Efficient and Information-Theoretical Secure Verifiable Secret Sharing over Bilinear Groups

Verifiable secret sharing （VSS） is an impor- tant technique which has been used as a basic tool in dis- tributed cryptosystems, secure multi-party computations, as well as safe guarding some confidential information such as cryptographic keys. By now, some secure and efficient non-interactlve VSS schemes for sharing secrets in a fi- nite field have been available. In this paper, we investi- gate verffiably sharing of a secret that is an element of a bilinear group. We present an efficient and information- theoretical secure VSS scheme for sharing such a secret which may be a private key for a pairing based cryptosys- tern. Our performance and security analysis indicates that the newly proposed scheme is more efficient and practical while enjoys the same level of security compared with sim- ilar protocols available. We also demonstrate two typical applications of our proposed VSS scheme. One is the shar- ing of a secret key of Boneh and Franklin＇s identity-based encryption scheme, and the other is the sharing or the dis- tributed generation of a secret key of the leakage resilient bilinear EIGamal encryption scheme.