The Public Key Cryptography (PKC) has been proved to be able to be applied in memory-constrained sensor nodes and have nice properties for secure Wireless Sensor and Actor Network (WSAN). In order to prevent the man-in-the-middle attack, the public keys of nodes in WSAN must be authenticated with each other before communication. In this paper, we propose the PEAN scheme for public key authentication based on the Merkle tree and the deployment location knowledge. By using the deployment knowledge and the unique properties of WSAN like the heterogeneity, PEAN scheme can reduce energy consumption and, trade off the communication overhead and memory usage of heterogeneous nodes in WSAN. By using the one?way hash functions, PEAN scheme can reduce computation complexity, communication overhead, and therefore save energy consumption comparing with the RSA algorithm and the ECC algorithm.