PAIRING-FRIENDLY ELLIPTIC CURVES OF EMBEDDING DEGREE 1 AND APPLICATIONS TO CRYPTOGRAPHY

Abstract

Recently, Wang et al. [1] proposed a new method for constructing pairing-friendly elliptic curves of embedding degree 1.  Authors claim that this method significantly improves the efficiency of generating elliptic curves.  In this paper, we give the arithmetic of pairing-friendly elliptic curves of embedding degree 1.  We prove that conventional classification of pairings into Type 1, 2, 3 and 4 is applicable for the elliptic curves of embedding degree 1 proposed by Wang et al.  We highlight the selection of pairing-friendly elliptic curves of embedding degree 1 for design of efficient cryptosystems.  We compare security and efficiency of cryptosystems based on these pairing-friendly elliptic curves with the existing cryptosystems.  By using these elliptic curves we propose a new asymmetric group key agreement (ASGKA) scheme from Tate pairing.  We discuss the security and efficiency of the proposed ASGKA scheme.