For modern cryptography, the security of a system is defined as the sum of the resources required to break it. With the advent of efficient quantum computers and the new algorithmic possibilities that this opens, this amount of resource is destined to change.In this thesis, we take a step towards a better understanding of this quantum threat. After an introduction to quantum computation and cryptography, we show quantum attacks against the Legendre PRF in the setting without superposition queries and reduced quantum memory. Afterwards, we present a general way to transpose boomerang attacks into quantum attacks as well as some applications. We continue on a doubling method for block ciphers inspired by the Encrypt-Mix-Encrypt scheme and prove its security. We end by building a quantum version of the 3G/4G/5G UMTS-AKA authentication protocol before showing the security as well as the underlying primitives Milenage and TUAK.
For modern cryptography, the security of a system is defined as the sum of the resources required to break it. With the advent of efficient quantum computers and the new algorithmic possibilities that this opens, this amount of resource is destined to change.In this thesis, we take a step towards a better understanding of this quantum threat. After an introduction to quantum computation and cryptography, we show quantum attacks against the Legendre PRF in the setting without superposition queries and reduced quantum memory. Afterwards, we present a general way to transpose boomerang attacks into quantum attacks as well as some applications. We continue on a doubling method for block ciphers inspired by the Encrypt-Mix-Encrypt scheme and prove its security. We end by building a quantum version of the 3G/4G/5G UMTS-AKA authentication protocol before showing the security as well as the underlying primitives Milenage and TUAK.
The existence of a quantum computer is one of the most significant threats cryptography has ever faced. However, it seems that real world protocols received little attention so far with respect to their future security. Indeed merely relying upon post-quantum primitives may not suffice in order for a security protocol to be resistant in a full quantum world. In this paper, we consider the fundamental UMTS key agreement used in 3G but also in 4G (LTE), and in the (recently deployed) 5G technology. We analyze the protocol in a quantum setting, with quantum communications (allowing superposition queries by the involved parties), and where quantum computation is granted to the adversary. We prove that, assuming the underlying symmetric-key primitive is quantum-secure, the UMTS key agreement is also quantum-secure. We also give a quantum security analysis of the underlying primitives, namely Milenage and TUAK. To the best of our knowledge this paper provides the first rigorous proof of the UMTS key agreement in a strong quantum setting. Our result shows that in the quantum world to come, the UMTS technology remains a valid scheme in order to secure the communications of billions of users.
The demands for secure communication systems have been growing rapidly as technologies in computer networks advance. However, classical cryptography employed in network systems is only secure when malicious users do not have enough computational power to break the security in a practical amount of time. Quantum cryptography provides theoretically unbreakable security since its security relies on quantum mechanical properties. This dissertation resolves the weakness of classical cryptography in computer networks by developing novel cryptographic schemes. First, a new encryption scheme, quantum commutative encryption (QCE), has been developed by utilizing quantum superposition states. The analysis of possible attacks to the developed encryption scheme, the advantages of the developed scheme, and the requirements to utilize the developed scheme in a communication system are presented. Also, an example of realization with current technologies is shown.
Considering all the characteristics of the developed encryption scheme, a key distribution protocol, two authentication protocols, secret sharing scheme, and the possible practical application of the secret sharing scheme are designed by making use of the developed encryption scheme. This dissertation also discusses the security analysis for each developed scheme. All developed quantum cryptographic schemes are theoretically unbreakable and can be realized with current technologies.
The main contributions of this dissertation are not only the proposal of novel schemes, but also a demonstration of how quantum mechanical properties can be utilized in computer engineering/science.
In this thesis, we study the security of cryptographic systems against an adversary who has access to a quantum computer. In quantum computing, we studied the hidden period and hidden shift problems, which are among the few known problems that have some applications in cryptogaphy and for which the best known quantum algorithm is more than polynomially faster than the best known classical algorithm. We proposed some improvements, new tradeoffs between classical and quantum time and memory, and extended their scope of applications to cases where only a classical oracle is available. In cryptanalysis, in symmetric cryptography, we proposed some attacks against symmetric constructions based on hidden shifts, and generalized many attacks using hidden periods to cases where the construction is only accessible classically. We proposed a quantum cryptanalysis of the different versions of the authenticated cipher AEZ and some quantum versions of multiple slide attacks, which are a classical family of cryptanalyses. This rewriting of attacks in the formalism of hidden periods has allowed us to propose a new classical attack against multiple variants of the cipher MiMC. In asymmetric cryptography, we proposed a concrete and asymptotic quantum security analysis of some isogeny-based key exchanges. Finally, we studied quantum security in some cases where these hidden structure problems do not apply, with in particular the first quantum security analysis of AES, the most used symmetric cipher to date.
The realm of this thesis is cryptographic protocol theory in the quantum world. We study the security of quantum and classical protocols against adversaries that are assumed to exploit quantum effects to their advantage. Security in the quantum world means that quantum computation does not jeopardize the assumption, underlying the protocol construction. But moreover, we encounter additional setbacks in the security proofs, which are mostly due to the fact that some well-known classical proof techniques are forbidden by certain properties of a quantum environment. Interestingly, we can exploit some of the very same properties to the benefit of quantum cryptography. Thus, this work lies right at the heart of the conflict between highly potential effects but likewise rather demanding conditions in the quantum world.
Quantum cryptography aims at solving the everlasting problem of unconditional security in private communication. Every time we send personal information over a telecom channel a sophisticate algorithm protect our privacy making our data unintelligible to unauthorized receivers. These protocols resulted from the long history of cryptography. The security of modern cryptographic systems is guaranteed by complexity: the computational power that would be needed for gaining info on the code key largely exceed available one. Security of actual crypto systems is not “by principle” but “practical”. On the contrary, quantum technology promises to make possible to realize provably secure protocols. Quantum cryptology exploits paradigmatic aspects of quantum mechanics, like superposition principle and uncertainty relations. In this contribution, after a brief historical introduction, we aim at giving a survey on the physical principles underlying the quantum approach to cryptography. Then, we analyze a possible continuous variable protocol.
Cryptographie à clé secrète et attaquant quantique dans le monde des télécommunications Pour la cryptographie moderne, la sécurité d'un système est définie comme la somme des ressources nécessaires pour le briser. Avec la venue d'ordinateurs quantiques efficaces et les nouvelles possibilités algorithmiques que cela ouvre, ce montant de ressources est voué à changer. Dans cette thèse, nous effectuons un pas en direction d'une meilleure compréhension de cette menace quantique. Après une introduction au calcul quantique et à la cryptographie, nous montrons des attaques quantiques contre la fonction pseudo-aléatoire de Legendre sans requête en superposition et en mémoire quantique réduite. Par la suite, nous exposons une manière générale de transposer les attaques boomerang en algorithmique quantique ainsi que quelques applications. Nous continuons sur une méthode de doublement de taille de blocs pour les chiffrements à blocs inspirée sur le schéma Encrypt-Mix-Encrypt et nous en montrons la sécurité. Nous finissons par la construction d'une version quantique du protocole d'authentification de la 3G/4G/5G UMTS-AKA avant d'en montrer la sécurité ainsi que celle des primitives sous-jacentes Milenage et TUAK.