Covert Communication in Fading Channels under Channel Uncertainty

A covert communication system under block fading channels is considered where users experience uncertainty about their channel knowledge. The transmitter seeks to hide the covert communication to a private user by exploiting a legitimate public communication link while the warden tries to detect this covert communication by using a radiometer. We derive the exact expression for the radiometers optimal threshold which determines the performance limit of the wardens detector. Furthermore for given transmission outage constraints the achievable rates for legitimate and covert users are analyzed while maintaining a specific level of covertness. Our numerical results illustrate how the achievable performance is affected by the channel uncertainty and required level of covertness.Comment: to appear in IEEE VTC2017-Sprin

The art of post-truth in quantum cryptography

L’établissement de clé quantique (abrégé QKD en anglais) permet à deux participants distants, Alice et Bob, d’établir une clé secrète commune (mais aléatoire) qui est connue uniquement de ces deux personnes (c’est-à-dire inconnue d’Ève et de tout autre tiers parti). La clé secrète partagée est inconditionnellement privée et peut être plus tard utilisée, par Alice et Bob, pour transmettre des messages en toute confidentialité, par exemple sous la forme d’un masque jetable. Le protocole d’établissement de clé quantique garantit la confidentialité inconditionnelle du message en présence d’un adversaire (Ève) limité uniquement par les lois de la mécanique quantique, et qui ne peut agir sur l’information que se partagent Alice et Bob que lors de son transit à travers des canaux classiques et quantiques. Mais que se passe-t-il lorsque Ève a le pouvoir supplémentaire de contraindre Alice et/ou Bob à révéler toute information, jusqu’alors gardée secrète, générée lors de l’exécution (réussie) du protocole d’établissement de clé quantique (éventuellement suite à la transmission entre Alice et Bob d’un ou plusieurs messages chiffrés classique à l’aide de cette clé), de manière à ce qu’Ève puisse reproduire l’entièreté du protocole et retrouver la clé (et donc aussi le message qu’elle a chiffré) ? Alice et Bob peuvent-ils nier la création de la clé de manière plausible en révélant des informations mensongères pour qu’Ève aboutisse sur une fausse clé ? Les protocoles d’établissement de clé quantiques peuvent-ils tels quels garantir la possibilité du doute raisonnable ? Dans cette thèse, c’est sur cette énigme que nous nous penchons. Dans le reste de ce document, nous empruntons le point de vue de la théorie de l’information pour analyser la possibilité du doute raisonnable lors de l’application de protocoles d’établissement de clé quantiques. Nous formalisons rigoureusement différents types et degrés de doute raisonnable en fonction de quel participant est contraint de révéler la clé, de ce que l’adversaire peut demander, de la taille de l’ensemble de fausses clés qu’Alice et Bob peuvent prétendre établir, de quand les parties doivent décider de la ou des clés fictives, de quelle est la tolérance d’Ève aux événements moins probables, et du recours ou non à des hypothèses de calcul. Nous définissons ensuite rigoureusement une classe générale de protocoles d’établissement de clé quantiques, basée sur un canal quantique presque parfait, et prouvons que tout protocole d’établissement de clé quantique appartenant à cette classe satisfait la définition la plus générale de doute raisonnable : à savoir, le doute raisonnable universel. Nous en fournissons quelques exemples. Ensuite, nous proposons un protocole hybride selon lequel tout protocole QKD peut être au plus existentiellement déniable. De plus, nous définissons une vaste classe de protocoles d’établissement de clé quantiques, que nous appelons préparation et mesure, et prouvons l’impossibilité d’instiller lors de ceux-ci tout degré de doute raisonnable. Ensuite, nous proposons une variante du protocole, que nous appelons préparation et mesure floues qui offre un certain niveau de doute raisonnable lorsque Ève est juste. Par la suite, nous proposons un protocole hybride en vertu duquel tout protocole d’établissement de clé quantique ne peut offrir au mieux que l’option de doute raisonnable existentiel. Finalement, nous proposons une variante du protocole, que nous appelons mono-déniable qui est seulement Alice déniable ou Bob déniable (mais pas les deux).Quantum Key Establishment (QKD) enables two distant parties Alice and Bob to establish a common random secret key known only to the two of them (i.e., unknown to Eve and anyone else). The common secret key is information-theoretically secure. Later, Alice and Bob may use this key to transmit messages securely, for example as a one-time pad. The QKD protocol guarantees the confidentiality of the key from an information-theoretic perspective against an adversary Eve who is only limited by the laws of quantum theory and can act only on the signals as they pass through the classical and quantum channels. But what if Eve has the extra power to coerce Alice and/or Bob after the successful execution of the QKD protocol forcing either both or only one of them to reveal all their private information (possibly also after one or several (classical) ciphertexts encrypted with that key have been transmitted between Alice and Bob) then Eve could go through the protocol and obtain the key (hence also the message)? Can Alice and Bob deny establishment of the key plausibly by revealing fake private information and hence also a fake key? Do QKD protocols guarantee deniability for free in this case? In this Thesis, we investigate this conundrum. In the rest of this document, we take an information-theoretic perspective on deniability in quantum key establishment protocols. We rigorously formalize different levels and flavours of deniability depending on which party is coerced, what the adversary may ask, what is the size of the fake set that surreptitious parties can pretend to be established, when the parties should decide on the fake key(s), and what is the coercer’s tolerance to less likely events and possibly also computational assumptions. We then rigorously define a general class of QKD protocols, based on an almost-perfect quantum channel, and prove that any QKD protocol that belongs to this class satisfies the most general flavour of deniability, i.e.,universal deniability. Moreover, we define a broad class of QKD protocols, which we call prepare-and-measure, and prove that these protocols are not deniable in any level or flavour. Moreover, we define a class of QKD protocols, which we refer to as fuzzy prepare-andmeasure, that provides a certain level of deniability conditioned on Eve being fair. Furthermore, we propose a hybrid protocol under which any QKD protocol can be at most existentially deniable. Finally, we define a class of QKD protocols, which we refer to as mono-deniable, which is either Alice or Bob (but not both) deniable

