Ungkapan terkini dalam pendaraban skalar yang berpengganda kembangan T-adic bukan bersebelahan
Suppose E an elliptical curve defined over F2m and Ττ is Frobenius endomorphism from set with E(F2m) to itself. Koblitz curve is a special type of curves with Ττ already being used to improve the performance of scalar multiplication nP’s computation. P is a point that goes through the curve. Wher...
| Main Authors: | , |
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| Format: | Article |
| Published: |
Malaysian Mathematical Society
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/102537/ |
| _version_ | 1848863823480487936 |
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| author | Yunos, Faridah Hadani, Nurul Hafizah |
| author_facet | Yunos, Faridah Hadani, Nurul Hafizah |
| author_sort | Yunos, Faridah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Suppose E an elliptical curve defined over F2m and Ττ is Frobenius endomorphism from set
with E(F2m) to itself. Koblitz curve is a special type of curves with Ττ already being used to
improve the performance of scalar multiplication nP’s computation. P is a point that goes through
the curve. Whereas its multiplier is a non-adjacent Ττ-adic (TNAF) form whose digits are generated
by repeating division of an integer in Z(Ττ) by Ττ. Previous research has found that Ττm = Ττm + smΤτ
with integers Ττm and sm play an important role in identifying the patterns of TNAF’s expansion.
In this paper, we give a formula for coefficients aim in sm for i ≤ 6. We apply triangle’s number,
pyramid’s number, Theorem Nicomachus and Faulhaber’s formula in addition to mathematical
induction to prove this formula. With this approach, the new expression for rm for some m can
be produced to identify odd and even situations in the pseudoTNAF’s system |
| first_indexed | 2025-11-15T13:39:02Z |
| format | Article |
| id | upm-102537 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:39:02Z |
| publishDate | 2022 |
| publisher | Malaysian Mathematical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1025372024-03-21T08:43:30Z http://psasir.upm.edu.my/id/eprint/102537/ Ungkapan terkini dalam pendaraban skalar yang berpengganda kembangan T-adic bukan bersebelahan Yunos, Faridah Hadani, Nurul Hafizah Suppose E an elliptical curve defined over F2m and Ττ is Frobenius endomorphism from set with E(F2m) to itself. Koblitz curve is a special type of curves with Ττ already being used to improve the performance of scalar multiplication nP’s computation. P is a point that goes through the curve. Whereas its multiplier is a non-adjacent Ττ-adic (TNAF) form whose digits are generated by repeating division of an integer in Z(Ττ) by Ττ. Previous research has found that Ττm = Ττm + smΤτ with integers Ττm and sm play an important role in identifying the patterns of TNAF’s expansion. In this paper, we give a formula for coefficients aim in sm for i ≤ 6. We apply triangle’s number, pyramid’s number, Theorem Nicomachus and Faulhaber’s formula in addition to mathematical induction to prove this formula. With this approach, the new expression for rm for some m can be produced to identify odd and even situations in the pseudoTNAF’s system Malaysian Mathematical Society 2022-11 Article PeerReviewed Yunos, Faridah and Hadani, Nurul Hafizah (2022) Ungkapan terkini dalam pendaraban skalar yang berpengganda kembangan T-adic bukan bersebelahan. Menemui Matematik (Discovering Mathematics), 44 (1). 60 - 77. ISSN 0126-9003 https://myjms.mohe.gov.my/index.php/dismath/article/view/20555 |
| spellingShingle | Yunos, Faridah Hadani, Nurul Hafizah Ungkapan terkini dalam pendaraban skalar yang berpengganda kembangan T-adic bukan bersebelahan |
| title | Ungkapan terkini dalam pendaraban skalar yang berpengganda kembangan T-adic bukan bersebelahan |
| title_full | Ungkapan terkini dalam pendaraban skalar yang berpengganda kembangan T-adic bukan bersebelahan |
| title_fullStr | Ungkapan terkini dalam pendaraban skalar yang berpengganda kembangan T-adic bukan bersebelahan |
| title_full_unstemmed | Ungkapan terkini dalam pendaraban skalar yang berpengganda kembangan T-adic bukan bersebelahan |
| title_short | Ungkapan terkini dalam pendaraban skalar yang berpengganda kembangan T-adic bukan bersebelahan |
| title_sort | ungkapan terkini dalam pendaraban skalar yang berpengganda kembangan t-adic bukan bersebelahan |
| url | http://psasir.upm.edu.my/id/eprint/102537/ http://psasir.upm.edu.my/id/eprint/102537/ |