Identity based cryptography (IBC) offers many security advantages over the conventional public key alternative. In the IBC, the bilinear pairing on elliptic curve accounts for the core operation. Such pairing operations are very complicated and slow for software realizations. Therefore, the dedicated hardware implementations and efficient architectures are desirable. In this paper, the Tate pairing in characteristic three is studied, and an efficient architecture is proposed, which can be applied to the Duursma-Lee and Kwon-BGOS algorithms. Analysis shows that our introduced architecture can achieve 2 times speedup over the conventional design with about the same hardware complexity.