Alternative method to find the number of points on Koblitz curve

• Main Authors: Hadani, Nurul Hafizah, Yunos, Faridah, Kamel Ariffin, Muhammad Rezal, Sapar, Siti Hasana, Nek Abd Rahman, Normahirah
• Format: Article
• Language: English
• Published: Institute for Mathematical Research, Universiti Putra Malaysia 2019
• Online Access: http://psasir.upm.edu.my/id/eprint/76372/1/2.pdf; http://psasir.upm.edu.my/id/eprint/76372/; http://einspem.upm.edu.my/journal/fullpaper/vol13saugust/2.pdf
• Institution: Universiti Putra Malaysia

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.