Fully Verifiable Outsourcing of Single and Composite Modular Exponentiation with Single Untrusted Cloud Server

Modular exponentiation is considered one of the most widely used, yet costly operations in public-key cryptography, especially for resource-constrained devices in a peer-to-peer networks such as net of IoT or sensor devices. However, it can be computed at a relatively low cost with the help of outsourcing. The first contribution of this paper is investigating the security of the Su et al.’s scheme which, our first attack confirms that the verifiability of this scheme is less than the authors’ claim and our second attack reveals that a malicious server is able to forge user signature. The second contribution of this paper is investigating the verifiability of Ding’s scheme, a scheme previously claimed to provide high verifiability, and we shows that this scheme is not verifiable. The third contribution is centered around proposing two practical and secure outsourcing schemes for outsourc-ing computations of single and composite modular exponentiation, in the single-server model. It is worth noting that both of our proposed schemes offer higher efficiency and security than the previous schemes as their verifiability are equal to one, while the recorded verifiability of the previous schemes decreases by the number of exponentiations utilized.