Quantum e-commerce: A comparative study of possible protocols for online shopping and other tasks related to e-commerce

A set of quantum protocols for online shopping is proposed and analyzed to establish that it is possible to perform secure online shopping using different types of quantum resources. Specifically, a single photon based, a Bell state based and two 3-qubit entangled state based quantum online shopping schemes are proposed. The Bell state based scheme, being a completely orthogonal state based protocol, is fundamentally different from the earlier proposed schemes which were based on conjugate coding. One of the 3-qubit entangled state based scheme is build on the principle of entanglement swapping which enables us to accomplish the task without transmission of the message encoded qubits through the channel. Possible ways of generalizing the entangled state based schemes proposed here to the schemes which use multiqubit entangled states is also discussed. Further, all the proposed protocols are shown to be free from the limitations of the recently proposed protocol of Huang et al. (Quantum Inf. Process. 14, 2211-2225, 2015) which allows the buyer (Alice) to change her order at a later time (after initially placing the order and getting it authenticated by the controller). The proposed schemes are also compared with the existing schemes using qubit efficiency.Comment: It's shown that quantum e-commerce is not a difficult task, and it can be done in various way

Beyond the Goldenberg-Vaidman protocol: Secure and efficient quantum communication using arbitrary, orthogonal, multi-particle quantum states

It is shown that maximally efficient protocols for secure direct quantum communications can be constructed using any arbitrary orthogonal basis. This establishes that no set of quantum states (e.g. GHZ states, W states, Brown states or Cluster states) has an advantage over the others, barring the relative difficulty in physical implementation. The work provides a wide choice of states for experimental realization of direct secure quantum communication protocols. We have also shown that this protocol can be generalized to a completely orthogonal state based protocol of Goldenberg-Vaidman (GV) type. The security of these protocols essentially arises from duality and monogamy of entanglement. This stands in contrast to protocols that employ non-orthogonal states, like Bennett-Brassard 1984 (BB84), where the security essentially comes from non-commutativity in the observable algebra.Comment: 7 pages, no figur

Orthogonal-state-based protocols of quantum key agreement

Two orthogonal-state-based protocols of quantum key agreement (QKA) are proposed. The first protocol of QKA proposed here is designed for two-party QKA, whereas the second protocol is designed for multi-party QKA. Security of these orthogonal-state-based protocols arise from monogamy of entanglement. This is in contrast to the existing protocols of QKA where security arises from the use of non-orthogonal state (non-commutativity principle). Further, it is shown that all the quantum systems that are useful for implementation of quantum dialogue and most of the protocols of secure direct quantum communication can be modified to implement protocols of QKA.Comment: 9 pages, no figur

Quantum mutual authentication scheme based on Bell state measurement

Authentication is one of the security services that ensures sufficient security of the system by identification and verification. Also, it assures the identity of the communicating party to be that the claimed one. To build a quantum channel between two unauthenticated to each other parties, first, a trusted authority is needed to establish a mutual authentication with each party. Using Bell measurement and entanglement swapping, we present a protocol that mutually authenticates the identity of the sender and the receiver, then constructs a quantum channel based on Bell basis. After, the sender and the receiver use the quantum channel to communicate using entanglement-assisted quantum communication protocols. Additionally, the protocol renews the shared secret key between the trusted authority and each user after each authentication process. The protocol provides the necessary authentication and key distribution to create a quantum channel between the sender and receiver

Some Directions beyond Traditional Quantum Secret Sharing

We investigate two directions beyond the traditional quantum secret sharing (QSS). First, a restriction on QSS that comes from the no-cloning theorem is that any pair of authorized sets in an access structure should overlap. From the viewpoint of application, this places an unnatural constraint on secret sharing. We present a generalization, called assisted QSS (AQSS), where access structures without pairwise overlap of authorized sets is permissible, provided some shares are withheld by the share dealer. We show that no more than $\lambda-1$ withheld shares are required, where $\lambda$ is the minimum number of {\em partially linked classes} among the authorized sets for the QSS. Our result means that such applications of QSS need not be thwarted by the no-cloning theorem. Secondly, we point out a way of combining the features of QSS and quantum key distribution (QKD) for applications where a classical information is shared by quantum means. We observe that in such case, it is often possible to reduce the security proof of QSS to that of QKD.Comment: To appear in Physica Scripta, 7 pages, 1 figure, subsumes arXiv:quant-ph/040720

Semi-quantum communication: Protocols for key agreement, controlled secure direct communication and dialogue

Semi-quantum protocols that allow some of the users to remain classical are proposed for a large class of problems associated with secure communication and secure multiparty computation. Specifically, first time semi-quantum protocols are proposed for key agreement, controlled deterministic secure communication and dialogue, and it is shown that the semi-quantum protocols for controlled deterministic secure communication and dialogue can be reduced to semi-quantum protocols for e-commerce and private comparison (socialist millionaire problem), respectively. Complementing with the earlier proposed semi-quantum schemes for key distribution, secret sharing and deterministic secure communication, set of schemes proposed here and subsequent discussions have established that almost every secure communication and computation tasks that can be performed using fully quantum protocols can also be performed in semi-quantum manner. Further, it addresses a fundamental question in context of a large number problems- how much quantumness is (how many quantum parties are) required to perform a specific secure communication task? Some of the proposed schemes are completely orthogonal-state-based, and thus, fundamentally different from the existing semi-quantum schemes that are conjugate-coding-based. Security, efficiency and applicability of the proposed schemes have been discussed with appropriate importance.Comment: 19 pages 1 figur

Deterministic and Efficient Three-Party Quantum Key Distribution

Quantum information processing is based on the laws of quantum physics and guarantees the unconditional security. In this thesis we propose an efficient and deterministic three-party quantum key distribution algorithm to establish a secret key between two users. Using the formal methodological approach, we study and model a quantum algorithm to distribute a secret key to a sender and a receiver when they only share entanglement with a trusted party but not with each other. It distributes a secret key by special pure quantum states using the remote state preparation and controlled gates. In addition, we employ the parity bit of the entangled pairs and ancillary states to help in preparing and measuring the secret states. Distributing a state to two users requires two maximally entangled pairs as the quantum channel and a two-particle von Neumann projective measurement. This protocol is exact and deterministic. It distributes a secret key of d qubits by 2d entangled pairs and on average d bits of classical communication. We show the security of this protocol against the entanglement attack and offer a method for privacy amplification. Moreover, we also study the problem of distributing Einstein-Podolsky-Rosen (EPR) in a metropolitan network. The EPR is the building block of entanglement-based and entanglement-assisted quantum communication protocols. Therefore, prior shared EPR pair and an authenticated classical channel allow two distant users to share a secret key. To build a network architecture where a centralized EPR source creates entangled states by the process of spontaneous parametric down-conversion (SPDC) then routes the states to users in different access networks. We propose and simulate a metropolitan optical network (MON) architecture for entanglement distribution in a typical telecommunication infrastructure. The architecture allows simultaneous transmission of classical and quantum signals in the network and offers a dynamic routing mechanism to serve the entire metropolitan optical network