TY - JOUR
T1 - On Some Specific Patterns of τ-Adic Non-Adjacent Form Expansion over Ring Z (τ)
AU - Yunos, F. AU - Suberi, S.M. AU - Said Husain, Sh.K. AU - Ariffin, M.R.K AU - Asbullah, M.A.
JO - Journal of Engineering and Applied Sciences
VL - 14
IS - 23
SP - 8609
EP - 8615
PY - 2019
DA - 2001/08/19
SN - 1816-949x
DO - jeasci.2019.8609.8615
UR - https://makhillpublications.co/view-article.php?doi=jeasci.2019.8609.8615
KW - element
KW -expansion
KW -Frobenius map
KW -successively
KW -τ-adic non-adjacent form
KW -Koblitz curve
KW -TNAF
AB - Let τ=(-1)1-a+√-7/2 for a∈{0, 1} is Frobenius map from the set Ea(F2m) to it self for a point (x, y) on
Koblitz curves Ea. Let P and Q be two points on this curves. τ-adic Non-Adjacent Form (TNAF) of α an element of the ring Z(τ) = {α = c+dτ|c, d∈Z} is an expansion where the digits are generated by successively dividing
α by τ, allowing remainders of -1, 0 or 1. The implementation of TNAF as the multiplier of scalar multiplication nP = Q
is one of the technique in elliptical curve cryptography. In this study, we find the formulas for TNAF that have
specific patterns [0, c1, …, c1-1], [-1, c1, …, c1-1], [1, c1, …, c1-1] and [0, 0, 0, c3, c4, …, c1-1].
ER -