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Security and Communication Networks

Multi‐stage quantum secure communication using polarization hopping

Mayssaa El Rifai, Kam Wai Clifford Chan, Pramode K. Verma

Published Oct 1, 2015• 10 citations
Publisher

Abstract

Abstract This paper proposes a generalized multi‐stage multi‐photon protocol that uses arbitrary polarization states to securely communicate between a sender and a receiver. Because the polarization measurement of an arbitrarily polarized state results in altering the state in an irreversible way, any such measurement produces noise in the measured state. The proposed multi‐stage protocol exploits this phenomenon to provide quantum secure communication. This paper assesses the vulnerability of the multi‐stage protocol to photon number splitting attack and Trojan horse attack. In addition, it presents an upper bound on the number of photons that can be used per pulse to exchange information while maintaining quantum‐level security. Determination of such a bound is important for the multi‐stage protocol to operate in the multi‐photon domain while maintaining a quantum level of security. Furthermore, this paper proposes a key/message expansion scheme that provides another layer of security to the multi‐stage protocol. The multi‐stage protocol, can potentially provide higher data rates as well as longer communication distances. Copyright © 2015 John Wiley & Sons, Ltd.

DOI
10.1002/sec.1364

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Abstract This paper proposes a generalized multi‐stage multi‐photon protocol that uses arbitrary polarization states to securely communicate between a sender and a receiver. Because the polarization measurement of an arbitrarily polarized state results in altering the state in an irreversible way, any such measurement produces noise in the measured state. The proposed multi‐stage protocol exploits this phenomenon to provide quantum secure communication. This paper assesses the vulnerability of the multi‐stage protocol to photon number splitting attack and Trojan horse attack. In addition, it presents an upper bound on the number of photons that can be used per pulse to exchange information while maintaining quantum‐level security. Determination of such a bound is important for the multi‐stage protocol to operate in the multi‐photon domain while maintaining a quantum level of security. Furthermore, this paper proposes a key/message expansion scheme that provides another layer of security to the multi‐stage protocol. The multi‐stage protocol, can potentially provide higher data rates as well as longer communication distances. Copyright © 2015 John Wiley & Sons, Ltd.
This dissertation presents a study of the security and performance of a quantum communication system using multi-stage multi-photon tolerant protocols. Multi-stage protocols are a generalization of the three-stage protocol proposed in 2006 by Subhash Kak. Multi-stage protocols use “Polarization Hopping,” which is the process of changing the polarization state at each stage of transmission. During the execution of a multi-stage protocol, the message transfer always starts by encoding a bit of information in a polarization state; for example, bit 0 is encoded using state |0⟩ and bit 1 is encoded using state|1⟩ whereas, on the channel, the state of polarization is given by α|├ 0⟩┤+β|├ 1⟩┤. In the following α and β are restricted to the real numbers i.e., the polarization stays on the equator of the Poincare sphere. A transformation applied by one communicating party at a given stage will result in new values of α and β. \nThis dissertation analyzes the security of multi-stage, multi-photon tolerant protocols and proposes an upper bound on the average number of photons per pulse in the cases where Fock states and the cases where coherent states are used in the implementation of the three-stage protocol. The derived average number of photons is the maximum limit at which the three-stage protocol can operate at a quantum secure level while operating in a multi-photon domain. In addition, this dissertation studies the vulnerability of the multi-stage protocol to the Trojan horse attack, Photon Number splitting attack (PNS), Amplification attack, as well as the man-in-the middle attack. Moreover, this dissertation proposes a modified version of the multi-stage protocol. This modified version uses an initialization vector and implements a chaining mode between consecutive implementations of the protocol. The modified version is proposed in the case of the three-stage protocol and named a key/message expansion four variables three-stage protocol. The proposed nomenclature is based on the fact that an additional variable is added to secure the three-stage protocol. The introduction of this additional variable has the potential to secure the multi-stage protocol in the multi-photon regime. It results in the eavesdropper having a set of simultaneous equations where the number of variables exceeds the number of equations. \nThe dissertation also addresses the performance of the multi-stage, multi-photon tolerant protocol. An average photon number of 1.5 photon/stage is used to calculate the maximum achievable distance and key transfer rates while using the single-stage protocol over fiber optic cables. We compute the increase in distance as well as data transfer rate while using the single-stage protocol. Channel losses as well as the detector losses are accounted for. \nFinally, an application of the multi-stage protocol in IEEE 802.11 is proposed. This application provides wireless networks with a quantum-level of security. It proposes the integration of multi-stage protocols into the four-way handshake of IEEE 802.11.
