Research On (t,n) Threshold Secret Sharing Scheme

Secret sharing is an important component of cryptography protocols which has a wide range of applications,such as key management,digital signatures and so on.In the(t,n)secret sharing scheme,a secret s is divided into n pieces called shares,which are then distributed among participants by the dealer.Only t or more participants can reconstruct the secret,and any t-1 participants cannot get any useful information about the secret.Unfortunately,the existing secret sharing schemes cannot apply to computationally weak devices and cannot efficiently guarantee fairness.In this paper,we proposed two novel secret sharing schemes.In order to solve the problems of the existing threshold secret sharing schemes such as user privacy leakage,inefficient secret sharing algorithm,and inapplicability to devices with weak computing power,we proposed an outsourcing secret sharing scheme based on homomorphism encryption.In the setting of outsourcing secret sharing,participants only need a small amount of decryption and verification operations,while the expensive reconstruction computation and verifiable computation can be outsourced to cloud service providers(CSP).The scheme does not require complex interactive argument or zero-knowledge proof.The malicious behavior of participants and CSP can be detected in time.Moreover,the CSP cannot get any useful information about the secret,and it is fair for every participant to obtain the secret.With the characteristics of decentralization,security and reliability of block chain technology,a fair hierarchical secret sharing scheme based on smart contract is proposed.In the scheme,secret shares are distributed to different levels of participants and any authorized subset of participants is able to recover the secret.Moreover,we proposed a secret sharing smart contract which is suitable for HTSS.Unlike previously proposed HTSS schemes,this is the first scheme that participants can reconstruct the secret fairly without relying on a trusted third party.Specifically,participants are required to initially put aside a certain amount of money,which will be paid back to them once they complete the protocol honestly.Otherwise the fuse will be given to the other participants for compensating them.That is to say,once the participants do not follow the protocol honestly,they would suffer financial penalties.Finally,we proved the security of the two schemes and given the corresponding formal proof.Moreover,we tested the schemes and compared them with other secret sharing schemes.