Remote data possession checking plays a crucial role in cloud data storage. It allows the owners to verify whether their data are correctly stored in the Cloud without downloading them. To solve this problem, there are many methods proposed such as MAC-based methods, RSA- based homomorphic methods and BLS-based homomorphic methods.This paper presents and compares auditing methods which are based on public key, including RSA- based homomorphic method, Paillier-based homomorphic method, and BLS-based homomorphic method.