(t, n) Threshold d-Level Quantum Secret Sharing

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 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.

Quantum Data Aggregation Using Secret Sharing and Genetic Algorithm

“…Assume Bobi denote set of all 1-hop neighbors of Alice where i<n in a quantum sensor network. Initially Alice randomly picks a polynomial f(x) of degree t such that the coefficients belongs to Zd t-1 [28] , a finite field where d is a prime number and n ≤ d ≤ 2n…”

“…Algorithm The purpose of this phase is to identify the compromised node by reconstructing the secret from any t nodes secret share out of n participants. Alice as in [28] prepares qudit particles and each particle has t qubits where t = [log2 d] and applies the QFT to the first particle. Alice performs respectively d-level CNOT operation on the particle r for (r = 1, 2, 3, …, t) and sends the particle |k〉r (r = 1,2, 3, …, t) to the corresponding participant Bobras in [28] through the authenticated quantum channel.…”

Computing on quantum shared secrets for general quantum access structures

“…While some of the well-established protocols have been experimentally performed [10,11,12], and even commercialized, new ones with different domains of applications are being proposed. Blind quantum computation [13,14], quantum homomorphic encryption [15], sharing of classical data [16,17,18] and quantum states [5,6,7,19], proactive quantum secret sharing [20], and even performing quantum computation on shared secrets [21] are good examples of these protocols.…”

Verifiable threshold quantum secret sharing with sequential communication

“…In this scheme, a secret is initially embedded into quantum states; then, any t or more than t participants sequentially apply Hadamard transformation and proper rotation operations on the quantum state; finally the secret can be regained after applying certain measurements on the state. Several quantum computation algorithms, such as phase shift operation or Quantum Fourier Transform, are also introduced to embed classical shares into quantum states [32][33][34].…”