Provably secure data hiding and tamper resistance for a simple loop program

We study the problem of computing with encrypted data. We propose a hiding scheme that allows a client to execute a simple loop program with real or complex inputs securely on a server. This is the first hiding scheme that we are aware of that applies to real and complex data. The scheme allows the client to efficiently determine with high probability whether the results returned by the server are correct. The scheme we propose uses new techniques that have not been used previously in this context.