Suppose that the renowned spymaster Alice controls a network of spies who all happen to be deployed in different geographical locations. Let us further assume that all spies have managed to get their hands on a small, albeit incomplete by itself, secret, which actually is just a part of a bigger secret. In this work, we consider the following problem: given the above situation, is it possible for the spies to securely transmit all these partial secrets to the spymaster so that they can be combined together in order to reveal the big secret to Alice? We call this problem, which, to the best of our knowledge, is a novel one for the relevant literature, the quantum secret aggregation problem. We propose a protocol, in the form of a quantum game, that addresses this problem in complete generality. Our protocol relies on the use of maximally entangled GHZ tuples, shared among Alice and all her spies. It is the power of entanglement that makes possible the secure transmission of the small partial secrets from the agents to the spymaster. As an additional bonus, entanglement guarantees the security of the protocol, by making it statistically improbable for the notorious eavesdropper Eve to steal the big secret.
Suppose that the renowned spymaster Alice controls a network of spies who all happen to be deployed in different geographical locations. Let us further assume that all spies have managed to get their hands on a small, albeit incomplete by itself, secret, which actually is just a part of a bigger secret. In this work, we consider the following problem: given the above situation, is it possible for the spies to securely transmit all these partial secrets to the spymaster so that they can be combined together in order to reveal the big secret to Alice? We call this problem, which, to the best of our knowledge, is a novel one for the relevant literature, the quantum secret aggregation problem. We propose a protocol, in the form of a quantum game, that addresses this problem in complete generality. Our protocol relies on the use of maximally entangled GHZ tuples, shared among Alice and all her spies. It is the power of entanglement that makes possible the secure transmission of the small partial secrets from the agents to the spymaster. As an additional bonus, entanglement guarantees the security of the protocol, by making it statistically improbable for the notorious eavesdropper Eve to steal the big secret.
This paper introduces the Symmetric Extensible Quantum Secret Sharing protocol, a novel quantum protocol for secret sharing. At its heart, it is an entanglement-based protocol that relies on the use of maximally entangled GHZ tuples, evenly distributed among the players, endowing the spymaster with the ability to securely share a secret message with the agents. Its security stems from the fact that it is highly improbable for a malicious eavesdropper or a rogue double agent to disrupt its successful execution. It is characterized by symmetry, since all agents are treated indiscriminately, utilizing identical quantum circuits. Furthermore, it can be seamlessly extended to an arbitrary number of agents. Finally, after the completion of the quantum part of the protocol, the spymaster will have to publicly transmit some information, in order to allow the agents to unlock the secret message. This part of the protocol can be considered as an additional advantage, due to the fact that it gives the spymaster the privilege of deciding if, or when, it is the right time for the agents to unlock the secret message, after the completion of the quantum part of the protocol.
This paper presents a new quantum protocol designed to transmit information from one source to many recipients simultaneously. The proposed protocol, which is based on the phenomenon of entanglement, is completely distributed and is provably information-theoretically secure. Numerous existing quantum protocols guarantee secure information communication between two parties but are not amenable to generalization in situations where the source must transmit information to two or more recipients. Hence, they must be executed sequentially two or more times to achieve the desired goal. The main novelty of the new protocol is its extensibility and generality to situations involving one party that must simultaneously communicate different, in general, messages to an arbitrary number of spatially distributed parties. This is achieved in the special way employed to encode the transmitted information in the entangled state of the system, one of the distinguishing features compared with previous protocols. This protocol can prove expedient whenever an information broker, say, Alice, must communicate distinct secret messages to her agents, all in different geographical locations, in one go. Due to its relative complexity compared with similar cryptographic protocols, as it involves communication among n parties and relies on |GHZn⟩ tuples, we provide an extensive and detailed security analysis so as to prove that it is information-theoretically secure. Finally, in terms of its implementation, the prevalent characteristics of the proposed protocol are its uniformity and simplicity, because it only requires CNOT and Hadamard gates and the local quantum circuits are identical for all information recipients.
Very recently, Lee et al. proposed a secure quantum teleportation protocol to transfer shared quantum secret between multiple parties in a network [Phys. Rev. Lett. 124 060501 (2020)]. This quantum network is encoded with a maximally entangled GHZ state. In this paper, we consider a partially entangled GHZ state as the entanglement channel, where it can achieve, probabilistically, unity fidelity transfer of the state. Two kinds of strategies are given. One arises when an auxiliary particle is introduced and a general evolution at any receiver’s location is then adopted. The other one involves performing a single generalized Bell-state measurement at the location of any sender. This could allow the receivers to recover the transmitted state with a certain probability, in which only the local Pauli operators are performed, instead of introducing an auxiliary particle. In addition, the successful probability is provided, which is determined by the degree of entanglement of the partially multipartite entangled state. Moreover, the proposed protocol is robust against the bit and phase flip noise.
