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...