With the rapid development of the Internet of things (IoT), more and more IoT devices are connected and communicate frequently. In this background, the traditional centralized security architecture of IoT will be limited in terms of data storage space, data reliability, scalability, operating costs and liability judgment. In this paper, we propose an new key information storage framework based on a small distributed database generated by blockchain technology and cloud storage. Specifically, all encrypted key communication data will be upload to public could server for enough storage, but the abstracts of these data (called "communication logs") will be recorded in "IoT ledger" (i.e., an distributed database) that maintained by all IoT devices according to the blockchain generation approach, which could solve the problem of data reliability, scalability and liability judgment. Besides, in order to efficiently search communication logs and not reveal any sensitive information of communication data, we design the secure search scheme for our "IoT ledger", which exploits the Asymmetric Scalar-product Preserving Encryption (ASPE) approach to guarantee the data security, and exploits the 2-layers index which is tailor-made for blockchain database to improve the search efficiency. Security analysis and experiments on synthetic dataset show that our schemes are secure and efficient.