A total norm of τ-adic non-adjacent form occurring among all element of ℤ(τ): An alternative formula

Abstract

In this paper, we give an alternative formula of total norms for τ-Adic Non-adjacent Forms (τ-NAF) expansion for an integer n element of ℤ(τ) in Koblitz curve. We apply the geometric series formula to simplify some series involving floor functions in total norms formula. With this approach, we can evaluate the total norm by using the length of τ-NAF expansion.

Even And Odd Nature For Pseudo Τ-Adic Non-Adjacent Form

“…This method (with an appropriate 0 + 1 ) is four percents more effective than the method of selecting TNAF and RTNAF. To estimate this cost more accurately, Ali and Yunos (2016) and Ali et al (2017) suggested the use of total, maximum and minimum norm formulas for TNAF that was occurring among of all elements in Z(τ). Whereas the selection of seven types of 0 + 1 involving even and odd situation for 0 and 1 as described in and Mohd Suberi et al (2016) should be considered.…”

“…; Avanzi et al (2010); Heuberger (2010); Hakuta et al (2010); Karthikeyan et al (2011); Heuberger and Krenn (2011, 2012); Yunos et al (2014); Yunos et al (2015a, 2015b); Yunos and Mohd Atan (2016), MohdSuberi et al (2016Suberi et al ( , 2018;Ali and Yunos (2016) andAli et al (2017).…”