Secret-shared RAM indefinite private and secure RAM execution of perfectly unrevealed programs

Secure and private computations over random access machine (RAM) are preferred over computations with circuits or Turing machines. Secure RAM executions become more and more important in the scope of avoiding information leakage when executing programs over a single computer, as well as the clouds. In this paper, we proposed a novel scheme for evaluating RAM programs without revealing any information on the computation, including the program, the data, and the result. We use Shamir Secret Sharing to share all the program instructions and the private string matching technique to ensure the execution of the right instruction sequence. We stress that our scheme obtains information-theoretical security and does not rely on any computational hardness assumptions.