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An algorithm was developed by previous researcher for elliptic scalar multiplication (SM) on Koblitz curve where the multiplier of SM is in the form of Pseudo -adic Non-Adjacent (pseudoTNAF).  PseudoTNAF of  an element of the ring Z ) where  is an expansion where the digits are generated by successively dividing  by , allowing remainders of , 0 or 1. Such a multiplier is in the form of .  In this paper, we refine some properties of the multiplier from previous researchers focusing on even and odd situation for  and . We also propose two properties of   when  is even and  is odd. As a result, the nature of   and  are depends on the nature of  and  when  is even. Whereas, the nature of   and  are not depends on the nature of  and  when is odd.   Keywords:   Pseudo -adic Non-Adjacent Form (pseudoTNAF); scalar multiplication (SM); Koblitz curve

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