Bilinear pairings on elliptic curves
Year: 2013
Type: preprint
Abstract: We give an elementary and self-contained introduction to pairings on elliptic curves over finite fields. For the first time in the literature, the three different definitions of the Weil pairing are stated correctly and proved to be equivalent using Weil reciprocity. Pairings with shorter loops, such as the ate, ate$_i$, R-ate and optimal pairings, together with their twisted variants, are presented with proofs of their bilinearity and non-degeneracy. Finally, we review different types of pairings in a cryptographic context. This article can be seen as an update chapter to A. Enge, Elliptic Curves and Their Applications to Cryptography - An Introduction, Kluwer Academic Publishers 1999.
Source: arXiv (Cornell University)
Author: Enge, Andreas
Language: English
Subfield: Information Systems
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4300783231