Decision Support Systems 392 1.1 The problem of perfect end-to-end secrecy Quantum cryptography claims to bring perfect secrecy to a given line, but speaking honestly, it is no more than this.Using a carrier that is sufficiently fragile to rule out copying it, naturally raises the question of how much distance can be bridged?In fact, nowadays available quantum cryptography allows for communication over a distance of up to 144 km, as demonstrated by Schmitt-Manderbach et al. (2007), but arbitrary distances can yet not be bridged.Although theoretical results due to Lo & Chau (1999) indicate that the noise problem can be overcome, making arbitrary ranges theoretically possible, building networks is inevitable for a global roll-out.Existing solutions mostly rely on trusted relay for that matter.However, why attack the quantum line, if attacking a relay node is fully sufficient?Under the assumption of perfectly protected lines, recent results indicate that without preexisting secrets that are exclusively known to the sender and the receiver, end-to-endsecurity is only achievable under hard constraints on the network topology.To be more precise, let G be a graph that models a network.Let V(G), E(G) be the sets of vertices and edges of G, and assume the sender s and receiver r to be parts of G, that is {s, r} ⊆ V(G).The adversary can be modelled by a set A ⊆ 2 V(G)\{s, r} (the powerset of V(G)\{s, r}), that is we assume that a selection of subsets of vertices can be compromised.If k such sets can become conquered simultaneously, then we face a k-active adversary.An infected vertex v is assumed fully under the adversary's control, so a message passing through v can be read, blocked or modified and v is free to create as many new messages as desired.There is no limitation on computational power or knowledge of the adversary.If removing from G the vertices in any k sets in the adversary structure A cannot disconnect s and r in G, then we call the graph A (k) (s,r)-subconnected.If, by doing so, the network cannot be disconnected at all, then the graph is said to be A (k) -subconnected.Referring to these notions, a network permits perfectly secure message delivery from s to r if and only if the graph G is A (2) (s,r)-subconnected.The reader may consult Ashwin Kumar et al. (2002) for a proof.Different, yet no less stringent requirements are imposed by Wang & Desmedt (2008): among related results, the following necessary condition best highlights the difficulty of achieving unconditional security in a real-life network: if for u ≥ 1, 3(ku) + 1 ≥ k + 1 directed node-disjoint paths from s to r exist, then a necessary condition for perfectly secure message transmission from s to r against a k-active adversary is that there are u directed node disjoint paths (these u paths are also disjoint from the 3(ku) + 1 paths from s to r) from r to s.The described adversary model applies to many situations, as for example machines running certain software may all suffer from the same security holes.Networks equipped with devices from different vendors may be considered vulnerable if one vendor's devices turn out to be insecure.A k-active adversary would correspond to k vendors cooperating, or equivalently arise, if k vendors obtained the same malicious module from a single fraudulent manufacturer, turning a heterogeneous set of products into a possible backdoor for an adversary. Decision theory and system securityMany results either guarantee or rule out perfectly secret communication, but this might not be satisfactory.If perfectly secure communication is not possible, then how much is achievable with the given resources?A variety of security metrics has been proposed, but a measure of security is yet missing.This work summarizes a decision-theoretic approach to quantifying risk in terms that can be specified to best suit the application at hand.www.intechopen.
We propose a simultaneous quantum secure direct communication scheme between one party and other three parties via four-particle GHZ states and swapping quantum entanglement. In the scheme, three spatially separated senders, Alice, Bob and Charlie, transmit their secret messages to a remote receiver Diana by performing a series of local operations on their respective particles according to the quadripartite stipulation. From Alice, Bob, Charlie and Diana's Bell measurement results, Diana can infer the secret messages. If a perfect quantum channel is used, the secret messages are faithfully transmitted from Alice, Bob and Charlie to Diana via initially shared pairs of four-particle GHZ states without revealing any information to a potential eavesdropper. As there is no transmission of the qubits carrying the secret message in the public channel, it is completely secure for the direct secret communication. This scheme can be considered as a network of communication parties where each party wants to communicate secretly with a central party or server.