Abstract
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 Bob1 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.
Highlights
A dealer who wants to share a secret among a group of participants, usually splits the secret into a few pieces
The proposed Quantum Secret Sharing (QSS) scheme consists of three phases: initialization phase, share distribution phase, and secret reconstruction phase
After analyzing the existing QSS schemes, we find some schemes cannot resist collusion attack, in which some participants can collude to get the private information of other participants
Summary
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. Compared with (n, n) threshold 2-level QSS, the proposed QSS provides better universality, flexibility, and practicability 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 existing QSS schemes can be classified into two categories: (n, n) QSS2–12, 18–20 and (t, n) QSS10, 11, 13–17 For the former, the secret cannot be reconstructed until all n shares are collected. The related preliminaries are introduced including quantum Fourier transform (QFT) and inverse quantum Fourier transform (IQFT), generalized Pauli operator, and Shamir’s (t, n) threshold SS These preliminaries will be used in presenting (t, n) threshold QSS scheme. The t participants can reconstruct the original secret a0 based on the above Equation (6)
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