Verifiable outsourcing computation for modular exponentiation from shareable functions

Abstract

Verifiable computation (VC) enables a computationally weak client to outsource the computation of a function f to a more powerful but untrusted server. The server returns an answer that allows the client to recover the correct result, accompanied by a proof of correctness. The basic requirement of a VC scheme is efficiency, i.e., the time consuming in preparing its input and verifying the server’s proof must be less than the time required to compute the function on its own. In this paper, we propose a novel outsourcing scheme for modular exponentiation from shareable functions, which is secure even in the presence of adaptive adversaries. Compared with previous works, our algorithm is superior in both efficiency and checkability. In order to keep the exponent privacy, our algorithm invokes the less subroutine, which accounts for the largest proportion of the time spent. The client can detect the error with overwhelming probability. We then gave a comparation that demonstrates the efficiency of the proposed outsourcing algorithm and scheme. Finally, we propose a generic scheme for shareable function family, and analyze the concrete security.