Homomorphic cryptography provides a third party with the ability to perform simple computations on encrypted data without revealing any information about the data itself. Typically, a third party can calculate one of the encrypted sum or the encrypted product of two encrypted messages. This is possible due to the fact that the encryption function is a group homomorphism, and thus preserves group operations. This makes homomorphic cryptosystems useful in a wide variety of privacy preserving protocols. A comprehensive survey of known homomorphic cryptosystems is provided, including formal definitions, security assumptions, and outlines of security proofs for each cryptosystem presented. Threshold variants of several homomorphic cryptosystems are also considered, with the first construction of a threshold Boneh-Goh-Nissim cryptosystem given, along with a complete proof of security under the threshold semantic security game of Fouque, Poupard, and Stern. This approach is based on Shoup's approach to threshold RSA signatures, which has been previously applied to the Paillier and Damg\aa rd-Jurik cryptosystems. The question of whether or not this approach is suitable for other homomorphic cryptosystems is investigated, with results suggesting that a different approach is required when decryption requires a reduction modulo a secret value. The wide variety of protocols utilizing homomorphic cryptography makes it difficult to provide a comprehensive survey, and while an overview of applications is given, it is limited in scope and intended to provide an introduction to the various ways in which homomorphic cryptography is used beyond simple addition or multiplication of encrypted messages. In the case of strong conditional oblivious tranfser, a new protocol implementing the greater than predicate is presented, utilizing some special properties of the Boneh-Goh-Nissim cryptosystem to achieve security against a malicious receiver.

Homomorphic cryptography provides a third party with the ability to perform simple computations on encrypted data without revealing any information about the data itself. Typically, a third party can calculate one of the encrypted sum or the encrypted product of two encrypted messages. This is possible due to the fact that the encryption function is a group homomorphism, and thus preserves group operations. This makes homomorphic cryptosystems useful in a wide variety of privacy preserving protocols. A comprehensive survey of known homomorphic cryptosystems is provided, including formal definitions, security assumptions, and outlines of security proofs for each cryptosystem presented. Threshold variants of several homomorphic cryptosystems are also considered, with the first construction of a threshold Boneh-Goh-Nissim cryptosystem given, along with a complete proof of security under the threshold semantic security game of Fouque, Poupard, and Stern. This approach is based on Shoup's approach to threshold RSA signatures, which has been previously applied to the Paillier and Damg\aa rd-Jurik cryptosystems. The question of whether or not this approach is suitable for other homomorphic cryptosystems is investigated, with results suggesting that a different approach is required when decryption requires a reduction modulo a secret value. The wide variety of protocols utilizing homomorphic cryptography makes it difficult to provide a comprehensive survey, and while an overview of applications is given, it is limited in scope and intended to provide an introduction to the various ways in which homomorphic cryptography is used beyond simple addition or multiplication of encrypted messages. In the case of strong conditional oblivious tranfser, a new protocol implementing the greater than predicate is presented, utilizing some special properties of the Boneh-Goh-Nissim cryptosystem to achieve security against a malicious receiver.

