Ungkapan terkini dalam pendaraban skalar yang berpengganda kembangan T-adic bukan bersebelahan - Yunos, Faridah; Hadani, Nurul Hafizah (Malaysian Mathematical Society, 2022)
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