Pairings on Generalized Huff Curves

TL;DR

This paper extends the computation of Tate pairings to generalized Huff curves, providing explicit formulas for addition and doubling steps, thereby advancing elliptic curve cryptography techniques.

Contribution

It introduces the computation of Tate pairings on generalized Huff curves, extending previous work on standard Huff curves with explicit complexity formulas.

Findings

Addition step performed in 1M + (k+15)m + 2c

Doubling step performed in 1M + 1S + (k+12)m + 5s + 2c

Extends pairing computation methods to generalized Huff curves

Abstract

This paper presents the Tate pairing computation on generalized Huff curves proposed by Wu and Feng. In fact, we extend the results of the Tate pairing computation on the standard Huff elliptic curves done previously by Joye, Tibouchi and Vergnaud. We show that the addition step of the Miller loop can be performed in $1\mathbf{M}+(k+15)\mathbf{m}+2\mathbf{c}$ and the doubling one in $1\mathbf{M} + 1\mathbf{S} + (k + 12) \mathbf{m} + 5\mathbf{s} + 2\mathbf{c}$ on the generalized Huff curve.