Research Of Verifiable Multi-Secret Sharing Scheme

Secret sharing is a method used to distribute, preserve and restore the secret information. It provides a very effective approach for key management and has become an important branch of modern cryptography and information security. Verifiable secret sharing scheme is a special secret sharing scheme which can prevent the dealer and participants from cheating effectively. Publicly verifiable secret sharing is an improvement of verifiable secret sharing. In a publicly verifiable secret sharing, anyone can verify the effectiveness of secret shares. Verifiable multi-secret sharing scheme can detect the cheating of dealer and participants effectively, but also can share several secrets in one secret sharing process. Further studies on verifiable multi-secret sharing scheme are done from two aspects of publicly verifiability and dynamic updating of secret shares. Main contributions are as follows.Focus on publicly verifiability of secret sharing scheme based on bilinear pairing, a pairing-based publicly verifiable multi-secret sharing scheme is presented by combining Hermite interpolation polynomial. The secret polynomial is reconstructed by making use of Hermite interpolation theorem. It breaks the limitation that traditional publicly verifiable secret sharing schemes are constructed only by Lagrange interpolation polynomial or Chinese remainder theorem. In addition, multiple secrets can be shared in one secret sharing process. Under the assumptions of elliptic curve discrete logarithm problem and bilinear Diffie-Hellman problem, this scheme can effectively resist internal and external attacks and has better security.In order to solve the problem that the dynamical refreshment of secret shares and public verifiability could not be satisfied simultaneously in previous multi-secret sharing schemes, a publicly verifiable and renewable multi-secret sharing scheme is proposed. The updated polynomials are constructed by using a one-way hash chain, which can make secret shares be updated periodically. The verification information is generated during the process of secret distribution. According to the public information, anyone could verify the validity of secret shares and renewed shares. Cheating of dealer and participants can be detected in time.The accuracy, security and performance of these schemes are analyzed and compared in detail. Analysis results show that the two schemes we proposed are correct and have better security and practicability.