Internet of things (IOT), which is based on radio frequency identifier (RFID) technology, has many important applications, especially in warehouse management. In a modern company, there are a huge amount of commodities that get in or get out of a warehouse. In order to make sure that every transaction in warehouse management is right, it is necessary to design a fast and light-weight commodity integrity detection algorithm. In this paper, we propose a commodity integrity detection algorithm (CIDA) based on Chinese remainder theorem (CRT), which compares the hash value of each commodity identifier and the product of these values with those values that have been stored in a database in advance. Then, we conduct experiments to compare the proposed algorithm with a typical commodity detection protocol, called trusted reader protocol (TRP). Experimental results show that the proposed algorithm has better properties: (1) it can detect the integrity of commodities very fast; (2) it can provide efficient security and privacy protection.