Verifiable Secret Sharing Over Bilinear Groups And Its Applications

Verifiable secret sharing (VSS for short) is an important method for information security and data protecting. It has been extensively used in fields such as dis-tributed key generation(DKG for short), threshold cryptosystem, key escrow and secure multiparty computation. Many researchers have focused on VSS since the birth of its concept and some VSS schemes, especially in finite fields, have been well established by now. Recently, the bilinear pairing-based cryptography has re-ceived much attention from the research community. Many bilinear pairing-based cryptographic schemes and protocols have been available. As in many pairing-based cryptosystems, the secret keys are random elements in some bilinear groups, it is of great importance to investigate the verifiably sharing of such secrets, as well as the distributed generation of such secret keys.Thus, this thesis do deep and extensive researches on verifiable secret sharing over bilinear groups and its applications, and some results are gotten.For research on the schemes of verifiable secret sharing in bilinear groups, two efficient and computationally secure VSS schemes in bilinear groups are presented in this thesis. The first one uses the polynomial method to share a secret which is more or less similar with such schemes in existence but has lower computational cost than those existing schemes. The second one employs matrix as the tool for sharing and is often known as linear threshold VSS that includes the first one as a special case. And after that we propose two efficient and information-theoretic secure VSS schemes in bilinear groups:a polynomial one that is more efficient than similar schemes available, and a linear one that includes the former as a special case. Then for general VSS based on bilinear groups, we propose verifiable secret sharing scheme with vector space access structures for the first time. We also demonstrate the security and analyze the efficiency for the new scheme in this thesis.For research on the applications of verifiable secret sharing schemes in bilinear groups, we do a serious study with respect to secure distributed key generation and construct such protocol using our new proposed VSS scheme with vector space access structures in bilinear groups. At last for applications in threshold cryptosystem we primarily study the threshold ElGamal decryption from bilinear pairings and give such scheme.