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Register a new userA Verifiable Quantum Secret Sharing Scheme Based on a Single Qubit
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Added by
Zhihui Li
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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To detect frauds from some internal participants or external attackers, some verifiable threshold quantum secret sharing schemes have been proposed. In this paper, we present a new verifiable threshold structure based on a single qubit using bivariate polynomial. First, Alice chooses an asymmetric bivariate polynomial and sends a pair of values from this polynomial to each participant. Then Alice and participants implement in sequence unitary transformation on the $d$-dimensional quantum state based on unbiased bases, where those unitary transformations are contacted by this polynomial. Finally, security analysis shows that the proposed scheme can detect the fraud from external and internal attacks compared with the exiting schemes and is comparable to the recent schemes.
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In the $left( {t,n} right)$ threshold quantum secret sharing scheme, it is difficult to ensure that internal participants are honest. In this paper, a verifiable $left( {t,n} right)$ threshold quantum secret sharing scheme is designed combined with classical secret sharing scheme. First of all, the distributor uses the asymmetric binary polynomials to generate the shares and sends them to each participant. Secondly, the distributor sends the initial quantum state with the secret to the first participant, and each participant performs unitary operation that using the mutually unbiased bases on the obtained $d$ dimension single bit quantum state ($d$ is a large odd prime number). In this process, distributor can randomly check the participants, and find out the internal fraudsters by unitary inverse operation gradually upward. Then the secret is reconstructed after all other participants simultaneously public transmission. Security analysis show that this scheme can resist both external and internal attacks.
How to construct an ideal multi-secret sharing scheme for general access structures is difficult. In this paper, we solve an open problem proposed by Spiez et al.recently [Finite Fields and Their Application, 2011(17) 329-342], namely to design an algorithm of privileged coalitions of any length if such coalitions exist. Furthermore, in terms of privileged coalitions, we show that most of the existing multi-secret sharing schemes based on Shamir threshold secret sharing are not perfect by analyzing Yang et al.s scheme and Pang et al.s scheme. Finally, based on the algorithm mentioned above, we devise an ideal multi-secret sharing scheme for families of access structures, which possesses more vivid authorized sets than that of the threshold scheme.
In single-qubit quantum secret sharing, a secret is shared between N parties via manipulation and measurement of one qubit at a time. Each qubit is sent to all N parties in sequence; the secret is encoded in the first participants preparation of the qubit state and the subsequent participants choices of state rotation or measurement basis. We present a protocol for single-qubit quantum secret sharing using polarization entanglement of photon pairs produced in type-I spontaneous parametric downconversion. We investigate the protocols security against eavesdropping attack under common experimental conditions: a lossy channel for photon transmission, and imperfect preparation of the initial qubit state. A protocol which exploits entanglement between photons, rather than simply polarization correlation, is more robustly secure. We implement the entanglement-based secret-sharing protocol with 87% secret-sharing fidelity, limited by the purity of the entangled state produced by our present apparatus. We demonstrate a photon-number splitting eavesdropping attack, which achieves no success against the entanglement-based protocol while showing the predicted rate of success against a correlation-based protocol.
Secret sharing was proposed primarily in 1979 to solve the problem of key distribution. In recent decades, researchers have proposed many improvement schemes. Among all these schemes, the verifiable multi-secret sharing (VMSS) schemes are studied sufficiently, which share multiple secrets simultaneously and perceive malicious dealer as well as participants. By pointing out that the schemes presented by Dehkordi and Mashhadi in 2008 cannot detect some vicious behaviors of the dealer, we propose two new VMSS schemes by adding validity check in the verification phase to overcome this drawback. Our new schemes are based on XTR public key system, and can realize $GF(p^{6})$ security by computations in $GF(p^{2})$ without explicit constructions of $GF(p^{6})$, where $p$ is a prime. Compared with the VMSS schemes using RSA and linear feedback shift register (LFSR) public key cryptosystems, our schemes can achieve the same security level with shorter parameters by using trace function. Whats more, our schemes are much simpler to operate than those schemes based on Elliptic Curve Cryptography (ECC). In addition, our schemes are dynamic and threshold changeable, which means that it is efficient to implement our schemes according to the actual situation when participants, secrets or the threshold needs to be changed.
Reversible data hiding in encrypted domain (RDH-ED) schemes based on symmetric or public key encryption are mainly applied to the security of end-to-end communication. Aimed at providing reliable technical supports for multi-party security scenarios, a separable RDH-ED scheme for secret image sharing based on Chinese remainder theorem (CRT) is presented. In the application of (t, n) secret image sharing, the image is first shared into n different shares of ciphertext. Only when not less than t shares obtained, can the original image be reconstructed. In our scheme, additional data could be embedded into the image shares. To realize data extraction from the image shares and the reconstructed image separably, two data hiding methods are proposed: one is homomorphic difference expansion in encrypted domain (HDE-ED) that supports data extraction from the reconstructed image by utilizing the addition homomorphism of CRT secret sharing; the other is difference expansion in image shares (DE-IS) that supports the data extraction from the marked shares before image reconstruction. Experimental results demonstrate that the proposed scheme could not only maintain the security and the threshold function of secret sharing system, but also obtain a better reversibility and efficiency compared with most existing RDH-ED algorithms. The maximum embedding rate of HDE-ED could reach 0.5000 bits per pixel and the average embedding rate of DE-IS is 0.0545 bits per bit of ciphertext.
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