Split-State Non-Malleable Codes and Secret Sharing Schemes for Quantum Messages

Non-malleable codes are fundamental objects at the intersection of cryptography and coding theory. These codes provide security guarantees even in settings where error correction and detection are impossible, and have found applications to several other cryptographic tasks. Roughly speaking, a non-malleable code for a family of tampering functions guarantees that no adversary can tamper (using functions from this family) the encoding of a given message into the encoding of a related distinct message. Non-malleable secret sharing schemes are a strengthening of non-malleable codes which satisfy additional privacy and reconstruction properties. We first focus on the $2$-split-state tampering model, one of the strongest and most well-studied adversarial tampering models. Here, a codeword is split into two parts which are stored in physically distant servers, and the adversary can then independently tamper with each part using arbitrary functions. This model can be naturally extended to the secret sharing setting with several parties by having the adversary independently tamper with each share. Previous works on non-malleable coding and secret sharing in the split-state tampering model only considered the encoding of \emph{classical} messages. Furthermore, until the recent work by Aggarwal, Boddu, and Jain (arXiv 2022), adversaries with quantum capabilities and \emph{shared entanglement} had not been considered, and it is a priori not clear whether previous schemes remain secure in this model. In this work, we introduce the notions of split-state non-malleable codes and secret sharing schemes for quantum messages secure against quantum adversaries with shared entanglement. We also present explicit constructions of such schemes that achieve low-error non-malleability

Universal Construction of Cheater-Identifiable Secret Sharing Against Rushing Cheaters without Honest Majority

For conventional secret sharing, if cheaters can submit possibly forged shares after observing shares of the honest users in the reconstruction phase, they can disturb the protocol and reconstruct the true secret. To overcome the problem, secret sharing scheme with properties of cheater-identification have been proposed. Existing protocols for cheater-identifiable secret sharing assumed non-rushing cheaters or honest majority. In this paper, we remove both conditions simultaneously, and give its universal construction from any secret sharing scheme. To resolve this end, we propose the concepts of individual identification and agreed identification

Some Applications of Coding Theory in Computational Complexity

Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable error-correcting codes, and their applications to complexity theory and to cryptography. Locally decodable codes are error-correcting codes with sub-linear time error-correcting algorithms. They are related to private information retrieval (a type of cryptographic protocol), and they are used in average-case complexity and to construct ``hard-core predicates'' for one-way permutations. Locally testable codes are error-correcting codes with sub-linear time error-detection algorithms, and they are the combinatorial core of probabilistically checkable proofs

CSI-SharK: CSI-FiSh with Sharing-friendly Keys

CSI-FiSh is one of the most efficient isogeny-based signature schemes, which is proven to be secure in the Quantum Random Oracle Model (QROM). However, there is a bottleneck in CSI-FiSh in the threshold setting, which is that its public key needs to be generated by using $k-1$ secret keys. This leads to very inefficient threshold key generation protocols and also forces the parties to store $k-1$ secret shares. We present CSI-SharK, a new variant of $\textit{CSI}$-FiSh that has more $\textit{Shar}$ing-friendly $\textit{K}$eys and is as efficient as the original scheme. This is accomplished by modifying the public key of the ID protocol, used in the original CSI-FiSh, to the equal length Structured Public Key (SPK), generated by a $\textit{single}$ secret key, and then proving that the modified ID protocol and the resulting signature scheme remain secure in the QROM. We translate existing CSI-FiSh-based threshold signatures and Distributed Key Generation (DKG) protocols to the CSI-SharK setting. We find that DKG schemes based on CSI-SharK outperform the state-of-the-art actively secure DKG protocols from the literature by a factor of about $3$, while also strongly reducing the communication cost between the parties. We also uncover and discuss a flaw in the key generation of the actively secure CSI-FiSh based threshold signature $\textit{Sashimi}$, that can prevent parties from signing. Finally, we discuss how (distributed) key generation and signature schemes in the isogeny setting are strongly parallelizable and we show that by using $C$ independent CPU threads, the total runtime of such schemes can basically be reduced by a factor $C$. As multiple threads are standard in modern CPU architecture, this parallelizability is a strong incentive towards using isogeny-based (distributed) key generation and signature schemes in practical scenarios

