A convinced commitment scheme for bilinear Diffie-Hellman problem

In 2010, Tseng and Wu proposed a convinced Diffie-Hellman computation scheme. Due to the proposed scheme can provide the convinced commitment property for the Diffie-Hellman problem, it may provide some specific security properties for security mechanisms such as group key agreement protocols with identifying malicious participants and secret sharing schemes with publicly verifiable property. Over the last few years, ID-based cryptography using bilinear pairing systems has received much attention from cryptographic researchers and its security is based on the related bilinear Diffie-Hellman assumptions. In this article, we propose a new convinced commitment scheme for bilinear Diffie-Hellman problem by extending Tseng and Wu's scheme. The proposed scheme can also be embedded in many ID-based group key agreement protocols and secret sharing schemes to provide extra security properties.