Pairing-friendly Elliptic Curves of Embedding Degree 1 and Applications to Cryptography
نویسندگان
چکیده
Recently, Wang et al. [1] proposed a new method for constructing pairingfriendly 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.
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