Journal of Intelligent Computing Kishor Kumar Reddy C, Anisha P R 7 2 2016 This paper proposes two integrity verification schemes based on Schnorr Signature Scheme, which are named Safety Integrity Verification Scheme (SIVS) and Efficient Integrity Verification Scheme (EIVS). In the two verification schemes, for the user’s each challenge, the cloud storage server chooses randomly the sets of file blocks and verification blocks to generate response values, and the user uses the set of signatures to verify response values. That is to check whether the cloud storage server preserves perfectly the user’s file or not. SIVS gives double integrity verification guarantee to cloud storage data. EIVS has more efficient verification guarantee in computational costs than SIVS. According to the different needs of users, EIVS cooperates with SIVS to improve efficiency when checking the integrity of cloud storage data. Compared with other schemes, at the same level of security, the two cooperative schemes get better integrity verification guarantee, and pay lower computational costs.