With the development of database-as-a-service (DaS), data in cloud is more interesting for researchers in both academia and commercial societies. Despite DaS’s convenience, there exist many considerable problems which concern end users about data loss and malicious deletion. In order to avoid these cases, users can rely on data auditing, which means verifying the existence of data stored in cloud without any malicious changes. Data owner can perform data auditing by itself or hire a third-party auditor. Until now, there are two challenges of data auditing as the computation cost in case of self auditing and data privacy preservation in case of hiding an auditor. In this paper, we propose a solution for auditing by a third-party auditor to verify data integrity with efficient computation and data privacy preservation. Our solution is built upon cryptographic hash function and Chinese Theorem Remainder with the advantage in efficient computation in all three sides including data owner, cloud server, and auditor. In addition, the privacy preservation can be guaranteed by proving the third-party auditor learns nothing about user’s data during auditing process.

RSA cryptosystem is the most popular public key cryptosystem which provides both secrecy and digital signatures. Due to RSA’s popularity, many attacks on it have been developed. In this paper, we consider experimentally attacks on low private exponent RSA and find that: (i) lattice attack using Gauss lattice reduction algorithm is more effective than Wiener attack, and (ii) it is not always to recover decryption exponent even if its bit-length is less than onequarter bit-length of the modulus. The results also raise an open question on the conditions to recover the RSA private key from public key.