The insufficient trustworthiness of fog nodes in fog computing leads to new security and privacy problems in communication between entities. Existing authentication schemes rely on a trusted third party, or assume that fog nodes are trustworthy, or the authentication overhead is high, which is inconsistent with the characteristics of fog computing. To solve the problem of secure communication in the fog computing environment, we propose an efficient blockchain-based secure remote authentication protocol for the fog-enabled Internet of Things (BSRA). Specifically, blockchain is introduced to construct distributed trust for the fog computing environment. Only lightweight cryptographic primitives, such as physical unclonable functions (PUFs) and cryptographic hash functions, are exploited to design the authentication scheme. In addition, we use temporary identities and the authentication-piggybacking-synchronization to ensure the anonymity and effectiveness of the authentication scheme. We conduct security analysis to demonstrate that BSRA can provide guarantees against various known attacks. We also evaluate the performance of BSRA from several aspects, and the results show that BSRA is effective.