[ES] La confianza es la base de las sociedades modernas. Sin embargo, las relaciones basadas en confianza son difíciles de establecer y pueden ser explotadas fácilmente con resultados devastadores. En esta tesis exploramos el uso de protocolos criptográficos distribuidos para construir sistemas confiables donde la confianza se vea reemplazada por garantías matemáticas y criptográficas. En estos nuevos sistemas dinámicos, incluso si una de las partes se comporta de manera deshonesta, la integridad y resiliencia del sistema están garantizadas, ya que existen mecanismos para superar este tipo de situaciones. Por lo tanto, hay una transición de sistemas basados en la confianza, a esquemas donde esta misma confianza es descentralizada entre un conjunto de individuos o entidades. Cada miembro de este conjunto puede ser auditado, y la verificación universal asegura que todos los usuarios puedan calcular el estado final en cada uno de estos métodos, sin comprometer la privacidad individual de los usuarios. La mayoría de los problemas de colaboración a los que nos enfrentamos como sociedad, pueden reducirse a dos grandes dilemas: el votar una propuesta, o un representante político, ó identificarnos a nosotros mismos como miembros de un colectivo con derecho de acceso a un recurso o servicio. Por ello, esta tesis doctoral se centra en los protocolos criptográficos distribuidos aplicados al voto electrónico y la identificación anónima. Hemos desarrollado tres protocolos para el voto electrónico que complementan y mejoran a los métodos más tradicionales, y además protegen la privacidad de los votantes al mismo tiempo que aseguran la integridad del proceso de voto. En estos sistemas, hemos empleado diferentes mecanismos criptográficos que proveen, bajo diferentes asunciones, de las propiedades de seguridad que todo sistema de voto debe tener. Algunos de estos sistemas son seguros incluso en escenarios pos-cuánticos. También hemos calculado minuciosamente la complejidad temporal de los métodos para demostrar que son eficientes y factibles de ser implementados. Además, hemos implementado algunos de estos sistemas, o partes de ellos, y llevado a cabo una detallada experimentación para demostrar el potencial de nuestras contribuciones. Finalmente, estudiamos en detalle el problema de la identificación y proponemos tres métodos no interactivos y distribuidos que permiten el registro y acceso anónimo. Estos protocolos son especialmente ligeros y agnósticos en su implementación, lo que permite que puedan ser integrados con múltiples propósitos. Hemos formalizado y demostrado la seguridad de nuestros protocolos de identificación, y hemos realizado una implementación completa de ellos para, una vez más, demostrar la factibilidad y eficiencia de las soluciones propuestas. Bajo este marco teórico de identificación, somos capaces de asegurar el recurso custodiado, sin que ello suponga una violación para el anonimato de los usuarios. / [CA] La confiança és la base de les societats modernes. No obstant això, les relacions basades en confiança són difícils d’establir i poden ser explotades fàcilment amb resultats devastadors. En aquesta tesi explorem l’ús de protocols criptogràfics distribuïts per a construir sistemes de confiança on la confiança es veja reemplaçada per garanties matemàtiques i criptogràfiques. En aquests nous sistemes dinàmics, fins i tot si una de les parts es comporta de manera deshonesta, la integritat i resiliència del sistema estan garantides, ja que existeixen mecanismes per a superar aquest tipus de situacions. Per tant, hi ha una transició de sistemes basats en la confiança, a esquemes on aquesta acarona confiança és descentralitzada entre un conjunt d’individus o entitats. Cada membre d’aquest conjunt pot ser auditat, i la verificació universal assegura que tots els usuaris puguen calcular l’estat final en cadascun d’aquests mètodes, sense comprometre la privacitat individual dels usuaris. La majoria dels problemes de colůlaboració als quals ens enfrontem com a societat, poden reduir-se a dos grans dilemes: el votar una proposta, o un representant polític, o identificar-nos a nosaltres mateixos com a membres d’un colůlectiu amb dret d’accés a un recurs o servei. Per això, aquesta tesi doctoral se centra en els protocols criptogràfics distribuïts aplicats al vot electrònic i la identificació anònima. Hem desenvolupat tres protocols per al vot electrònic que complementen i milloren als mètodes més tradicionals, i a més protegeixen la privacitat dels votants al mateix temps que asseguren la integritat del procés de vot. En aquests sistemes, hem emprat diferents mecanismes criptogràfics que proveeixen, baix diferents assumpcions, de les propietats de seguretat que tot sistema de vot ha de tindre. Alguns d’aquests sistemes són segurs fins i tot en escenaris post-quàntics. També hem calculat minuciosament la complexitat temporal dels mètodes per a demostrar que són eficients i factibles de ser implementats. A més, hem implementats alguns d’aquests sistemes, o parts d’ells, i dut a terme una detallada experimentació per a demostrar la potencial de les nostres contribucions. Finalment, estudiem detalladament el problema de la identificació i proposem tres mètodes no interactius i distribuïts que permeten