomy of the addition chain problem to build up an understanding of the problem. We then examine the mathematics behind...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Intelektual Pustaka Media Utama
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/113090/ http://psasir.upm.edu.my/id/eprint/113090/1/113090.pdf |
| _version_ | 1848866124412747776 |
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| author | Mohamed, Mohamad Afendee Shawai, Yahaya Garba Derahman, Mohd Noor Mamat, Abd Rasid Mohd Satar, Siti Dhalila Amri Abidin, Ahmad Faisal Abdul Kadir, Mohd Fadzil |
| author_facet | Mohamed, Mohamad Afendee Shawai, Yahaya Garba Derahman, Mohd Noor Mamat, Abd Rasid Mohd Satar, Siti Dhalila Amri Abidin, Ahmad Faisal Abdul Kadir, Mohd Fadzil |
| author_sort | Mohamed, Mohamad Afendee |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The idea of an addition chain can be applied to scalar multiplication involving huge number operations in elliptic curve cryptosystems. In this article, initially, we study the taxonomy of the addition chain problem to build up an understanding of the problem. We then examine the mathematics behind an optimal addition chain that includes the theoretical boundary for the upper limit and lower limit which laid the foundation for experimentation hereafter. In the following, we examine different addition chain solutions that were used to increase efficiency in scalar multiplication. To avoid any possible confusion, we intentionally separated the discussion into two modules called integer recoding method and chain generator based on the heuristics method. These methods were developed by considering various aspects such as the space within which the operation is executed, the curve that is selected, the formulation to express the original equation, and the choices of operation and arithmetic, all together to improve operational efficiency. |
| first_indexed | 2025-11-15T14:15:37Z |
| format | Article |
| id | upm-113090 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:15:37Z |
| publishDate | 2024 |
| publisher | Intelektual Pustaka Media Utama |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1130902024-11-15T09:08:14Z http://psasir.upm.edu.my/id/eprint/113090/ Addition chain heuristics in application to elliptic curve cryptosystems Mohamed, Mohamad Afendee Shawai, Yahaya Garba Derahman, Mohd Noor Mamat, Abd Rasid Mohd Satar, Siti Dhalila Amri Abidin, Ahmad Faisal Abdul Kadir, Mohd Fadzil The idea of an addition chain can be applied to scalar multiplication involving huge number operations in elliptic curve cryptosystems. In this article, initially, we study the taxonomy of the addition chain problem to build up an understanding of the problem. We then examine the mathematics behind an optimal addition chain that includes the theoretical boundary for the upper limit and lower limit which laid the foundation for experimentation hereafter. In the following, we examine different addition chain solutions that were used to increase efficiency in scalar multiplication. To avoid any possible confusion, we intentionally separated the discussion into two modules called integer recoding method and chain generator based on the heuristics method. These methods were developed by considering various aspects such as the space within which the operation is executed, the curve that is selected, the formulation to express the original equation, and the choices of operation and arithmetic, all together to improve operational efficiency. Intelektual Pustaka Media Utama 2024 Article PeerReviewed text en cc_by_sa_4 http://psasir.upm.edu.my/id/eprint/113090/1/113090.pdf Mohamed, Mohamad Afendee and Shawai, Yahaya Garba and Derahman, Mohd Noor and Mamat, Abd Rasid and Mohd Satar, Siti Dhalila and Amri Abidin, Ahmad Faisal and Abdul Kadir, Mohd Fadzil (2024) Addition chain heuristics in application to elliptic curve cryptosystems. International Journal of Advances in Applied Sciences, 13 (3). pp. 546-555. ISSN 2252-8814; eISSN: 2722-2594 https://ijaas.iaescore.com/index.php/IJAAS/article/view/21103 10.11591/ijaas.v13.i3.pp546-555 |
| spellingShingle | Mohamed, Mohamad Afendee Shawai, Yahaya Garba Derahman, Mohd Noor Mamat, Abd Rasid Mohd Satar, Siti Dhalila Amri Abidin, Ahmad Faisal Abdul Kadir, Mohd Fadzil Addition chain heuristics in application to elliptic curve cryptosystems |
| title | Addition chain heuristics in application to elliptic curve cryptosystems |
| title_full | Addition chain heuristics in application to elliptic curve cryptosystems |
| title_fullStr | Addition chain heuristics in application to elliptic curve cryptosystems |
| title_full_unstemmed | Addition chain heuristics in application to elliptic curve cryptosystems |
| title_short | Addition chain heuristics in application to elliptic curve cryptosystems |
| title_sort | addition chain heuristics in application to elliptic curve cryptosystems |
| url | http://psasir.upm.edu.my/id/eprint/113090/ http://psasir.upm.edu.my/id/eprint/113090/ http://psasir.upm.edu.my/id/eprint/113090/ http://psasir.upm.edu.my/id/eprint/113090/1/113090.pdf |