In the communication environment of smart homes, personal data, control messages, and sensitive data are transmitted through wireless sensor networks (WSNs). Therefore, to prevent an invasion of privacy, communication has to be encrypted, and the data have to be stored securely. In this paper, we propose a new secure privacy-preserving authentication scheme for smart homes. we propose the concept of non-interactive chaotic zero-knowledge (NCZIP) and use it for our scheme to resist ephemeral secrets leakage (ESL) impersonation attack, which assures that the adversary can extract the sensitive information stored in gateway note, and use it to impersonate as a legal user. In addition, the formal security analysis Random-or-real is used to prove that our scheme is secure against different known attacks. In the end, according to the experiment, our scheme has low computation and communication costs compare with other related schemes.