Most of Quantum Secret Sharing(QSS) are (n, n) threshold 2-level schemes, in which the 2-level secret cannot be reconstructed until all n shares are collected. In this paper, we propose a (t, n) threshold d-level QSS scheme, in which the d-level secret can be reconstructed only if at least t shares are collected. Compared with (n, n) threshold 2-level QSS, the proposed QSS provides better universality, flexibility, and practicability. Moreover, in this scheme, any one of the participants does not know the other participants’ shares, even the trusted reconstructor Bob 1 is no exception. The transformation of the particles includes some simple operations such as d-level CNOT, Quantum Fourier Transform(QFT), Inverse Quantum Fourier Transform(IQFT), and generalized Pauli operator. The transformed particles need not to be transmitted from one participant to another in the quantum channel. Security analysis shows that the proposed scheme can resist intercept-resend attack, entangle-measure attack, collusion attack, and forgery attack. Performance comparison shows that it has lower computation and communication costs than other similar schemes when 2 < t < n − 1.

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To detect frauds by a dealer or some participants, researchers have proposed verifiable threshold quantum state sharing (VTQSTS) schemes. However, the existing VTQSTS schemes either have lowcomputation efficiency or weak security. In this paper, a verifiable (t, n) threshold quantum state sharing against denial attack (VTQSTS-ADA) scheme is proposed to overcome the above limitations, in which the dealer Alice encodes the quantum secret sequence into two quantum message sequences and a quantum signature sequence. First, for each participant in the authorization subset, the received quantum signature sequence is validated by a quantum verification algorithm, and then a unitary transformation with a rotation key is performed on the received quantum message sequence; next, a new quantum signature sequence is generated by a quantum signature algorithm with the signature key. Each participant sends the new message sequences and signature sequence to the next participant. The original quantum secret sequence can be reconstructed when t(t ≤ n) participants collaborate. The security analysis shows that the proposed VTQSTS-ADA scheme can detect the fraud instances raised by the dealer and participants and provide stronger security such as resisting denial attacks and man-in-middle attacks compared with the existing schemes. The performance analysis shows that the proposed VTQSTS-ADA scheme outperforms the earlier VTQSTS scheme and is comparable to the recent scheme.INDEX TERMS Threshold quantum state sharing, quantum state digital signature, denial attack, man-in-middle attack.