From Classical to Quantum Secret Sharing

Dans ce mémoire, nous nous pencherons tout particulièrement sur une primitive cryptographique connue sous le nom de partage de secret. Nous explorerons autant le domaine classique que le domaine quantique de ces primitives, couronnant notre étude par la présentation d’un nouveau protocole de partage de secret quantique nécessitant un nombre minimal de parts quantiques c.-à-d. une seule part quantique par participant. L’ouverture de notre étude se fera par la présentation dans le chapitre préliminaire d’un survol des notions mathématiques sous-jacentes à la théorie de l’information quantique ayant pour but primaire d’établir la notation utilisée dans ce manuscrit, ainsi que la présentation d’un précis des propriétés mathématique de l’état de Greenberger-Horne-Zeilinger (GHZ) fréquemment utilisé dans les domaines quantiques de la cryptographie et des jeux de la communication. Mais, comme nous l’avons mentionné plus haut, c’est le domaine cryptographique qui restera le point focal de cette étude. Dans le second chapitre, nous nous intéresserons à la théorie des codes correcteurs d’erreurs classiques et quantiques qui seront à leur tour d’extrême importances lors de l’introduction de la théorie quantique du partage de secret dans le chapitre suivant. Dans la première partie du troisième chapitre, nous nous concentrerons sur le domaine classique du partage de secret en présentant un cadre théorique général portant sur la construction de ces primitives illustrant tout au long les concepts introduits par des exemples présentés pour leurs intérêts autant historiques que pédagogiques. Ceci préparera le chemin pour notre exposé sur la théorie quantique du partage de secret qui sera le focus de la seconde partie de ce même chapitre. Nous présenterons alors les théorèmes et définitions les plus généraux connus à date portant sur la construction de ces primitives en portant un intérêt particulier au partage quantique à seuil. Nous montrerons le lien étroit entre la théorie quantique des codes correcteurs d’erreurs et celle du partage de secret. Ce lien est si étroit que l’on considère les codes correcteurs d’erreurs quantiques étaient de plus proches analogues aux partages de secrets quantiques que ne leur étaient les codes de partage de secrets classiques. Finalement, nous présenterons un de nos trois résultats parus dans A. Broadbent, P.-R. Chouha, A. Tapp (2009); un protocole sécuritaire et minimal de partage de secret quantique a seuil (les deux autres résultats dont nous traiterons pas ici portent sur la complexité de la communication et sur la simulation classique de l’état de GHZ).In this thesis, we will focus on a cryptographic primitive known as secret sharing. We will explore both the classical and quantum domains of such schemes culminating our study by presenting a new protocol for sharing a quantum secret using the minimal number of possible quantum shares i.e. one single quantum share per participant. We will start our study by presenting in the preliminary chapter, a brief mathematical survey of quantum information theory (QIT) which has for goal primarily to establish the notation used throughout the manuscript as well as presenting a précis of the mathematical properties of the Greenberger-Horne-Zeilinger (GHZ)-state, which is used thoroughly in cryptography and in communication games. But as we mentioned above, our main focus will be on cryptography. In chapter two, we will pay a close attention to classical and quantum error corrections codes (QECC) since they will become of extreme importance when we introduce quantum secret sharing schemes in the following chapter. In the first part of chapter three, we will focus on classical secret shearing, presenting a general framework for such a primitive all the while illustrating the abstract concepts with examples presented both for their historical and analytical relevance. This first part (chapters one and two) will pave the way for our exposition of the theory of Quantum Secret Sharing (QSS), which will be the focus of the second part of chapter three. We will present then the most general theorems and definitions known to date for the construction of such primitives putting emphasis on the special case of quantum threshold schemes. We will show how quantum error correction codes are related to QSS schemes and show how this relation leads to a very solid correspondence to the point that QECC’s are closer analogues to QSS schemes than are the classical secret sharing primitives. Finally, we will present one of the three results we have in A. Broadbent, P.-R. Chouha, A. Tapp (2009) in particular, a secure minimal quantum threshold protocol (the other two results deal with communication complexity and the classical simulation of the GHZ-state)

