Elliptic net scalar multiplication upon Koblitz curves
Elliptic net scalar multiplication (ENSM) is a recent trend in cryptography. The first ENSM was constructed using short Weierstrass's division polynomials over a prime field. However, the ENSM over binary field is unknown. Hence, this study proposes a scalar multiplication via elliptic net upon...
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| Format: | Article |
| Language: | English |
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Universiti Putra Malaysia Press
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/88783/ http://psasir.upm.edu.my/id/eprint/88783/1/3.%20Norliana%20Muslim.pdf |
| _version_ | 1848860695302504448 |
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| author | Muslim, Norliana Yunos, Faridah Razali, Zuren Md Said, Mohamad Rushdan |
| author_facet | Muslim, Norliana Yunos, Faridah Razali, Zuren Md Said, Mohamad Rushdan |
| author_sort | Muslim, Norliana |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Elliptic net scalar multiplication (ENSM) is a recent trend in cryptography. The first ENSM was constructed using short Weierstrass's division polynomials over a prime field. However, the ENSM over binary field is unknown. Hence, this study proposes a scalar multiplication via elliptic net upon Koblitz curves over binary field. The objectives outlined in this study are to investigate the relationships between division polynomials, elliptic divisibility sequences, and two types of Koblitz curve over binary field. Additionally, this study looked into the new relationship established between elliptic net and its scalar multiplication. The explicit formulae for ENSM are proposed and their computational costs of field operations are evaluated and discussed. |
| first_indexed | 2025-11-15T12:49:19Z |
| format | Article |
| id | upm-88783 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:49:19Z |
| publishDate | 2020 |
| publisher | Universiti Putra Malaysia Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-887832021-11-03T03:59:35Z http://psasir.upm.edu.my/id/eprint/88783/ Elliptic net scalar multiplication upon Koblitz curves Muslim, Norliana Yunos, Faridah Razali, Zuren Md Said, Mohamad Rushdan Elliptic net scalar multiplication (ENSM) is a recent trend in cryptography. The first ENSM was constructed using short Weierstrass's division polynomials over a prime field. However, the ENSM over binary field is unknown. Hence, this study proposes a scalar multiplication via elliptic net upon Koblitz curves over binary field. The objectives outlined in this study are to investigate the relationships between division polynomials, elliptic divisibility sequences, and two types of Koblitz curve over binary field. Additionally, this study looked into the new relationship established between elliptic net and its scalar multiplication. The explicit formulae for ENSM are proposed and their computational costs of field operations are evaluated and discussed. Universiti Putra Malaysia Press 2020 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/88783/1/3.%20Norliana%20Muslim.pdf Muslim, Norliana and Yunos, Faridah and Razali, Zuren and Md Said, Mohamad Rushdan (2020) Elliptic net scalar multiplication upon Koblitz curves. Malaysian Journal of Mathematical Sciences, 14 (3). 373 - 388. ISSN 1823-8343 https://einspem.upm.edu.my/journal/fullpaper/vol14no3/3.%20Norliana%20Muslim.pdf |
| spellingShingle | Muslim, Norliana Yunos, Faridah Razali, Zuren Md Said, Mohamad Rushdan Elliptic net scalar multiplication upon Koblitz curves |
| title | Elliptic net scalar multiplication upon Koblitz curves |
| title_full | Elliptic net scalar multiplication upon Koblitz curves |
| title_fullStr | Elliptic net scalar multiplication upon Koblitz curves |
| title_full_unstemmed | Elliptic net scalar multiplication upon Koblitz curves |
| title_short | Elliptic net scalar multiplication upon Koblitz curves |
| title_sort | elliptic net scalar multiplication upon koblitz curves |
| url | http://psasir.upm.edu.my/id/eprint/88783/ http://psasir.upm.edu.my/id/eprint/88783/ http://psasir.upm.edu.my/id/eprint/88783/1/3.%20Norliana%20Muslim.pdf |