el registre i accés anònim. Aquests protocols són especialment lleugers i agnòstics en la seua implementació, la qual cosa permet que puguen ser integrats amb múltiples propòsits. Hem formalitzat i demostrat la seguretat dels nostres protocols d’identificació, i hem realitzat una implementació completa d’ells per a, una vegada més, demostrar la factibilitat i eficiència de les solucions proposades. Sota aquest marc teòric d’identificació, som capaces d’assegurar el recurs custodiat, sense que això supose una violació per a l’anonimat dels usuaris. / [EN] Trust is the base of modern societies. However, trust is difficult to achieve and can be exploited easily with devastating results. In this thesis, we explore the use of distributed cryptographic protocols to build reliable systems where trust can be replaced by cryptographic and mathematical guarantees. In these adaptive systems, even if one involved party acts dishonestly, the integrity and robustness of the system can be ensured as there exist mechanisms to overcome these scenarios. Therefore, there is a transition from systems based in trust, to schemes where trust is distributed between decentralized parties. Individual parties can be audited, and universal verifiability ensures that any user can compute the final state of these methods, without compromising individual users’ privacy. Most collaboration problems we face as societies can be reduced to two main dilemmas: voting on a proposal or electing political representatives, or identifying ourselves as valid members of a collective to access a service or resource. Hence, this doctoral thesis focuses on distributed cryptographic protocols for electronic voting and anonymous identification. We have developed three electronic voting schemes that enhance traditional methods, and protect the privacy of electors while ensuring the integrity of the whole election. In these systems, we have employed different cryptographic mechanisms, that fulfill all the desired security properties of an electronic voting scheme, under different assumptions. Some of them are secure even in post-quantum scenarios. We have provided a detailed time-complexity analysis to prove that our proposed methods are efficient and feasible to implement. We also implemented some voting protocols, or parts of them, and carried out meticulous experimentation to show the potential of our contributions. Finally, we study in detail the identification problem and propose three distributed and non-interactive methods for anonymous registration and access. These three protocols are especially lightweight and application agnostic, making them feasible to be integrated with many purposes. We formally analyze and demonstrate the security of our identification protocols, and provide a complete implementation of them to once again show the feasibility and effectiveness of the developed solutions. Using this identification framework, we can ensure the security of the guarded resource, while also preserving the anonymity of the users. / Larriba Flor, AM. (2023). Distributed Cryptographic Protocols [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/198106

Au cours de la dernière décennie, avec la standardisation d’Internet, le développement des réseaux à haut débit, le paiement à l’usage et la quête sociétale de la mobilité, le monde informatique a vu se populariser un nouveau paradigme, le Cloud. Le recours au cloud est de plus en plus remarquable compte tenu de plusieurs facteurs, notamment ses architectures rentables, prenant en charge la transmission, le stockage et le calcul intensif de données. Cependant, ces services de stockage prometteurs soulèvent la question de la protection des données et de la conformité aux réglementations, considérablement due à la perte de maîtrise et de gouvernance. Cette dissertation vise à surmonter ce dilemme, tout en tenant compte de deux préoccupations de sécurité des données, à savoir la confidentialité des données et l’intégrité des données. En premier lieu, nous nous concentrons sur la confidentialité des données, un enjeu assez considérable étant donné le partage de données flexible au sein d’un groupe dynamique d’utilisateurs. Cet enjeu exige, par conséquence, un partage efficace des clés entre les membres du groupe. Pour répondre à cette préoccupation, nous avons, d’une part, proposé une nouvelle méthode reposant sur l’utilisation de la cryptographie basée sur l’identité (IBC), où chaque client agit comme une entité génératrice de clés privées. Ainsi, il génère ses propres éléments publics et s’en sert pour le calcul de sa clé privée correspondante. Grâce aux propriétés d’IBC, cette contribution a démontré sa résistance face aux accès non autorisés aux données au cours du processus de partage, tout en tenant compte de deux modèles de sécurité, à savoir un serveur de stockage honnête mais curieux et un utilisateur malveillant. D’autre part, nous définissons CloudaSec, une solution à base de clé publique, qui propose la séparation de la gestion des clés et les techniques de chiffrement, sur deux couches. En effet, CloudaSec permet un déploiement flexible d’un scénario de partage de données ainsi que des garanties de sécurité solides pour les données externalisées sur les serveurs du