Department of Computer Engineering

The challenge we address in this thesis is to design a peer-to-peer threshold-based group key generation protocol where there is no centralized authority and peers do not learn anything about the generated key other than their shares albeit they are involved in the key generation. To address this challenge, we propose a password-authenticated threshold-based group key agreement protocol that resembles secret sharing. However, the construction of our proposal is the opposite. In legacy secret-sharing schemes, a trusted third party shares a secret value that it initially knows. In our proposal, principals collaborate to create shares without the knowledge of the constructed group key in a peer-to-peer fashion. We employ zero-knowledge protocols for verifying the authenticity of principals' contributions to the protocol. Zero-knowledge proofs help principals verify the veracity of data without sharing the data. In addition to the threshold-based group key agreement protocol, we also propose a novel zero-knowledge proof scheme based on equal partition problem on groups and prove that this novel zero-knowledge proof scheme is secure. We present the security and performance analysis of these two proposals that complement each other and show that they are secure and efficient.