We present the concept of threshold collaborative unitary transformation or threshold quantum cryptography, which is a kind of quantum version of threshold cryptography. Threshold quantum cryptography states that classical shared secrets are distributed to several parties and a subset of them, whose number is greater than a threshold, collaborates to compute a quantum cryptographic function, while keeping each share secretly inside each party. The shared secrets are reusable if no cheating is detected. As a concrete example of this concept, we show a distributed protocol (with threshold) of conjugate coding.
Quantum secret sharing is an important branch of quantum cryptography, and secure multi-party quantum key distribution protocols can be constructed using quantum secret sharing. In this paper, we construct a quantum secret sharing scheme built on a constrained (t, n ) threshold access structure, where n is the number of participants and t is the threshold number of participants and the distributor. Participants from two different sets perform the corresponding phase shift operations on two particles in the GHZ state passed to them, and then t−1 participants with the distributor can recover the key, where the participant recovering the key measures the particles received by himself and finally obtains the key through the collaboration of the distributors. Security analysis shows that this protocol can be resistant to direct measurement attacks, interception retransmission attacks, and entanglement measurement attacks. This protocol is more secure, flexible, and efficient compared with similar existing protocols, which can save more quantum resources.
We propose a (t, n)-threshold quantum secret sharing protocol of secure direct communication following some ideas of Zhang's protocol [Phys. Lett. A 342 (2005) 60] and Tokunaga et al.'s protocol [Phys. Rev. A 71 (2005) 012314]. The sender distributes the classical secret shares to his or her n agents and each agent owns a secret share in advance. The sender's secure direct communication message can be extracted by an agent subset by collaboration in such a way that at least t or more agents can obtain the secret message with the mutual assistances but any t - 1 or fewer agents cannot. In contrast to the previous multiparty quantum secret sharing protocols in which the sender's secret message can be recovered only if all the agents collaborate, our protocol is more practical and more flexible.
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.
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.
A quantum secret sharing scheme is a cryptographic protocol by which a dealer can share a secret among a group of
n players so that only certain subsets of players can recover the secret by collaboration. In this paper we propose communication efficient quantum threshold secret sharing schemes. They minimize the amount of quantum communication required to reconstruct the secret when more than the necessary number of players collaborate. They are based on a class of staircase codes proposed by Bitar and El Rouayheb. In a standard
((k,n)) quantum threshold scheme, any subset of
k or more players can recover the secret. The quantum communication cost for reconstruction in such schemes is
k qudits for each secret qudit. Using the proposed construction, any subset of $d\ensuremath{\ge}k$ players can also collaborate to recover the secret with a communication cost of
d qudits for $d\ensuremath{-}k+1$ secret qudits. In other words, for the proposed schemes the quantum communication cost is only $\frac{d}{d\ensuremath{-}k+1}$ qudits for every secret qudit. For
d>k, proposed schemes are communication efficient with respect to standard schemes; and when $d=2k\ensuremath{-}1$, the quantum communication cost is reduced by a factor
O(k). Further, when $n=2k\ensuremath{-}1$, the proposed schemes have optimal communication cost for secret reconstruction.
Abstract: Cryptography is the science of keeping private information from unauthorized access of ensuring data integrity and authentication, and it is the strongest tool for controlling against much kind of security threats. Role of cryptography appears in many secured area like government agencies, large banks, telecommunications companies and other corporations who handle sensitive or military data. Quantum cryptography is an emerging technology in which two parties may simultaneously generate shared, secret cryptographic key material using the transmission of quantum states of light. This paper consists of the main aspects of quantum cryptography and it investigates the information about where and all quantum cryptography takes place. Keywords- cryptography; photons; quantum key distribution; Protocols; I.