Malaysian Journal of Mathematical Sciences, August 2019, Vol. 13(S)
Special Issue: The 6th International Cryptology and Information Security Conference (CRYPTOLOGY2018)
Alternative Method to Find the Number of Points on Koblitz Curve
Hadani, N. H., Yunos, F., Ariffin, M. R. K., Sapar, S. H., and Rahman, N. N. A.
Corresponding Email: faridahy@upm.edu.my
Received date: -
Accepted date: -
Abstract:
A Koblitz curve \(E_a\) is defined over field \(F_{2^{m}}\). Let \(\tau =\frac{(-1)^{1-a}+\sqrt{-7}}{2}\) where \(a \in \left \{0,1\right \}\) denotes the Frobenius endomorphism from the set \(E(F_{2^{m}})\) 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 \(\tau^{m}=r_{m}+s_{m}\tau\) where \(r_{m}\) and \(s_{m}\) are integers is introduced.
Through this approach, we discover an alternative method to find the number of points through the curve \(E_a\).
Keywords: Koblitz curve, scalar multiplication, Frobenius endomorphism, elliptic curve cryptosystem, number of points
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