A ($t$, $n$) threshold quantum secret sharing (QSS) is proposed based on a single $d$-level quantum system. It enables the ($t$, $n$) threshold structure based on Shamir's secret sharing and simply requires sequential communication in the $d$-level quantum system to recover secret. Besides, the scheme employs an additional qudit to detect cheats and eavesdropping during secret reconstruction, and allows a participant to use the share repeatedly. Analyses show that the proposed scheme is resistant to typical attacks. The scheme is scalable in the number of participants and easier to realize compared to related schemes. More generally, our scheme also presents a generic method to construct new ($t$, $n$) threshold QSS schemes based on $d$-level quantum system with other classical threshold secret sharing.
(t, n) Threshold Quantum Secret Sharing based on a Single d-level Quantum System
A (t, n) threshold quantum secret sharing (QSS) is proposed based on a single d-level quantum system. It enables the (t, n) threshold structure based on Shamir's secret sharing and simply requires sequential communication in the d-level quantum system to recover secret. Besides, the scheme employs an additional qudit to detect cheats and eavesdropping during secret reconstruction, and allows a participant to use the share repeatedly. Analyses show that the proposed scheme is resistant to typical attacks. The scheme is scalable in the number of participants and easier to realize compared to related schemes. More generally, our scheme also presents a generic method to construct new (t, n) threshold QSS schemes based on d-level quantum system with other classical threshold 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 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.
(t,n) Threshold d-level quantum secret sharing based on quantum Fourier transformation
Quantum secret sharing (QSS) is an important branch of secure multiparty quantum computation. Several schemes for (n,n) threshold QSS based on quantum Fourier transformation (QFT) have been proposed. Inspired by the flexibility of (t,n) threshold schemes, Song {\it et al.} (Scientific Reports, 2017) have proposed a (t,n) threshold QSS utilizing QFT. Later, Kao and Hwang (arXiv:1803.00216) have identified a loophole in the scheme but have not suggested any remedy. In this present study, we have proposed a (t,n) threshold QSS scheme to share a d dimensional classical secret. This scheme can be implemented using local operations (such as QFT, generalized Pauli operators and local measurement) and classical communication. Security of the proposed scheme is described against outsider and participants' eavesdropping.
Abstract Threshold quantum secret sharing is a typical method for quantum secret sharing (QSS) schemes. In this paper, we propose a verifiable t , n threshold QSS scheme based on the d -dimensional Bell state and asymmetric binary polynomial. In this scheme, the dealer encodes the secret using the asymmetric binary polynomial and generates the corresponding secret share for each participant. Then, the dealer prepares the d -dimensional Bell state, and the participants perform corresponding unitary operations on the particles in transmission to recover the secret. With the hash function and the session key pairs, not only the cheating behavior of the dishonest participants can be detected, but also the specific cheaters can be identified. Furthermore, we consider the case when no less than t participants cooperate to recover the secret, which makes the proposed scheme more practical. Analyses show that the scheme can resist forgery attack, collusion attack and other common attacks.
Abstract Threshold quantum secret sharing is a cryptography technique for dividing and reconstructing secret information. The dealer shares a secret based on quantum mechanics principles, and a subset of participants cooperate to recover that secret. For example, in k , n quantum threshold scheme and n , n quantum threshold scheme, the former can only reconstruct the secret when at least k shares are collected. The latter requires all n shares to be collected to reconstruct the secret. However, in real scenarios, the priority of participant identities may vary. In order to meet the actual needs of participants with different rights, this paper proposes a w , ω , n quantum secret sharing (QSS) scheme. When the sum of participants’ weights w is greater than or equal to a threshold ω, they can cooperate to reconstruct the secret. In order to achieve this, this paper uses the entangled state of single particles and constructs a verifiable QSS scheme based on the Chinese remainder theorem. Significantly, in case of a dishonest participant, the dealer can delete the participant before recovering the secret to ensure the security of the communication. This scheme is more flexible than other threshold protocols. At the same time, it reduces the communication cost of the participants. In addition, security analysis shows that the scheme resists typical external and internal attacks.
We present DQ-(5,11), a dealer-based (5,11) threshold quantum secret sharing (QSS) scheme where any 5 of the 11 participants can find a dealer's secret and 4 or fewer get nothing about it. A key point is that, due to the Cleve-Gottesman-Lo no-cloning bound, there is only a (k,n) threshold scheme for any quantum secret if n < 2k. Since 11≥10, is a (5,11) quantity, the threshold scheme is impossible for quantum secrets, and in any (5,11) quantum secret sharing scheme there is a classical secret that is encrypted in a way that is protected by quantum communication. DQ-(5,11) is a combination of Shamir's polynomial sharing over GF13 and a single-qudit reconstruction in dimension d=13. Each of the five cooperating participants in DQ-(5,11) performs one phase operation with the share of the quantum secret and a zero-sum mask so that the intermediate states will not have any partial sum. Decoy qudits from two mutually unbiased bases detect eavesdropping, and a dealer-published commitment lets participants check the reconstructed value. We achieve correctness of all 462 subsets of the network, information-theoretic secrecy against coalitions of up to four insiders and a requirement for the success of intercept-resend attacks to be (d+1)/2d)m for m decoys (8.6×10-9) for m=30). We use numerical data to verify the deterministic reconstruction for all 2,310 runs and show the effect of depolarizing noise (79.1% success at 5% noise at each stage) and channel loss. Furthermore, we compare our orbital-angular-momentum and time-bin qudit model to Trojan-horse countermeasures and other schemes.
Quantum secret sharing (QSS) is a cryptographic protocol in which a quantum secret is distributed among a number of parties where some subsets of the parties are able to recover the secret while some subsets are unable to recover the secret. In the standard ((k, n)) quantum threshold secret sharing scheme, any subset of k or more parties out of the total n parties can recover the secret while other subsets have no information about the secret. But recovery of the secret incurs a communication cost of at least k qudits for every qudit in the secret. Recently, a class of communication efficient QSS schemes were proposed which can improve this communication cost to d−k+1d by contacting d ≥ k parties where d is fixed prior to the distribution of shares. In this paper, we propose a more general class of ((k, n)) quantum secret sharing schemes with low communication complexity. In these schemes the combiner can contact any d parties at the time of recovery where k ≤ d ≤ n. This is the first such class of universal communication efficient quantum threshold schemes.