Preservation of privacy in public-key cryptography

This work in this thesis can be divided into two aspects. Firstly, we consider confidentiality and anonymity under a scenario where an untrusted third party is involved in a cryptographic system to check all the messages received. Then we study confidentiality, anonymity and integrity under a special atack called related-key attack. Lastly, we pay attention to data integrity in the setting of related-key attacks, and show how data integrity can be broken in a proof of retrievability system by a related-key attack and show how data integrity can be broken in a proof of retrievability system by a related-key attack adversary and how to prevent such attacks.