An Efficient Instance Hiding Scheme

Delegating computation, which is applicable to many practical contexts such as cloud computing or pay-TV system, concerns the task where a computationally weak client wants to securely compute a very complex function f on a given input with the help of a remote computationally strong but untrusted server. The requirement is that the computation complexity of the client is much more efficient than that of f, ideally it should be in constant time or in NC0. This task has been investigated in several contexts such as instance hiding, randomized encoding, fully homomorphic encryption, garbling schemes, and verifiable scheme. In this work, we specifically consider the context where only the client has an input and gets an output, also called instance hiding. Concretely, we first give a survey of delegating computation, we then propose an efficient instance hiding scheme with passive input privacy. In our scheme, the computation complexity of the client is in NC0 and that of the server is exactly the same as the original function f. Regarding communication complexity, the client in our scheme just needs to transfer 4textbarftextbar + textbarxtextbar bits to the server, where textbarftextbar is the size of the circuit representing f and textbarxtextbar is the length of the input of f.