Research On Key Technologies Of(t,n) Threshold Secret Shring

Secret sharing is the foundation of cryptography and has an important position in modern cryptography.The idea of secret sharing is to split the secret key into different shares,and the shares are kept by different participants.Secret sharing is an important cryptographic primitive and has a wide range of applications in politics,economy,military affairs,and diplomacy.However,the existing secret sharing schemes have problems such as conspiracy of participants,unfair calculation,and low efficiency of secret verification algorithms.The paper combines cloud outsourcing computing,reputation model,lattice theory,and blockchain technology to study secret sharing,and designs corresponding secret sharing schemes.The main research contents are as follows:(1)In order to solve the problem of the low efficiency of the secret verification algorithm in the existing hierarchical secret sharing schemes,we proposed an outsourcing hierarchical secret sharing(HTSS)scheme based on reputation.In this scheme,participants from different levels need only a few operations to reconstruct the secrets fairly,and the scheme only needs to run one time.The cloud service provider(CSP)uses powerful computing resources to help participants complete homomorphic encryption and complex verification operations,and the CSP cannot obtain any valuable information about the secret.The scheme does not require complex interactive argument and can detect malicious behaviors of participants and CSP in time.The reputation system can effectively prevent participants from collusion with the server,assuming that each participant has its own reputation value.The reputation value of participants who deviate from the protocol will decrease,and the reputation value of participants who honestly abide by the protocol will increase.(2)In order to solve the problem of unfair calculation and the problem of not being able to resist quantum attacks in existing secret sharing,we proposed a lattice-secret sharing scheme based on blockchain.The scheme does not require dealer to repeatedly distribute secret shares,and each share can be better hidden and can be reused.The scheme is based on a one-way function of lattice,which can effectively resist quantum attacks.Blockchain technology can effectively guarantee the fairness.Participants make a commitment to the secret shares and submit a deposit to blockchain.The commitment is public,and all participants can get the secret shares at the same time.When the participant completes the protocol honestly,the deposit will be returned to their account;when the participant deviates from the protocol,the corresponding financial penalty will be imposed,and other participants can receive financial compensation.The scheme ensures that each participant has an incentive to execute the protocol honestly.