On some specific patterns of τ-Adic non-adjacent form expansion over ring Z (τ)
Let τ=(-1)1-a+√-7/2 for a∈{0, 1} is Frobenius map from the set Ea(F2m) to it self for a point (x, y) on Koblitz curves Ea. Let P and Q be two points on this curves. τ-adic Non-Adjacent Form (TNAF) of α an element of the ring Z(τ) = {α = c+dτ|c, d∈Z} is an expansion where the digits are generated by...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Medwell
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/81534/ http://psasir.upm.edu.my/id/eprint/81534/1/On%20Some%20Specific%20Patterns.pdf |
| _version_ | 1848859127376248832 |
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| author | Yunos, Faridah Mohd Suberi, Syahirah Said Husain, Sharifah Kartini Kamel Ariffin, Muhammad Rezal Asbullah, Muhammad Asyraf |
| author_facet | Yunos, Faridah Mohd Suberi, Syahirah Said Husain, Sharifah Kartini Kamel Ariffin, Muhammad Rezal Asbullah, Muhammad Asyraf |
| author_sort | Yunos, Faridah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Let τ=(-1)1-a+√-7/2 for a∈{0, 1} is Frobenius map from the set Ea(F2m) to it self for a point (x, y) on Koblitz curves Ea. Let P and Q be two points on this curves. τ-adic Non-Adjacent Form (TNAF) of α an element of the ring Z(τ) = {α = c+dτ|c, d∈Z} is an expansion where the digits are generated by successively dividing α by τ, allowing remainders of -1, 0 or 1. The implementation of TNAF as the multiplier of scalar multiplication nP = Q is one of the technique in elliptical curve cryptography. In this study, we find the formulas for TNAF that have specific patterns [0, c1, …, c1-1], [-1, c1, …, c1-1], [1, c1, …, c1-1] and [0, 0, 0, c3, c4, …, c1-1]. |
| first_indexed | 2025-11-15T12:24:24Z |
| format | Article |
| id | upm-81534 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:24:24Z |
| publishDate | 2019 |
| publisher | Medwell |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-815342022-09-05T03:32:48Z http://psasir.upm.edu.my/id/eprint/81534/ On some specific patterns of τ-Adic non-adjacent form expansion over ring Z (τ) Yunos, Faridah Mohd Suberi, Syahirah Said Husain, Sharifah Kartini Kamel Ariffin, Muhammad Rezal Asbullah, Muhammad Asyraf Let τ=(-1)1-a+√-7/2 for a∈{0, 1} is Frobenius map from the set Ea(F2m) to it self for a point (x, y) on Koblitz curves Ea. Let P and Q be two points on this curves. τ-adic Non-Adjacent Form (TNAF) of α an element of the ring Z(τ) = {α = c+dτ|c, d∈Z} is an expansion where the digits are generated by successively dividing α by τ, allowing remainders of -1, 0 or 1. The implementation of TNAF as the multiplier of scalar multiplication nP = Q is one of the technique in elliptical curve cryptography. In this study, we find the formulas for TNAF that have specific patterns [0, c1, …, c1-1], [-1, c1, …, c1-1], [1, c1, …, c1-1] and [0, 0, 0, c3, c4, …, c1-1]. Medwell 2019 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/81534/1/On%20Some%20Specific%20Patterns.pdf Yunos, Faridah and Mohd Suberi, Syahirah and Said Husain, Sharifah Kartini and Kamel Ariffin, Muhammad Rezal and Asbullah, Muhammad Asyraf (2019) On some specific patterns of τ-Adic non-adjacent form expansion over ring Z (τ). Journal of Engineering and Applied Sciences, 14 (23). pp. 8609-8615. ISSN 1816-949x; ESSN: 1818-7803 https://medwelljournals.com/abstract/?doi=jeasci.2019.8609.8615 10.36478/jeasci.2019.8609.8615 |
| spellingShingle | Yunos, Faridah Mohd Suberi, Syahirah Said Husain, Sharifah Kartini Kamel Ariffin, Muhammad Rezal Asbullah, Muhammad Asyraf On some specific patterns of τ-Adic non-adjacent form expansion over ring Z (τ) |
| title | On some specific patterns of τ-Adic non-adjacent form expansion over ring Z (τ) |
| title_full | On some specific patterns of τ-Adic non-adjacent form expansion over ring Z (τ) |
| title_fullStr | On some specific patterns of τ-Adic non-adjacent form expansion over ring Z (τ) |
| title_full_unstemmed | On some specific patterns of τ-Adic non-adjacent form expansion over ring Z (τ) |
| title_short | On some specific patterns of τ-Adic non-adjacent form expansion over ring Z (τ) |
| title_sort | on some specific patterns of τ-adic non-adjacent form expansion over ring z (τ) |
| url | http://psasir.upm.edu.my/id/eprint/81534/ http://psasir.upm.edu.my/id/eprint/81534/ http://psasir.upm.edu.my/id/eprint/81534/ http://psasir.upm.edu.my/id/eprint/81534/1/On%20Some%20Specific%20Patterns.pdf |