Author:
Srinivasa Rao Subramanya Rao
Affiliation:
The Australian National University, Australia
Keyword(s):
Scalar Multiplication, Montgomery Curves, Differential Addition, Edwards Curves, Twisted Edwards Curves,
Binary Edwards Curves, Homogeneous Projective, Inverted Coordinates, Extended Homogeneous Projective
Coordinates, w-coordinate Differential addition.
Related
Ontology
Subjects/Areas/Topics:
Applied Cryptography
;
Cryptographic Techniques and Key Management
;
Data Engineering
;
Databases and Data Security
;
Information and Systems Security
;
Network Security
;
Wireless Network Security
Abstract:
Cryptographic algorithms in smart cards and other constrained environments increasingly rely on Elliptic
Curves and thus it is desirable to have fast algorithms for elliptic curve arithmetic. In this paper, we provide
(i) faster differential addition formulae for elliptic curve arithmetic on Generalized Edwards’ Curves
improving upon the currently known formulae in the literature, proposed by Justus and Loebenberger at
IWSEC 2010,
(ii) more efficient affine differential addition formulae for a new model of Binary Edwards Curves
proposed by Wu, Tang and Feng at INDOCRYPT 2012 and
(iii) an algorithm for point doubling on Twisted Edwards Curves with a smaller footprint when the
implementation is desired to work across Homogeneous Projective, Inverted and Extended Homogeneous
Projective Coordinates.