Alternative formula of Tm in scalar multiplication on Koblitz curve

Hadani, Nurul Hafizah; Yunos, Faridah

doi:10.1063/1.5041533

Cited by 4 publications

(1 citation statement)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the construction of 𝒔 𝒎 in Propositions 1.3 and 1.4 are still rather complex. They are based upon the pyramid number formula, Nichomacus's theorem and Faulhaber's formula, as described by Hadani and Yunos (2018). The primary objective of this research is to derive TNAF of A-F in a more concise form by applying 𝝉 𝒎 = −𝟐𝒔 𝒎−𝟏 + 𝒔 𝒎 𝝉,…”

mentioning

confidence: 99%

On Some Patterns of Tnaf for Scalar Multiplication Over Koblitz Curve

Yunos

Rosli²,

Muslim³

2022

MJS

Self Cite

View full text Add to dashboard Cite

A τ-adic non-adjacent form (TNAF) of an element α of the ring Z(τ) is an expansion whereby the digits are generated by iteratively dividing α by τ, allowing the remainders of -1,0 or 1. The application of TNAF as a multiplier of scalar multiplication (SM) on the Koblitz curve plays a key role in Elliptical Curve Cryptography (ECC). There are several patterns of TNAF (α) expansion in the form of [c0,0,…,0,cl-1 ], [c0,0,…,c(l-1)/2,…,0,c(l-1)], 2+2k, 3+4k, 5+4k and 8k1+8k2 that have been produced in prior work in the literature. However, the construction of their properties based upon pyramid number formulas such as Nichomacus’s theorem and Faulhaber’s formula remains to be rather complex. In this work, we derive such types of TNAF in a more concise manner by applying the power of Frobenius map (τm) based on v-simplex and arithmetic sequences.

show abstract

mentioning

confidence: 99%