Designing Secret Sharing Scheme Based On Generic Access Structure

Cryptography is the core technology of information security, in which the encryption and decryption, identity authentication, digital signature and private key exchange are important mechanism to protect information security. And the security of them is based on the secret of private key. Secret sharing can provide better protection mechanism for the security of private key. Therefore, secret sharing became a hot research topic in recent years.This thesis presents several kinds of secret sharing schemes, including threshold secret sharing scheme and the scheme based on general access structure, and proposes a plane-based access structure scheme, which improves the existing graph-based scheme to overcome their disadvantage. This scheme is based on the assumptions that if any two among a set of three participants in a graph contain an edge, then these participants constitute a prohibited structure which is not able to recover the master key. Otherwise, the set of three participants constitute an access structure which can recover the master key. This thesis proves the validity and security of the proposed scheme by theoretical analysis and experiment, and compares its performance to the existing graph-based schemes. The result shows that it has the properties of high efficiency, less storage overhead and high security. Moreover, it can efficiently validate the participant cheater.In order to extend the plane-based scheme, this thesis proposes a generic k-dimensional secret sharing scheme, in which the share distributed to every participant is a k-dimensional vector, and all vectors are linearly independent and satisfy a set of k-dimensional linear equations, where the constant is the sharing key. No less than k participants cooperation can recover the sharing key in secret recovery phase. This scheme has the property of better scalability, and it can conveniently add or delete participants, moreover, it can validate the participant cheater. The theoretical analysis shows that the scheme is feasible in computing performance, and has the property of high security.Both the proposed secret sharing schemes can be used in many applications, such as secure communication networks, and secure database systems. In particular, they are very important for access control in an application environment where the number of participants is large.