This paper proposes a quantum secure communication protocol using multiple photons to represent each bit of a message to be shared. The multi-photon tolerant approach to quantum cryptography provides a quantum level security while using more than a single photon per transmission. The protocol proposed is a multi-stage protocol; an explanation of its operation and implementation are provided. The multi-stage protocol is based on the use of unitary transformations known only to Alice and Bob. This paper studies the security aspects of the multi-stage protocol by assessing its vulnerability to different attacks. It is well known that as the number of photons increases, the level of vulnerability of the multi-stage protocol increases. This paper sets a limit on the number of photons that can be used while keeping the multi-stage protocol a multi-photon tolerant quantum secure method for communication. The analysis of the number of photons to be used is based on the probability of success of a Helstrom discrimination done by an eavesdropper on the channel. Limiting the number of photons up to certain threshold per stage makes it impossible for an eavesdropper to decipher the message sent over the channel. The proposed protocol obviates the disadvantages associated with single photon implementations, such as limited data rates and distances along with the need to have no more than a single photon per time slot. The multi-stage protocol is a step toward direct quantum communication rather than quantum key distribution associated with single photon approaches.
This paper presents an investigation of practical quantum secure communication using multi-photon tolerant protocols. Multi-photon tolerant protocols loosen the limit on the number of photons imposed by currently used quantum key distribution protocols. The multi-photon tolerant protocols investigated in this paper are multi-stage protocols that do not require any prior agreement between a sender Alice and a receiver Bob. The security of such protocols stems from the fact that the optimal detection strategies between the legitimate users and the eavesdropper are asymmetrical, allowing Bob to obtain measurement results deterministically while imposing unavoidable quantum noise to the eavesdropper Eve's measurement. Multi-photon tolerant protocols are based on the use of transformations known only to the communicating party applying them i.e. either Alice or Bob. In this paper multi-photon tolerant protocols are used in order to share a key or a message between a sender Alice and a receiver Bob. Thus such protocols can be either used as quantum key distribution (QKD) protocols or quantum communication protocols. In addition, multi-stage protocols can be used to share a key between Alice and Bob, followed by the shared key used as a seed key to a single-stage protocol, called the braiding concept. This paper presents a practical study of multi-photon tolerant multi-stage protocols. Security aspects as well as challenges to the practical implementation are discussed. In addition, secret raw key generation rates are calculated with respect to both losses and distances over a fiber optical channel. It is well-known that raw key generation rates decreases with the increase in channel losses and distances. In this paper, coherent non-decoying quantum states are used to transfer the encoded bits from Alice to Bob. Raw key generation rates are calculated for different average photon numbers µ and compared with the case of µ=0.1, which is the average number of photons used in most single-photon based QKD protocols. Furthermore, an optimal average number of photons to be used within the secure region of the multi-photon tolerant protocols is calculated. It is worth noting that, with the increased key generation rates and distances of communication offered by the multi-photon tolerant protocols, quantum secure communication need not be restricted to quantum key distribution; it can be elevated to attain direct quantum secure communication.
This paper presents a multi-stage, multi-photon quantum key distribution protocol based on the double-lock cryptography.It exploits the asymmetry in the detection strategies between the legitimate users and the eavesdropper.The security analysis of the protocol is presented with coherent states under the interceptresend attack, the photon number splitting attack, and the man-in-the-middle attack.It is found that the mean photon number can be much larger 1.This complements the recent interest in multi-photon quantum communication protocols that require a pre-shared key between the legitimate users.
The proposed protocols of quantum secure direct communication based on single photons up-to-date are almost two-way communication protocols, in which the probability of Trojan horse attack reduces the security of the communication. The aim of photons transferred forward and backward is to let the receiver know the code bases and the initial states of the photons. One-way quantum secure direct communication protocol based on single photons is proposed, in which the XOR operation by bits of the information sequence and random sequence is taken before coding. Then the code bases and the random sequence can be published if the quantum channel is secure, so the receiver can measure in the correct basis to get the information; even there exists eavesdropper, the information sequence is still secure. This protocol has the advantages of higher security, longer communication distance compared with two-way scheme and easier implementation than others.