Alternative method to find the number of points on Koblitz curve
A Koblitz curve Ea is defined over field F2m. Let τ = (-1)1-a+√-7/2 where a ∈ {0, 1} denotes the Frobenius endomorphism from the set E(F2m) to itself. It can be used to improve the performance of computing scalar multiplication on Koblitz Curves. In this paper, another version of formula for τ m = r...
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| Format: | Article |
| Language: | English |
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Institute for Mathematical Research, Universiti Putra Malaysia
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/76372/ http://psasir.upm.edu.my/id/eprint/76372/1/2.pdf |
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| author | Hadani, Nurul Hafizah Yunos, Faridah Kamel Ariffin, Muhammad Rezal Sapar, Siti Hasana Nek Abd Rahman, Normahirah |
| author_facet | Hadani, Nurul Hafizah Yunos, Faridah Kamel Ariffin, Muhammad Rezal Sapar, Siti Hasana Nek Abd Rahman, Normahirah |
| author_sort | Hadani, Nurul Hafizah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A Koblitz curve Ea is defined over field F2m. Let τ = (-1)1-a+√-7/2 where a ∈ {0, 1} denotes the Frobenius endomorphism from the set E(F2m) to itself. It can be used to improve the performance of computing scalar multiplication on Koblitz Curves. In this paper, another version of formula for τ m = rm + smτ where rm and sm are integers is introduced. Through this approach, we discover an alternative method to find the number of points through the curve Ea. |
| first_indexed | 2025-11-15T12:05:41Z |
| format | Article |
| id | upm-76372 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:05:41Z |
| publishDate | 2019 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-763722020-02-04T04:09:01Z http://psasir.upm.edu.my/id/eprint/76372/ Alternative method to find the number of points on Koblitz curve Hadani, Nurul Hafizah Yunos, Faridah Kamel Ariffin, Muhammad Rezal Sapar, Siti Hasana Nek Abd Rahman, Normahirah A Koblitz curve Ea is defined over field F2m. Let τ = (-1)1-a+√-7/2 where a ∈ {0, 1} denotes the Frobenius endomorphism from the set E(F2m) to itself. It can be used to improve the performance of computing scalar multiplication on Koblitz Curves. In this paper, another version of formula for τ m = rm + smτ where rm and sm are integers is introduced. Through this approach, we discover an alternative method to find the number of points through the curve Ea. Institute for Mathematical Research, Universiti Putra Malaysia 2019 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/76372/1/2.pdf Hadani, Nurul Hafizah and Yunos, Faridah and Kamel Ariffin, Muhammad Rezal and Sapar, Siti Hasana and Nek Abd Rahman, Normahirah (2019) Alternative method to find the number of points on Koblitz curve. Malaysian Journal of Mathematical Sciences, 13 (spec. Aug.). pp. 13-30. ISSN 1823-8343; ESSN: 2289-750X http://einspem.upm.edu.my/journal/fullpaper/vol13saugust/2.pdf |
| spellingShingle | Hadani, Nurul Hafizah Yunos, Faridah Kamel Ariffin, Muhammad Rezal Sapar, Siti Hasana Nek Abd Rahman, Normahirah Alternative method to find the number of points on Koblitz curve |
| title | Alternative method to find the number of points on Koblitz curve |
| title_full | Alternative method to find the number of points on Koblitz curve |
| title_fullStr | Alternative method to find the number of points on Koblitz curve |
| title_full_unstemmed | Alternative method to find the number of points on Koblitz curve |
| title_short | Alternative method to find the number of points on Koblitz curve |
| title_sort | alternative method to find the number of points on koblitz curve |
| url | http://psasir.upm.edu.my/id/eprint/76372/ http://psasir.upm.edu.my/id/eprint/76372/ http://psasir.upm.edu.my/id/eprint/76372/1/2.pdf |