Secure Outsourcing Algorithms of Modular Exponentiations in Edge Computing

As one of the most expensive computations in public-key cryptosystems, modular exponentiation is typically out-sourced to the cloud servers. Traditional cloud-based outsourcing algorithms depend on multiple untrusted servers to guarantee the security, which may lead to vulnerability to the collusion attack. Although recent single-server multiple-requests outsourcing algorithms are more secure, they have to perform multiple requests to the single untrusted server to guarantee the security and checkability of the data, which will incur unacceptable latency and local computational costs. In comparison, the edge computing paradigm enhances security since it has multiple computational nodes, including some highly secure local computational nodes. In this paper, we propose the secure outsourcing algorithm of modular exponentiation for the edge computing paradigm. To address the dilemma that the computational resources of different nodes vary significantly, we design two lightweight algorithms to adaptively separate the modular exponentiation to the nodes based on the computational resources. To guarantee the outsourcing checkability, we propose a protocol verify the result returned from each node. We formally prove the security and checkability of our algorithm and validate the efficiency of our algorithm based on experiments and case studies.