关于环Z(τ)上τ-进非邻接形式展开的一些特殊模式:一个替代公式

Nurul Hafizah Hadani, F. Yunos, S. M. Suberi
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引用次数: 1

摘要

设τ=(−1)1−a+−72,对于a e{0,1}是Koblitz曲线Ea上点(x, y)从集合Ea (F2m)到自身的Frobenius映射。设P和Q是该曲线上的两个点。环Z(τ)={α = c + dτ |c, d∈Z}的元素α的τ-进非邻接形式(TNAF)是一个展开式,其中的数字由α连续除以τ生成,允许余数为- 1,0或1。将TNAF作为标量乘法nP = Q的乘法器是椭圆曲线密码技术中的一种技术。在这篇文章中,我们找到替代公式的重视特定模式(c0 0…0 cl-1], [c0 0…,Cl−12,…,0,cl-1], [0, c1,…,cl-1],[−1,c1,…,cl-1]和[0,0,0,c3、c4…,cl-1]通过应用τm =−2 sm-1 + sm对smτ=∑我+ 12 = 1 | |(−2)我−1 tm + 1(−1)!∏j = 12我−2 (m−j)。设τ=(−1)1−a+−72,对于a e{0,1}是Koblitz曲线Ea上点(x, y)从集合Ea (F2m)到自身的Frobenius映射。设P和Q是该曲线上的两个点。环Z(τ)={α = c + dτ |c, d∈Z}的元素α的τ-进非邻接形式(TNAF)是一个展开式,其中的数字由α连续除以τ生成,允许余数为- 1,0或1。将TNAF作为标量乘法nP = Q的乘法器是椭圆曲线密码技术中的一种技术。在这篇文章中,我们找到替代公式的重视特定模式(c0 0…0 cl-1], [c0 0…,Cl−12,…,0,cl-1], [0, c1,…,cl-1],[−1,c1,…,cl-1]和[0,0,0,c3、c4…,cl-1]通过应用τm =−2 sm-1 + sm对smτ=∑我+ 12 = 1 | |(−2)我−1 tm + 1(−1)!∏j = 12我−2 (m−j)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On some specific patterns of τ-adic non-adjacent form expansion over ring Z(τ): An alternative formula
Let τ=(−1)1−a+−72 for a e {0,1} is Frobenius map from the set Ea (F2m) to itself 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 paper, we find the alternative formulas for TNAF that have specific patterns [c0, 0, …, 0, cl-1], [c0, 0, …, Cl−12, …, 0, cl-1], [0, c1, …, cl-1], [−1, c1, …, cl-1] and [0,0,0,c3, c4, …, cl-1] by applying τm = −2sm-1 + sm τ for sm=∑i=1| m+12 |(−2)i−1tm+1(i−1)!∏j=12i−2(m−j).Let τ=(−1)1−a+−72 for a e {0,1} is Frobenius map from the set Ea (F2m) to itself 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 paper, we find the alternative formulas for TNAF that have specific patterns [c0, 0, …, 0, cl-1], [c0, 0, …, Cl−12, …, 0, cl-1], [0, c1, …, cl-1], [−1, c1, …, cl-1] and [0,0,0,c3, c4, …, cl-1] by applying τm = −2sm-1 + sm τ for sm=∑i=1| m+12 |(−2)i−1tm+1(i−1)!∏j=12i−2(m−j).
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