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International Conference on Ubiquitous Networking (UNet)

A Game-Theoretic Approach with Decoy Qubits for Quantum Superdense Coding Security

Amal Sayari, Slim Rekhis, Ali Mabrouk

Published Jun 26, 2024• 2 citations
Publisher

Abstract

Quantum superdense coding protocol is addressed in the literature as a promising approach for efficient quantum communication. It allows two parties, to transmit classical bits using quantum bits. However, its security is threatened by a scrambling attack that involves modifying the automated gate specification to effectively scramble the final measurement, and by a bijection attack that performs a bijective transformation on the final measured strings. In this paper, we propose a novel approach to preventing such attacks by introducing decoy qubits into the superdense coding protocol, which act as a source of randomness that can detect any tampering with the entangled states and enable the detection of an eavesdropper. To strategize the selection and sending of these decoy qubits and address the interaction between the sender, receiver, and eavesdropper, we propose a dynamic non-cooperative game-based approach evaluated with a Q-learning algorithm to model and analyze this problem as a benefit-cost model. The utility functions of the proposed game are based on the concepts of return on protection, which illustrates the gain of selecting and sending a decoy qubit, and return on attack, which illustrates the reward of the eavesdropper for performing an attack to compromise the communication. Moreover, we discuss and analyze the Nash equilibrium convergence of this attack-defense model. Finally, we perform simulation work using a Q-learning algorithm to show the effectiveness of the proposed model in assessing the behavior of the players and its ability to reach equilibrium within a finite number of steps.

