Securely utilizing external computing power

Suppose a weak power device Alice (e.g. a smart card) has some private program p. When carried outside, she may capture some private data x and want to compute p(x) but lacks the resources to do it. This paper presents a solution that allows a semi-honest Bob to execute the program in such an oblivious way that both x and p are computationally hidden and p(x) is disclosed to Bob only if Alice so wishes. We describe a procedure of encrypting a general program as well as explore the information hiding properties. Our solution is generic for most deterministic polynomial-time programs and it provides a programming interface for Alice, a compiler for Carol and a circuit evaluator program for Bob.