Abstract
The dishonest participants have many advantages to gain others’ shares by cheating in quantum secret sharing (QSS) protocols. However, the traditional methods such as identity authentication and message authentication can not resolve this problem due to the reason that the share has already been released to dishonest participants before realizing the deception. In this paper, a continuous variable QSS (CVQSS) scheme is proposed with fairness which ensures all participants can acquire or can not acquire the secret simultaneously. The quantum channel based on two-mode squeezing states provides secure communications through which it can send shares successfully, as long as setting the squeezing and modulation parameters according to the quantum channel transmission efficiency and the Shannon information of shares. In addition, the Chinese Remainder Theorem (CRT) can provides tunable threshold structures according to demands of the complex quantum network and the strategy for fairness can be incorporated with other sharing schemes, resulting in perfect compatibility for practical implementations.
Highlights
The secret sharing (SS) plays a significant role in cryptography
The quantum channel based on two-mode squeezing states provides secure communication, which is proved that it can send shares successfully, as long as setting proper the squeezing and modulation parameters according to the quantum channel transmission efficiency and the Shannon information of shares
We have suggested a continuous variable QSS (CVQSS) scheme with fairness to resist dishonest participants keeping silence or returning error shares after receiving other ones’ shares, which would be detected in verifying process
Summary
The secret sharing (SS) plays a significant role in cryptography. Since 1999, Hillery et al [1] firstly invited SS to the quantum domain by applying three-particle and four-particle GHZ states, more and more. In quantum domain, Liu et al [18] designed a QSS protocol based on partially and maximally entangled states, in which a secure and fair reconstruction mechanism is firstly organized to realize each participant can learn or cannot learn the secret simultaneously. In order to ensure every participant learn or do not learn the secret simultaneously without the simultaneous channel, a fair construction is designed, in which a check sequence is used to hide real secret sequence, a determine pointer is used to find the hidden secret and a verify sequence is used to verify the recovered message This fair protocol can be incorporated with other sharing schemes.
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