Private Data Base Access Schemes Avoiding Data Distribution

In this thesis we introduce and solve three privacy problems in Secure Database Access protocols: Database Privacy, the Data Replication Problem, and the Secure user Identity problem. Database Privacy is concerned with keeping the databases information secure from the user. The Data Replication problem (DRP) deals with a new security concern for databases that emanates from the need to replicate and distribute their contents in order to achieve security for the user. The Secure user ID problem is concerned with keeping private the user's identity, so that no information can be associated with or learned about that identity. Our results rely on an existing Private Information Retrieval scheme which achieves privacy for the user's query by relying on the multiple database model. This model allows for information theoretic results and sublinear communication complexity in the size of the database. We present two schemes which solve, in addition to what was achieved previously, Database Privacy and the Data Replication problem. We achieve two different degrees of security for DRP. The first one is private-datadistribution which means that all the databases in the scheme are k-wise independent for some constant k. The second is no-data-distribution security which means that the database's in the scheme contain data that is completely independent. The user's security in our scheme relies on the Private Information Retrieval scheme introduced in [14] which guaranties that the message the user sends to a database is uniformly distributed over all possible queries. We show two reductions: Theorem: For any k > 2 given any Private Information Retrieval k-database scheme for n data bits with communication complexity R(k, n) there exists a privatedata-distribution and database private 2k-database scheme with communication complexity O(R(k, n) log(n)) where each database holds O(n) bits. Theorem: For any k > 2 given any retrieval k-database scheme for n data bits with communication complexity R(k, n) there exists a no-data-distribution and database private 2k-database scheme with communication complexity O(R(k, n) log(n)) where each database holds O(n) bits. Secure ID In addition, we solve the Secure ID problem by presenting a protocol for a network of a user U, n databases of size m with an additional server S. A database in the network does not know whether U asked him a query or asked a query from another database. Therefore, we say that he does not know the identity of the users that are querying him. The communication complexity of that scheme is O(log(n)R(n, kl) + log(m)R(m, k2)) for constants k1 and k2. Thesis Supervisor: Shafi Goldwasser Title: RSA Professor