| In this thesis, we study Private Information Retrieval and Oblivious Transfer, two strong cryptographic tools that are widely used in various security-related applications, such as private data-mining schemes and secure function evaluation protocols. The first non-interactive, secure dot-product protocol, widely used in private data-mining schemes, is proposed based on trace functions over finite fields. We further improve the communication overhead of the best, previously known Oblivious Transfer protocol from O ((log(n))2) to O (log(n)), where n is the size of the database. Our communication-efficient Oblivious Transfer protocol is a non-interactive, single-database scheme that is generally built on Homomorphic Encryption Functions. We also introduce a new protocol that reduces the computational overhead of Private Information Retrieval protocols. This protocol is shown to be computationally secure for users, depending on the security of McEliece public-key cryptosystem. The total online computational overhead is the same as the case where no privacy is required. The computation-saving protocol can be implemented entirely in software, without any need for installing a secure piece of hardware, or replicating the database among servers. |
