CExp: secure and verifiable outsourcing of composite modular exponentiation with single untrusted server

Outsourcing computing allows users with resource-constrained devices to outsource their complex computation workloads to cloud servers that may not be honest. In this paper, we propose a new algorithm for securing the outsourcing of composite modular exponentiation, which is one of the most complex computing tasks in discrete-log based cryptographic protocols. Unlike algorithms based on two untrusted servers, we outsource modular exponentiation operation to only a single server, which eliminates the potential for a collusion attack when using two servers. Moreover, our proposed algorithm can hide the base and exponent of the outsourced data, which prevents the exposure of sensitive information to cloud servers. In addition, compared with the state-of-the-art algorithms, our scheme has remarkably better checkability. The user could detect any misbehavior with a probability of one if the server returns a fault result.