Research On The Construction And Related Properties Of Two Quantum Secret Sharing Schemes

Quantum secret sharing is an important issue in quantum cryptography,which combines classical secret sharing and quantum theory and plays an important role in applied cryptography.It means that the dealer can divide quantum or classical secret information into several shares and sent them to participants,only authorized participants can recover the secret,and no one or more unauthorized participants can recover the secret.In the(t,n)threshold secret sharing scheme,the dealer divides the secret into n shares and send them to t participants,of which any t or more participants can recover the secret,but less than t participants cannot recover the secret.Many schemes have been proposed while neither considers two main security issues:the attacker may pretend to be the dealer to send false information to the participants and some participants may provide the wrong shares,causing them to be unable to recover the correct secret.Therefore,the verifiability of the scheme appears especially important.At the same time,with the advantages of both classical and quantum secret sharing,many practical hybrid secret sharing scheme also has been proposed.In this paper,we propose a verifiable quantum secret sharing scheme and a hybrid verifiable quantum secret sharing scheme.The main research results are as follows.(1)A(t,n)threshold quantum secret sharing scheme based on d-dimensional single qudit,mutually unbiased basis and asymmetric bivariate polynomial is proposed.It can detect frauds form certain internal participants or external attackers.The proposed scheme has the following advantages.During the secret distribution phase,the distributor chooses an asymmetric binary polynomial to replace the original unary polynomial.The classical information of the participants' unitary transformation is obtained by their respective secret shares,which will be supervised by the dealer so as to make sure that participants are honest;The pair of keys can ensure the identity authentication between them,so as to guarantee that the identity of the authorized user is not stolen by the eavesdropper,thereby realizing the practicality and feasibility of the scheme;If a dishonest participant is found during the secret sharing phase,the dishonest participant will be found and removed.In the next secret sharing process,the dealer simply re-prepares a binary polynomial and a quantum state to recover the secret,which will prevent internal attacks;The classic information exchanged by the participants during the secret recovery phase can be protected by paired keys,so that the pair of participants can distinguish each other's identities to achieve identity authentication and also prevents external attacks in terms of computing security.(2)With the advantages of classical and quantum secret sharing scheme,a practical hybrid quantum secret sharing scheme based on mutually unbiased basis and monotone span program is proposed.It uses a d-dimensional state(qudit)instead of a 2-dimensional state(qubit).The participants can check the authenticity of the recovered secret and it needs fewer quantum resources and quantum operations.It has general access structure and reduces the communication costs and computation complexity.In addition,the correctness,verifiability and security analysis of the scheme have been proved.A specific example and a comparison are given to further clarify the advantages and practicality of our scheme.