At present, there is a considerable increase in the amount of data stored in storage services, along with dramatic evolution of networking techniques. In storage services with huge data, the storage servers may want to reduce the volume of stored data, and the clients may want to monitor the integrity of their data with a low cost, since the cost of the functions related to data storage increase in proportion to the size of the data. To achieve these goals, secure deduplication and integrity auditing delegation techniques have been studied, which can reduce the volume of data stored in storage by eliminating duplicated copies and permit clients to efficiently verify the integrity of stored files by delegating costly operations to a trusted party, respectively. So far many studies have been conducted on each topic, separately, whereas relatively few combined schemes, which support the two functions simultaneously, have been researched. In this paper, we design a combined technique, which performs both secure deduplication of encrypted data and public integrity auditing of data. To support the two functions, the proposed scheme performs challenge-response protocols using the BLS signature-based homomorphic linear authenticator. We utilize a third party auditor for performing public audit, in order to help low-powered clients. The proposed scheme satisfies all the fundamental security requirements. We also propose two variances that provide higher security and better performance.