Data deduplication is an attractive technology to reduce storage space for increasing vast amount of duplicated and redundant data. In a cloud storage system with data deduplication, duplicate copies of data will be eliminated and only one copy will be kept in the storage. To protect the confidentiality of sensitive data while supporting deduplication, the convergent encryption technique has been proposed to encrypt the data before outsourcing. However, the issue of keyword search over encrypted data in deduplication storage system has to be addressed for efficient data utilization. This paper firstly proposes two constructions which support secure keyword search in this scenario. In these constructions, the integrity of the data can be realized by just checking the convergent key, without other traditional integrity auditing mechanisms. Then, two extensions are presented to support fuzzy keyword search and block-level deduplication. Finally, security analysis is given. Peer Reviewed