EF-CRT: Group Key Update and Batch Verification Based on Euler Function and Chinese Remainder Theorem for Edge-Fog Computing Networks

In edge-fog computing networks, it is very crucial to ensure that group keys are secure and reliable. In recent years, there has been much interest in group key updating schemes based on Chinese remainder theorem (CRT). It is mostly necessary to utilize the extended Euclidean algorithm to compute the inverse element in conventional schemes. But it does not always exist an inverse element. It leads to the computation being complicated and infeasible. Thus, we propose a scheme for updating group keys and batch verification based on Euler function and Chinese remainder theorem (EF-CRT). Group keys can be constructed directly using Euler function without requiring inverse elements. In addition, we design a batch verification scheme using the updated group key. The proposed EF-CRT scheme accomplishes dynamic group key updates, message integrity authentication, forward and backward security, and conditional privacy protection. Simultaneously, we prove that the security of EF-CRT is existentially unforgeable under the chosen message attack. In experiments with the java pairing-based cryptography library, the proposed scheme shows efficiency both in computational and communication overhead.