This dissertation proposes an efficient representation of a sparse Merkle tree (SMT): an authenticated data structure that supports logarithmic insertion, removal, and look-up in a verifiable manner. The proposal is general in the sense that it can be implemented using a variety of underlying non-authenticated data structures, and it allows trading time for space by the use of an abstract model which represents caching strategies. Both theoretical evaluations and performance results from a proof-of-concept implementation are provided, and the proposed SMT is applied to another authenticated data structure referred to as Balloon. The resulting Balloon has preserved efficiency in the expected case, and is improved with respect to worst case scenarios.

Cryptographic digital signatures provide authentication to communicating parties over communication networks. They are integral asymmetric primitives in cryptography. The current digital signature infrastructure adopts schemes that rely on the hardness of finding discrete logarithms and factoring in finite groups. Given the recent advances in physics which point towards the eventual construction of large scale quantum computers, these hard problems will be solved in polynomial time using Shor’s algorithm. Hence, there is a clear need to migrate the cryptographic infrastructure to post-quantum secure alternatives. Such an initiative is demonstrated by the PQCRYPTO project and the current Post-Quantum Cryptography (PQC) standardization competition run by the National Institute of Standards and Technology (NIST). This dissertation considers hash-based digital signature schemes. Such algorithms rely on simple security notions such as preimage, and weak and strong collision resistances of hash functions. These notions are well-understood and their security against quantum computers has been well-analyzed. However, existing hash-based signature schemes have large signature sizes and high computational costs. Moreover, the signature size increases with the number of messages to be signed by a key pair. The goal of this work is to develop hash-based digital signature schemes to overcome the aforementioned limitations. First, FORS, the underlying few-time signature scheme of the NIST PQC alternate candidate SPHINCS+ is analyzed against adaptive chosen message attacks, and DFORS, a few-time signature scheme with adaptive chosen message security, is proposed. Second, a new variant of SPHINCS+ is introduced that improves the computational cost and security level. Security analysis for the new variant is presented. In addition, the hash-based group digital signature schemes, Group Merkle (GM) and Dynamic Group Merkle (DGM), are studied and their security is analyzed. Group Merkle Multi-Treem (GMMT) is proposed to solve some of the limitations of the GM and DGM hash-based group signature schemes. / Graduate

Ces dernières années, les systèmes informatiques (Cloud Computing, systèmes embarqués, etc.) sont devenus omniprésents. La plupart de ces systèmes utilisent des espaces de stockage (flash,RAM, etc.) non fiables ou non dignes de confiance pour stocker du code ou des données. La confidentialité et l’intégrité de ces données peuvent être menacées par des attaques matérielles (espionnage de bus de communication entre le composant de calcul et le composant de stockage) ou logicielles. Ces attaques peuvent ainsi révéler des informations sensibles à l’adversaire ou perturber le bon fonctionnement du système. Dans cette thèse, nous nous sommes focalisés, dans le contexte des systèmes embarqués, sur les attaques menaçant la confidentialité et l’intégrité des données qui transitent sur le bus de communication avec la mémoire ou qui sont stockées dans celle-ci.Plusieurs primitives de protection de confidentialité et d’intégrité ont déjà été proposées dans la littérature, et notamment les arbres de Merkle, une structure de données protégeant efficacement l’intégrité des données notamment contre les attaques par rejeu. Malheureusement,ces arbres ont un impact important sur les performances et sur l’empreinte mémoire du système.Dans cette thèse, nous proposons une solution basée sur des variantes d’arbres de Merkle (arbres creux) et un mécanisme de gestion adapté du cache afin de réduire grandement l’impact de la vérification d’intégrité d’un espace de stockage non fiable. Les performances de cette solution ont été évaluées théoriquement et à l’aide de simulations. De plus, une preuve est donnée de l’équivalence, du point de vue de la sécurité, avec les arbres de Merkle classiques.Enfin, cette solution a été implémentée dans le projet SecBus, une architecture matérielle et logicielle ayant pour objectif de garantir la confidentialité et l’intégrité du contenu des mémoires externes d’un système à base de microprocesseurs. Un prototype de cette architecture a été réalisé et les résultats de l’évaluation de ce dernier sont donnés. / During the past few years, computer systems (Cloud Computing, embedded systems...) have become ubiquitous. Most of these systems use unreliable or untrusted storage (flash, RAM...)to store code or data. The confidentiality and integrity of these data can be threaten by hardware (spying on the communication bus between the processing component and the storage component) or software attacks. These attacks can disclose sensitive information to the adversary or disturb the behavior of the system. In this thesis, in the context of embedded systems, we focused on the attacks that threaten the confidentiality and integrity of data that are transmittedover the memory bus or that are stored inside the memory. Several primitives used to protect the confidentiality and integrity of data have been proposed in the literature, including Merkle trees, a data structure that can protect the integrity of data including against replay attacks. However, these trees have a large impact on the performances and the memory footprint of the system. In this thesis, we propose a solution based on variants of Merkle trees (hollow trees) and a modified cache management mechanism to greatly reduce the impact of the verification of the integrity. The performances of this solution have been evaluated both theoretically and in practice using simulations. In addition, a proof a security equivalence with regular Merkle treesis given. Finally, this solution has been implemented in the SecBus architecture which aims at protecting the integrity and confidentiality of the content of external memories in an embedded system. A prototype of this architecture has been developed and the results of its evaluation are given.