A self-pairing map and its applications to cryptography

Abstract

In this paper, we propose a bilinear pairing map on finitely generated free R-modules with rank two where R is a commutative ring with 1, and apply this pairing to elliptic curves over fields. We also verify the pairing on elliptic curves can be applicable to the current cryptographic schemes. © 2003 Elsevier Inc. All rights reserved.