Pseudo τ - adic non adjacent form for scalar multiplication on Koblitz curves
In ECC, scalar multiplication is the dominant operation, namely computing nP from a point P on an elliptic curve where the multiplier n is an integer, defined as the point resulting from adding P + P + ∙∙∙ + P , n times. The τ-NAF proposed by Solinas, is one of the most efficient algorithms to compu...
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| Format: | Conference or Workshop Item |
| Language: | English |
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Institute for Mathematical Research, Universiti Putra Malaysia
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/66484/ http://psasir.upm.edu.my/id/eprint/66484/1/Cryptology2014-5.pdf |
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| author | Yunos, Faridah Mohd Atan, Kamel Ariffin Kamel Ariffin, Muhammad Rezal Md. Said, Mohamad Rushdan |
| author_facet | Yunos, Faridah Mohd Atan, Kamel Ariffin Kamel Ariffin, Muhammad Rezal Md. Said, Mohamad Rushdan |
| author_sort | Yunos, Faridah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In ECC, scalar multiplication is the dominant operation, namely computing nP from a point P on an elliptic curve where the multiplier n is an integer, defined as the point resulting from adding P + P + ∙∙∙ + P , n times. The τ-NAF proposed by Solinas, is one of the most efficient algorithms to compute scalar multiplications on Koblitz curves. In this paper, we introduced an equivalent multiplier to τ-NAF namely pseudoTNAF. It is based on the idea of transforming the τ-NAF expression to a reduced τ -NAF that has been done by some researchers. It can eliminate the elliptic doublings in scalar multiplication method, and double the number of elliptic additions. We provide the formula for obtaining a total of lattice points in Voronoi region of modulo r + sτ where r + sτ an element of ring Z (τ). This helps us to find all the multipliers n that based on τ-NAF. We also discuss the estimation of operational costs when using pseudoTNAF as a multiplier of scalar multiplication. |
| first_indexed | 2025-11-15T11:28:04Z |
| format | Conference or Workshop Item |
| id | upm-66484 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:28:04Z |
| publishDate | 2014 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-664842019-03-03T23:54:35Z http://psasir.upm.edu.my/id/eprint/66484/ Pseudo τ - adic non adjacent form for scalar multiplication on Koblitz curves Yunos, Faridah Mohd Atan, Kamel Ariffin Kamel Ariffin, Muhammad Rezal Md. Said, Mohamad Rushdan In ECC, scalar multiplication is the dominant operation, namely computing nP from a point P on an elliptic curve where the multiplier n is an integer, defined as the point resulting from adding P + P + ∙∙∙ + P , n times. The τ-NAF proposed by Solinas, is one of the most efficient algorithms to compute scalar multiplications on Koblitz curves. In this paper, we introduced an equivalent multiplier to τ-NAF namely pseudoTNAF. It is based on the idea of transforming the τ-NAF expression to a reduced τ -NAF that has been done by some researchers. It can eliminate the elliptic doublings in scalar multiplication method, and double the number of elliptic additions. We provide the formula for obtaining a total of lattice points in Voronoi region of modulo r + sτ where r + sτ an element of ring Z (τ). This helps us to find all the multipliers n that based on τ-NAF. We also discuss the estimation of operational costs when using pseudoTNAF as a multiplier of scalar multiplication. Institute for Mathematical Research, Universiti Putra Malaysia 2014 Conference or Workshop Item PeerReviewed text en http://psasir.upm.edu.my/id/eprint/66484/1/Cryptology2014-5.pdf Yunos, Faridah and Mohd Atan, Kamel Ariffin and Kamel Ariffin, Muhammad Rezal and Md. Said, Mohamad Rushdan (2014) Pseudo τ - adic non adjacent form for scalar multiplication on Koblitz curves. In: 4th International Cryptology and Information Security Conference 2014 (CRYPTOLOGY2014), 24-26 June 2014, Putrajaya, Malaysia. (pp. 120-130). |
| spellingShingle | Yunos, Faridah Mohd Atan, Kamel Ariffin Kamel Ariffin, Muhammad Rezal Md. Said, Mohamad Rushdan Pseudo τ - adic non adjacent form for scalar multiplication on Koblitz curves |
| title | Pseudo τ - adic non adjacent form for scalar multiplication on Koblitz curves |
| title_full | Pseudo τ - adic non adjacent form for scalar multiplication on Koblitz curves |
| title_fullStr | Pseudo τ - adic non adjacent form for scalar multiplication on Koblitz curves |
| title_full_unstemmed | Pseudo τ - adic non adjacent form for scalar multiplication on Koblitz curves |
| title_short | Pseudo τ - adic non adjacent form for scalar multiplication on Koblitz curves |
| title_sort | pseudo τ - adic non adjacent form for scalar multiplication on koblitz curves |
| url | http://psasir.upm.edu.my/id/eprint/66484/ http://psasir.upm.edu.my/id/eprint/66484/1/Cryptology2014-5.pdf |