Paper 2018/1179 Original: eprint.iacr.org/2018/1179 ↗

Elliptic Curves in Generalized Huff's Model

Abstract

Abstract This paper introduces a new form of elliptic curves in generalized Huff's model. These curves endowed with the addition are shown to be a group over a finite field. We present formulae for point addition and doubling point on the curves, and evaluate the computational cost of point addition and doubling point using projective, Jacobian, Lopez-Dahab coordinate systems, and embedding of the curves into \mathbb{P}^{1}\times\mathbb{P}^{1} system. We also prove that the curves are birationally equivalent to Weierstrass form. We observe that the computational cost on the curves for point addition and doubling point is lowest by embedding the curves into \mathbb{P}^{1}\times\mathbb{P}^{1} system than the other mentioned coordinate systems and is nearly optimal to other known Huff's models.