Multipoint-Interconnected Quantum Communication Networks

As quantum computers with sufficient computational power are becoming mature, the security of classical communication and cryptography may compromise, which is based on the mathematical complexity. Quantum communication technology is a promising solution to secure communication based on quantum mechanics. To meet the secure communication requirements of multiple users, multipoint-interconnected quantum communication networks are specified, including quantum key distribution networks and quantum teleportation networks. The enabling technologies for quantum communication are the important bases for multipoint-interconnected quantum communication networks. To achieve the better connection, resource utilization, and resilience of multipoint-interconnected quantum communication networks, the efficient network architecture and optimization methods are summarized, and open issues in quantum communication networks are discussed

Quantum Machine Learning for 6G Communication Networks: State-of-the-Art and Vision for the Future

The upcoming 5th Generation (5G) of wireless networks is expected to lay a foundation of intelligent networks with the provision of some isolated Artificial Intelligence (AI) operations. However, fully-intelligent network orchestration and management for providing innovative services will only be realized in Beyond 5G (B5G) networks. To this end, we envisage that the 6th Generation (6G) of wireless networks will be driven by on-demand self-reconfiguration to ensure a many-fold increase in the network performanceandservicetypes.Theincreasinglystringentperformancerequirementsofemergingnetworks may finally trigger the deployment of some interesting new technologies such as large intelligent surfaces, electromagnetic-orbital angular momentum, visible light communications and cell-free communications – tonameafew.Ourvisionfor6Gis–amassivelyconnectedcomplexnetworkcapableofrapidlyresponding to the users’ service calls through real-time learning of the network state as described by the network-edge (e.g., base-station locations, cache contents, etc.), air interface (e.g., radio spectrum, propagation channel, etc.), and the user-side (e.g., battery-life, locations, etc.). The multi-state, multi-dimensional nature of the network state, requiring real-time knowledge, can be viewed as a quantum uncertainty problem. In this regard, the emerging paradigms of Machine Learning (ML), Quantum Computing (QC), and Quantum ML (QML) and their synergies with communication networks can be considered as core 6G enablers. Considering these potentials, starting with the 5G target services and enabling technologies, we provide a comprehensivereviewoftherelatedstate-of-the-artinthedomainsofML(includingdeeplearning),QCand QML, and identify their potential benefits, issues and use cases for their applications in the B5G networks. Subsequently,weproposeanovelQC-assistedandQML-basedframeworkfor6Gcommunicationnetworks whilearticulatingitschallengesandpotentialenablingtechnologiesatthenetwork-infrastructure,networkedge, air interface and user-end. Finally, some promising future research directions for the quantum- and QML-assisted B5G networks are identified and discussed

Ideal quantum protocols in the non-ideal physical world

The development of quantum protocols from conception to experimental realizations is one of the main sources of the stimulating exchange between fundamental and experimental research characteristic to quantum information processing. In this thesis we contribute to the development of two recent quantum protocols, Universal Blind Quantum Computation (UBQC) and Quantum Digital Signatures (QDS). UBQC allows a client to delegate a quantum computation to a more powerful quantum server while keeping the input and computation private. We analyse the resilience of the privacy of UBQC under imperfections. Then, we introduce approximate blindness quantifying any compromise to privacy, and propose a protocol which enables arbitrary levels of security despite imperfections. Subsequently, we investigate the adaptability of UBQC to alternative implementations with practical advantages. QDS allow a party to send a message to other parties which cannot be forged, modified or repudiated. We analyse the security properties of a first proof-of-principle experiment of QDS, implemented in an optical system. We estimate the security failure probabilities of our system as a function of protocol parameters, under all but the most general types of attacks. Additionally, we develop new techniques for analysing transformations between symmetric sets of states, utilized not only in the security proofs of QDS but in other applications as well