cloud. Les résultats expérimentaux, sous OpenStack Swift, ont prouvé l’efficacité de CloudaSec, en tenant compte de l’impact des opérations cryptographiques sur le terminal du client. En deuxième lieu, nous abordons la problématique de la preuve de possession de données (PDP). En fait, le client du cloud doit avoir un moyen efficace lui permettant d’effectuer des vérifications périodiques d’intégrité à distance, sans garder les données localement. La preuve de possession se base sur trois aspects : le niveau de sécurité, la vérification publique, et les performances. Cet enjeu est amplifié par des contraintes de stockage et de calcul du terminal client et de la taille des données externalisées. Afin de satisfaire à cette exigence de sécurité, nous définissons d’abord un nouveau protocole PDP, sans apport de connaissance, qui fournit des garanties déterministes de vérification d’intégrité, en s’appuyant sur l’unicité de la division euclidienne. Ces garanties sont considérées comme intéressantes par rapport à plusieurs schémas proposés, présentant des approches probabilistes. Ensuite, nous proposons SHoPS, un protocole de preuve de possession de données capable de traiter les trois relations d’ensembles homomorphiques. SHoPS permet ainsi au client non seulement d’obtenir une preuve de la possession du serveur distant, mais aussi de vérifier que le fichier, en question, est bien réparti sur plusieurs périphériques de stockage permettant d’atteindre un certain niveau de la tolérance aux pannes. En effet, nous présentons l’ensemble des propriétés homomorphiques, qui étend la malléabilité du procédé aux propriétés d’union, intersection et inclusion / Recent technological advances have given rise to the popularity and success of cloud. This new paradigm is gaining an expanding interest, since it provides cost efficient architectures that support the transmission, storage, and intensive computing of data. However, these promising storage services bring many challenging design issues, considerably due to the loss of data control. These challenges, namely data confidentiality and data integrity, have significant influence on the security and performances of the cloud system. This thesis aims at overcoming this trade-off, while considering two data security concerns. On one hand, we focus on data confidentiality preservation which becomes more complex with flexible data sharing among a dynamic group of users. It requires the secrecy of outsourced data and an efficient sharing of decrypting keys between different authorized users. For this purpose, we, first, proposed a new method relying on the use of ID-Based Cryptography (IBC), where each client acts as a Private Key Generator (PKG). That is, he generates his own public elements and derives his corresponding private key using a secret. Thanks to IBC properties, this contribution is shown to support data privacy and confidentiality, and to be resistant to unauthorized access to data during the sharing process, while considering two realistic threat models, namely an honest but curious server and a malicious user adversary. Second, we define CloudaSec, a public key based solution, which proposes the separation of subscription-based key management and confidentiality-oriented asymmetric encryption policies. That is, CloudaSec enables flexible and scalable deployment of the solution as well as strong security guarantees for outsourced data in cloud servers. Experimental results, under OpenStack Swift, have proven the efficiency of CloudaSec in scalable data sharing, while considering the impact of the cryptographic operations at the client side. On the other hand, we address the Proof of Data Possession (PDP) concern. In fact, the cloud customer should have an efficient way to perform periodical remote integrity verifications, without keeping the data locally, following three substantial aspects : security level, public verifiability, and performance. This concern is magnified by the client’s constrained storage and computation capabilities and the large size of outsourced data. In order to fulfill this security requirement, we first define a new zero-knowledge PDP proto- col that provides deterministic integrity verification guarantees, relying on the uniqueness of the Euclidean Division. These guarantees are considered as interesting, compared to several proposed schemes, presenting probabilistic approaches. Then, we propose SHoPS, a Set-Homomorphic Proof of Data Possession scheme, supporting the 3 levels of data verification. SHoPS enables the cloud client not only to obtain a proof of possession from the remote server, but also to verify that a given data file is distributed across multiple storage devices to achieve a certain desired level of fault tolerance. Indeed, we present the set homomorphism property, which extends malleability to set operations properties, such as union, intersection and inclusion. SHoPS presents high security level and low processing complexity. For instance, SHoPS saves energy within the cloud provider by distributing the computation over multiple nodes. Each node provides proofs of local data block sets. This is to make applicable, a resulting proof over sets of data blocks, satisfying several needs, such as, proofs aggregation