DOI
10.1109/unet62310.2024.10794739

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Quantum superdense coding protocol is addressed in the literature as a promising approach for efficient quantum communication. It allows two parties, to transmit classical bits using quantum bits. However, its security is threatened by a scrambling attack that involves modifying the automated gate specification to effectively scramble the final measurement, and by a bijection attack that performs a bijective transformation on the final measured strings. In this paper, we propose a novel approach to preventing such attacks by introducing decoy qubits into the superdense coding protocol, which act as a source of randomness that can detect any tampering with the entangled states and enable the detection of an eavesdropper. To strategize the selection and sending of these decoy qubits and address the interaction between the sender, receiver, and eavesdropper, we propose a dynamic non-cooperative game-based approach evaluated with a Q-learning algorithm to model and analyze this problem as a benefit-cost model. The utility functions of the proposed game are based on the concepts of return on protection, which illustrates the gain of selecting and sending a decoy qubit, and return on attack, which illustrates the reward of the eavesdropper for performing an attack to compromise the communication. Moreover, we discuss and analyze the Nash equilibrium convergence of this attack-defense model. Finally, we perform simulation work using a Q-learning algorithm to show the effectiveness of the proposed model in assessing the behavior of the players and its ability to reach equilibrium within a finite number of steps.
The development of automated gate specification for quantum communications and quantum networked computation opens up the way for malware designed at corrupting the automation software, changing the automated quantum communications protocols and algorithms. We study two types of attacks on automated quantum communications protocols and simulate these attacks on the superdense coding protocol, using remote access to IBM's Quantum Computers available through IBM Q Experience to simulate these attacks on what would be a low noise quantum communications network. The first type of attack leads to a hacker-controlled bijective transformation of the final measured strings, the second type of attack is a unitary scrambling attack that modifies the automated gate specification to effectively scramble the final measurement, disrupting quantum communications and taking advantage of quantum randomness upon measurement in a way that makes it difficult to distinguish from hardware malfunction or from a sudden rise in environmental noise. We show that, due to quantum entanglement and symmetries, the second type of attack works as a way to strategically disrupt quantum communications networks and quantum networked computation in a way that makes it difficult to ascertain which node was attacked. The main findings are discussed in the wider setting of quantum cybersecurity and quantum networked computation, where ways of hacking including the role of insider threats are discussed.
In quantum information theory, superdense coding allows two network entities to exchange two classical bits via a quantum channel using a single quantum bit (qubit) transmission, provided they have pre-shared an entangled qubit. An attacker intercepting the qubit during transmission cannot extract meaningful data without the other entangled qubit from the pair. However, an attacker can disrupt the communication by introducing its own qubit to the receiver. To enhance the security of superdense coding, we propose an authentication mechanism through a classical communication channel.
This work is mainly based on quantum game-theoretic techniques and their application to quantum information theory.Quantum game theory is an important development in quantum computation and may have implications for quantum information and quantum communication.The select of quantum memory on quantum games have been studied.Three di􀀞erent games such as, Prisoner Dilemma, Battle of the Sexes and Chicken have been analyzed in the quantum domain. By considering the restricted game \nsituation, it is shown that the ects of quantum memory and decoherence become e􀀞ective in a maximally entangled case.For which the quantum player can out perform the classical player in all the three games. It is also shown that the quantum player enjoys an advantage over the classical player in Battle of the Sexes game for the amplitude-damping and the depolarizing channels.The quantum memory compensates the reduction in player pay is due to decoherence. It has no ect on the Nash equilibria of the three games.A generalization of two-player quantization scheme to a three-player Prisoners Dilemma game under the ect of correlated noise is also presented.In a restricted game scenario, it is shown the quantumplayer is always better; for all values of the decoherence parameter for the entire range of memory parameter.It is seen that for maximum degree of correlation, the game does not become \nnoiseless and quantum player can still outscore the classical players for the entire range of the decoherence parameter producing an interesting result in comparison with a two-player quantum game.It is also shown that correlated noise has not on the Nash equilibrium of the game.By exploiting the three-player quantization scheme, we have studiedthe communication aspects of a three-player Prisoner Dilemma quantum game. It is shown that entanglement plays a dominant role in a three-player quantum game.On the baois of initial state and the measurement basis entanglement parameters, a relation among different pay is established.It is investigated that the strategies of the players act as information carriers in quantum games. A relationship for the information shared among the parties is also established.A scheme for quantum key distribution is proposed in which a secret key can be generated from the data coming through a partially entanglement breaking channel.This scheme is rather deterministic andcient in the sense that two classical bits can be transferred \nper entangled pair of qubits.Furthermore, it is important to point out that, in this scheme, same symbol can be used for Eve detection and key generation. It is also worth noting that the eavesdropper, Eve, can be detected very easily from the disturbance of the elements of the decoding bimatrix. We have checked for the \nsecurity of the scheme and found it secure against individual attacks.It is further investigated that quantum games are useful in developing quantum cryptographic protocols.A multiparty quantum cryptographic protocol using tripartite entangled GHZ states is devised using game-theoretic techniques.In this protocol, two classical bits can be transferred per entangled pair of qubits to the communicating parties.Unitary operators applied by the sender on a tripartite entangled state encodes a classical symbol that can be decoded at receiver end with the help of a decoding matrix. In this protocol, if Eve interferes during the transmission, she can be detected by the disturbance of the decoding matrix. Our security analysis shows that this protocol is also secure against intercept/re-send attacks.
We analyze utility of communication channels in absence of any short of quantum or classical correlation shared between the sender and the receiver. To this aim, we propose a class of two-party communication games, and show that the games cannot be won given a noiseless 1 -bit classical channel from the sender to the receiver. Interestingly, the goal can be perfectly achieved if the channel is assisted with classical shared randomness. This resembles an advantage similar to the quantum superdense coding phenomenon where pre-shared entanglement can enhance the communication utility of a perfect quantum communication line. Quite surprisingly, we show that a qubit communication without any assistance of classical shared randomness can achieve the goal, and hence establishes a novel quantum advantage in the simplest communication scenario. In pursuit of a deeper origin of this advantage, we show that an advantageous quantum strategy must invoke quantum interference both at the encoding step by the sender and at the decoding step by the receiver. We also study communication utility of a class of non-classical toy systems described by symmetric polygonal state spaces. We come up with communication tasks that can be achieved neither with 1 -bit of classical communication nor by communicating a polygon system, whereas 1 -qubit communication yields a perfect strategy, establishing quantum advantage over them. To this end, we show that the quantum advantages are robust against imperfect encodings-decodings, making the protocols implementable with presently available quantum technologies.
Recently, a genuine five-qubit entangled state has been achieved by Brown et al.[ J. Phys. A 38 (2005) 1119 ]. Later it was indicated that this state can be used for quantum teleportation and quantum state sharing. Here we build a quantum secure direct communication protocol with this state, and prove that it is secure in ideal conditions. In the protocol, the sender performs unitary transformations to encode a secret message on his/her particles and sends them to the receiver. The receiver then performs projective determinate measurement to decode the secret message directly. Furthermore, this protocol utilizes superdense coding to achieve a high intrinsic efficiency and source capacity.
Built based on the fundamental principles of quantum mechanics, Quantum Key Distribution (QKD) enables secure communication for distant parties. Entanglement-based protocols are a type of QKD protocol that uses the phenomenon of entanglement for detecting eavesdroppers between two communicating parties. In this paper, a novel QKD protocol is devised that uses the concept of superdense coding and padding bits to share the one-time pad, i.e., the key. The super dense coding is achieved by sharing a pre-existing entangled pair of qubits by leveraging the beautiful property of entanglement. The communicating parties can share a one-time pad using this protocol securely. This paper will demonstrate this phenomenon using the proposed protocol by showing the experimental results which has been surfaced with IBM Qiskit simulator, and the simulation establishes the applicability of the protocol and shows its effectiveness in detecting eavesdropping attempts while being simple to implement.