An average density of τ-adic Naf (τ-NAF) representation: an alternative proof
In order to improve the efficiency of scalar multiplications on elliptic Koblitz curves, expansions of the scalar to a complex base associated with the Frobenius endomorphism are commonly used. One such expansion is the τ-adic Non Adjacent Form (τ-NAF), introduced by Solinas (1997). Some properties...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Universiti Putra Malaysia Press
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30019/ http://psasir.upm.edu.my/id/eprint/30019/1/30019.pdf |
| _version_ | 1848846560289357824 |
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| author | Yunos, Faridah Mohd Atan, Kamel Ariffin |
| author_facet | Yunos, Faridah Mohd Atan, Kamel Ariffin |
| author_sort | Yunos, Faridah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In order to improve the efficiency of scalar multiplications on elliptic Koblitz curves, expansions of the scalar to a complex base associated with the Frobenius endomorphism are commonly used. One such expansion is the τ-adic Non Adjacent Form (τ-NAF), introduced by Solinas (1997). Some properties of this expansion, such as the average density, are well known. However in the literature there is no description on the same sequences occuring as length- NAF's and length-l τ-NAF's to proof that the average density is approximately 1/3. In this paper we provide an alternative proof of this fact. |
| first_indexed | 2025-11-15T09:04:39Z |
| format | Article |
| id | upm-30019 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:04:39Z |
| publishDate | 2013 |
| publisher | Universiti Putra Malaysia Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-300192015-05-27T01:45:35Z http://psasir.upm.edu.my/id/eprint/30019/ An average density of τ-adic Naf (τ-NAF) representation: an alternative proof Yunos, Faridah Mohd Atan, Kamel Ariffin In order to improve the efficiency of scalar multiplications on elliptic Koblitz curves, expansions of the scalar to a complex base associated with the Frobenius endomorphism are commonly used. One such expansion is the τ-adic Non Adjacent Form (τ-NAF), introduced by Solinas (1997). Some properties of this expansion, such as the average density, are well known. However in the literature there is no description on the same sequences occuring as length- NAF's and length-l τ-NAF's to proof that the average density is approximately 1/3. In this paper we provide an alternative proof of this fact. Universiti Putra Malaysia Press 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30019/1/30019.pdf Yunos, Faridah and Mohd Atan, Kamel Ariffin (2013) An average density of τ-adic Naf (τ-NAF) representation: an alternative proof. Malaysian Journal of Mathematical Sciences, 7 (1). pp. 111-123. ISSN 1823-8343 http://einspem.upm.edu.my/journal/volume7.1.php |
| spellingShingle | Yunos, Faridah Mohd Atan, Kamel Ariffin An average density of τ-adic Naf (τ-NAF) representation: an alternative proof |
| title | An average density of τ-adic Naf (τ-NAF) representation:
an alternative proof |
| title_full | An average density of τ-adic Naf (τ-NAF) representation:
an alternative proof |
| title_fullStr | An average density of τ-adic Naf (τ-NAF) representation:
an alternative proof |
| title_full_unstemmed | An average density of τ-adic Naf (τ-NAF) representation:
an alternative proof |
| title_short | An average density of τ-adic Naf (τ-NAF) representation:
an alternative proof |
| title_sort | average density of τ-adic naf (τ-naf) representation:
an alternative proof |
| url | http://psasir.upm.edu.my/id/eprint/30019/ http://psasir.upm.edu.my/id/eprint/30019/ http://psasir.upm.edu.my/id/eprint/30019/1/30019.pdf |