Research On Cloud-aided Secrete Sharing Scheme And Its Applications

Secret sharing is one of critical technologies in cryptography,which employs the threshold theory to divide a secret into several parts and gives them to multiple participants for storage so that authorized subsets of participants can cooperate to recover the original secret,but the unauthorized subsets cannot obtain any information about the secret.Secret sharing technology guarantees the security and integrity of information and enhances the stability of the information system.However,some existed threshold secret sharing schemes need a lot of repeated calculation and complicated communication,which will inevitably affect the execution efficiency of the system in practical applications.Therefore,how to improve the system's execution efficiency and ensure the fairness of participants while guaranteeing the security and integrity of secret information has become a current hot research topic.This thesis makes a study on the basic secret-sharing model and cloud computing security,divides the secret sharing model into two parts: trusted distribution center model and no distribution center model,and proposes the corresponding cloud assistance schemes for the two models.Given the trusted distribution center model,this thesis proposes a cloud-aided efficient and fair secret sharing scheme,taking into account the problems of repeated calculation,complex communication,and participant fairness in the Shamir(t,n)threshold sharing scheme.This scheme outsources the reconstruction computation to the cloud server,simplifies the communication mode in the reconstruction phase,and presents a matrix operation to figure out the secret,which replaces the original Lagrange interpolation algorithm,in order to avoid the cloud server attention.To protect the privacy of secret share and original secret,we use the additive homomorphism of polynomials to encrypt secret shares.Besides,this scheme proposes an effective verification scheme to guarantee the fairness of participants.For the no distribution center model,a cloud-aided secret sharing scheme without distribution center is proposed.In the secret distribution phase,we use the additive homomorphism of secret sharing to achieve the purpose of participants' collaborative selection of secret and secret shares,and design a practical verification method to verify the validity of secret shares.In the secret reconstruction phase,this scheme adopts the same model as a cloud-aided efficient and fair secret sharing scheme,which outsources the reconstructed computing to the cloud server,guarantees the security of secret share and original secret and improves the execution efficiency of the system.Based on the two proposed schemes,we design an application scheme for group key agreement in the sensor network.The scheme utilizes the feature of symmetric polynomials to guarantee the fairness of each node.It uses the cloud to assist computing to improve the efficiency of group key agreement while ensuring the security of key.This thesis analyzes two cloud-assisted secret sharing schemes and one group key agreement scheme from three aspects of correctness,security,and efficiency.The analysis results show that the two cloud-assisted secret sharing schemes can protect the secret and its shares,ensure participants' fairness,and improve efficiency.The group key agreement scheme is easy to implement and has high security.