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

Verifiable secret sharing (VSS) is an important technique which has been used as a basic tool in distributed cryptosystems, secure multi-party computations, as well as safe guarding some confidential information such as cryptographic keys. By now, some secure and efficient non-interactive VSS schemes for sharing secrets in a finite field have been available. In this paper, we investigate verifiably sharing of a secret that is an element of a bilinear group. We present an efficient and informationtheoretical secure VSS scheme for sharing such a secret which may be a private key for a pairing based cryptosystem. 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 similar protocols available. We also demonstrate two typical applications of our proposed VSS scheme. One is the sharing of a secret key of Boneh and Franklin's identity-based encryption scheme, and the other is the sharing or the distributed generation of a secret key of the leakage resilient bilinear ElGamal encryption scheme.