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IEEE International Symposium on Information Theory (ISIT)

Detectability of Denial-of-Service Attacks on Arbitrarily Varying Classical-Quantum Channels

Holger Boche, Minglai Cai, H. Vincent Poor, Rafael F. Schaefer

Published Jul 12, 2021• 6 citations
Publisher

Abstract

Communication systems are subject to adversarial attacks since malevolent adversaries might harm and disrupt legitimate transmissions intentionally. Of particular interest in this paper are so-called denial-of-service (DoS) attacks in which the jammer completely prevents any transmission. Arbitrarily varying classical-quantum channels, providing a suitable model to capture the jamming attacks of interest, are studied. Algorithmic detection frameworks are developed based on Turing machines and also Blum-Shub-Smale (BSS) machines, where the latter can process and store arbitrary real numbers. It is shown that Turing machines are not capable of detecting DoS attacks. However, BSS machines are capable thereof implying that real number signal processing enables the algorithmic detection of DoS attacks.

DOI
10.1109/isit45174.2021.9517916

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Communication systems are subject to adversarial attacks since malevolent adversaries might harm and disrupt legitimate transmissions intentionally. Of particular interest in this paper are so-called denial-of-service (DoS) attacks in which the jammer completely prevents any transmission. Arbitrarily varying classical-quantum channels, providing a suitable model to capture the jamming attacks of interest, are studied. Algorithmic detection frameworks are developed based on Turing machines and also Blum-Shub-Smale (BSS) machines, where the latter can process and store arbitrary real numbers. It is shown that Turing machines are not capable of detecting DoS attacks. However, BSS machines are capable thereof implying that real number signal processing enables the algorithmic detection of DoS attacks.
We study the problem of data transmission under the influence of a jammer, which is typical for wireless systems and commonly modeled as an arbitrarily varying channel (AVC) in information theory. AVC fulfilling a certain set of linear equations are called symmetrizable and are known to be prone to denial of service attacks. Recent work has shown that deciding if a given AVC is symmetrizable or not is a non-Turing computable problem. By relaxing the formulation of symmetrizability, we show the existence of a polynomial-time algorithm that determines whether a given AVC is non-symmetrizable, but displays a critical dependence on the number of jammer input states. We then show how imposing an energy constraint on the jammer allows the same algorithm to efficiently identify large classes of AVCs which are non-symmetrizable.
Arbitrarily varying channels offer a powerful framework for analyzing the robustness of quantum communication systems, especially for classical-quantum models, where the analysis displays strengths or weaknesses of specific signal constellations under generic attacks. In this work, we provide a coding theorem for a large class of practically relevant arbitrarily varying channel models. Namely, we give an explicit capacity formula for the lossy bosonic channel subject to semi-classical attacks, where an adversary injects semi-classical states into the transmission line. Mathematically, this is modeled via a beam-splitter setup, with transmitter and jammer controlling different input ports and the receiver observing one output port. We show how a recently conjectured new quantum entropy power inequality relates to our capacity formula.
In recent years, we have seen an increase in computer attacks through our communication networks worldwide, whether due to cybersecurity systems’ vulnerability or their absence. This paper presents three quantum models to detect distributed denial of service attacks. We compare Quantum Support Vector Machines, hybrid QuantumClassical Neural Networks, and a two-circuit ensemble model running parallel on two quantum processing units. Our work demonstrates quantum models’ effectiveness in supporting current and future cybersecurity systems by obtaining performances close to 100%, being 96% the worst-case scenario. It compares our models’ performance in terms of accuracy and consumption of computational resources.
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We analyze arbitrarily varying classical-quantum wiretap channels. These channels are subject to two attacks at the same time: one passive (eavesdropping) and one active (jamming). We elaborate on our previous studies [H. Boche et al., Quantum Inf. Process. 15(11), 4853–4895 (2016) and H. Boche et al., Quantum Inf. Process. 16(1), 1–48 (2016)] by introducing a reduced class of allowable codes that fulfills a more stringent secrecy requirement than earlier definitions. In addition, we prove that non-symmetrizability of the legal link is sufficient for equality of the deterministic and the common randomness assisted secrecy capacities. Finally, we focus on analytic properties of both secrecy capacities: We completely characterize their discontinuity points and their super-activation properties.
Distributed Denial-of-Service (DDoS) attacks are a significant issue in classical networks. These attacks have been shown to impact the critical infrastructure of a nation, such as its major financial institutions. The possibility of DDoS attacks has also been identified for quantum networks. In this theoretical work, we introduce a quantum analogue of classical entropic DDoS detection systems and apply it in the context of detecting an attack on a quantum network. In particular, we examine DDoS attacks on a quantum repeater and harness the associated entanglement entropy for the detection system. Our results extend the applicability of quantum information from the domain of data security to the area of network security.