New algorithm for secure outsourcing of modular exponentiation with optimal checkability based on single untrusted server

Nowadays, cloud computing is increasingly popular. As its important application, outsourcing has aroused great concern. Modular exponentiation is an expensive discrete-logarithm operation and it is difficult for users to calculate locally. Therefore, securely outsourcing modular exponentiation to cloud is a good choice for resource-limited users to reduce computation overhead. In this paper, to outsource modular exponentiation calculation, we dope out a fully verifiable secure outsourcing scheme with single server, so as to eliminate the collusion attacks which occur in algorithms based on two untrusted servers. Meanwhile, our algorithm allows outsourcers to detect any misbehavior with probability 1, which means the checkability of our algorithm shows a significant improvement in comparison to other single server based schemes. Furthermore, to protect data privacy, we propose a new division method to hide the primitive outsourced data. Compared with the state-of-the-art schemes, our secure outsourcing algorithm has an outstanding performance in both efficiency and checkability.