Verifiable Outsourcing Computation of Modular Exponentiations with Single Server

Verifiable computation (VC) allows a computationally weak client to outsource evaluation of a function on many inputs to a powerful but untrusted server. In this paper, we propose an algorithm of verifiable outsourcing computation with single server on modular exponentiation, which has wide applications in public key cryptosystems. We also extend the algorithm to verifiable outsourcing of simultaneous modular exponentiations. The proposed two algorithms improve checkability based on one server compare with the previous ones, where the outsourcer can detect the failure with probability close to 1 if the server misbehaves. The experiments show that our algorithms are the implementations of secure and verifiable outsourcing for single modular exponentiation and simultaneous modular exponentiations.