Fundamental Limits of Communication with Low Probability of Detection

This paper considers the problem of communication over a discrete memoryless channel (DMC) or an additive white Gaussian noise (AWGN) channel subject to the constraint that the probability that an adversary who observes the channel outputs can detect the communication is low. Specifically, the relative entropy between the output distributions when a codeword is transmitted and when no input is provided to the channel must be sufficiently small. For a DMC whose output distribution induced by the "off" input symbol is not a mixture of the output distributions induced by other input symbols, it is shown that the maximum amount of information that can be transmitted under this criterion scales like the square root of the blocklength. The same is true for the AWGN channel. Exact expressions for the scaling constant are also derived.Comment: Version to appear in IEEE Transactions on Information Theory; minor typos in v2 corrected. Part of this work was presented at ISIT 2015 in Hong Kon

Covert communication with finite blocklength in AWGN channels

Covert communication is to achieve a reliable transmission from a transmitter to a receiver while guaranteeing an arbitrarily small probability of this transmission being detected by a warden. In this work, we study the covert communication in AWGN channels with finite blocklength, in which the number of channel uses is finite. Specifically, we analytically prove that the entire block (all available channel uses) should be utilized to maximize the effective throughput of the transmission subject to a predetermined covert requirement. This is a nontrivial result because more channel uses results in more observations at the warden for detecting the transmission. We also determine the maximum allowable transmit power per channel use, which is shown to decrease as the blocklength increases. Despite the decrease in the maximum allowable transmit power per channel use, the maximum allowable total power over the entire block is proved to increase with the blocklength, which leads to the fact that the effective throughput increases with the blocklength.ARC Discovery Projects Grant DP15010390

Delay-Intolerant Covert Communications with Either Fixed or Random Transmit Power

In this paper, we study delay-intolerant covert communications in additive white Gaussian noise (AWGN) channels with a finite block length, i.e., a finite number of channel uses. Considering the maximum allowable number of channel uses to be N, it is not immediately clear whether the actual number of channel uses, denoted by n, should be as large as N or smaller for covert communications. This is because a smaller n reduces a warden’s chance to detect the communications due to fewer observations, but also reduces the chance to transmit information. We show that n=N is indeed optimal to maximize the amount of information bits that can be transmitted, subject to any covert communication constraint in terms of the warden’s detection error probability. To better make use of the warden’s uncertainty due to the finite block length, we also propose to use uniformly distributed random transmit power to enhance covert communications. Our examination shows that the amount of information that can be covertly transmitted logarithmically increases with the number of random power levels, which indicates that most of the benefit of using random transmit power is achieved with just a few different power levels.This work was supported by the Australian Research Council’s Discovery Projects under Grant DP180104062