Short undeniable signatures:design, analysis, and applications

Digital signatures are one of the main achievements of public-key cryptography and constitute a fundamental tool to ensure data authentication. Although their universal verifiability has the advantage to facilitate their verification by the recipient, this property may have undesirable consequences when dealing with sensitive and private information. Motivated by such considerations, undeniable signatures, whose verification requires the cooperation of the signer in an interactive way, were invented. This thesis is mainly devoted to the design and analysis of short undeniable signatures. Exploiting their online property, we can achieve signatures with a fully scalable size depending on the security requirements. To this end, we develop a general framework based on the interpolation of group elements by a group homomorphism, leading to the design of a generic undeniable signature scheme. On the one hand, this paradigm allows to consider some previous undeniable signature schemes in a unified setting. On the other hand, by selecting group homomorphisms with a small group range, we obtain very short signatures. After providing theoretical results related to the interpolation of group homomorphisms, we develop some interactive proofs in which the prover convinces a verifier of the interpolation (resp. non-interpolation) of some given points by a group homomorphism which he keeps secret. Based on these protocols, we devise our new undeniable signature scheme and prove its security in a formal way. We theoretically analyze the special class of group characters on Z*n. After studying algorithmic aspects of the homomorphism evaluation, we compare the efficiency of different homomorphisms and show that the Legendre symbol leads to the fastest signature generation. We investigate potential applications based on the specific properties of our signature scheme. Finally, in a topic closely related to undeniable signatures, we revisit the designated confirmer signature of Chaum and formally prove the security of a generalized version

Another Look at Some Isogeny Hardness Assumptions

The security proofs for isogeny-based undeniable signature schemes have been based primarily on the assumptions that the One-Sided Modified SSCDH problem and the One-More SSCDH problem are intractable. We challenge the validity of these assumptions, showing that both the decisional and computational variants of these problems can be solved in polynomial time. We further demonstrate an attack, applicable to two undeniable signature schemes, one of which was proposed at PQCrypto 2014. The attack allows to forge signatures in 24λ/5 steps on a classical computer. This is an improvement over the expected classical security of 2λ, where λ denotes the chosen security parameter.SCOPUS: cp.kinfo:eu-repo/semantics/publishedCryptographers Track at the RSA Conference, CT-RSA 2020; San Francisco; United States; 24 February 2020 through 28 February 2020ISBN: 978-303040185-

Secure Many-to-One Communications in Wireless Sensor Networks

Wireless Sensor Networks (WSN) are formed by nodes with limited computational and power resources. WSNs are finding an increasing number of applications, both civilian and military, most of which require security for the sensed data being collected by the base station from remote sensor nodes. In addition, when many sensor nodes transmit to the base station, the implosion problem arises. Providing security measures and implosion-resistance in a resource-limited environment is a real challenge. This article reviews the aggregation strategies proposed in the literature to handle the bandwidth and security problems related to many-to-one transmission in WSNs. Recent contributions to secure lossless many-to-one communication developed by the authors in the context of several Spanish-funded projects are surveyed. Ongoing work on the secure lossy many-to-one communication is also sketched

Design and Analysis of Opaque Signatures

Digital signatures were introduced to guarantee the authenticity and integrity of the underlying messages. A digital signature scheme comprises the key generation, the signature, and the verification algorithms. The key generation algorithm creates the signing and the verifying keys, called also the signer’s private and public keys respectively. The signature algorithm, which is run by the signer, produces a signature on the input message. Finally, the verification algorithm, run by anyone who knows the signer’s public key, checks whether a purported signature on some message is valid or not. The last property, namely the universal verification of digital signatures is undesirable in situations where the signed data is commercially or personally sensitive. Therefore, mechanisms which share most properties with digital signatures except for the universal verification were invented to respond to the aforementioned need; we call such mechanisms “opaque signatures”. In this thesis, we study the signatures where the verification cannot be achieved without the cooperation of a specific entity, namely the signer in case of undeniable signatures, or the confirmer in case of confirmer signatures; we make three main contributions. We first study the relationship between two security properties important for public key encryption, namely data privacy and key privacy. Our study is motivated by the fact that opaque signatures involve always an encryption layer that ensures their opacity. The properties required for this encryption vary according to whether we want to protect the identity (i.e. the key) of the signer or hide the validity of the signature. Therefore, it would be convenient to use existing work about the encryption scheme in order to derive one notion from the other. Next, we delve into the generic constructions of confirmer signatures from basic cryptographic primitives, e.g. digital signatures, encryption, or commitment schemes. In fact, generic constructions give easy-to-understand and easy-to-prove schemes, however, this convenience is often achieved at the expense of efficiency. In this contribution, which constitutes the core of this thesis, we first analyze the already existing constructions; our study concludes that the popular generic constructions of confirmer signatures necessitate strong security assumptions on the building blocks, which impacts negatively the efficiency of the resulting signatures. Next, we show that a small change in these constructionsmakes these assumptions drop drastically, allowing as a result constructions with instantiations that compete with the dedicated realizations of these signatures. Finally, we revisit two early undeniable signatures which were proposed with a conjectural security. We disprove the claimed security of the first scheme, and we provide a fix to it in order to achieve strong security properties. Next, we upgrade the second scheme so that it supports a iii desirable feature, and we provide a formal security treatment of the new scheme: we prove that it is secure assuming new reasonable assumptions on the underlying constituents

A post-quantum digital signature scheme based on supersingular isogenies

We present the first general-purpose digital signature scheme based on supersingular elliptic curve isogenies secure against quantum adversaries in the quantum random oracle model with small key sizes. This scheme is an application of Unruh’s construction of non-interactive zero-knowledge proofs to an interactive zero-knowledge proof proposed by De Feo, Jao, and Plut. We implement our proposed scheme on an x86- 64 PC platform as well as an ARM-powered device. We exploit the stateof-the-art techniques to speed up the computations for general C and assembly. Finally, we provide timing results for real world applications

Security and privacy issues in some special-puropse networks

This thesis is about providing security and privacy to new emergent applications which are based on special-purpose networks. More precisely, we study different aspects regarding security and privacy issues related to sensor networks, mobile ad hoc networks, vehicular ad hoc networks and social networks.Sensor networks consist of resource-constrained wireless devices with sensor capabilities. This emerging technology has a wide variety of applications related to event surveillance like emergency response, habitat monitoring or defense-related networks.Ad hoc networks are suited for use in situations where deploying an infrastructure is not cost effective or is not possible for any other reason. When the nodes of an ad hoc network are small mobile devices (e.g. cell phones or PDAs), such a network is called mobile ad hoc network. One of many possible uses of MANETs is to provide crisis management services applications, such as in disaster recovery, where the entire communication infrastructure is destroyed and reestablishing communication quickly is crucial. Another useful situation for MANETs is a scenario without fixed communication systems where there is the need for any kind of collaborative computing. Such situation can occur in both business and military environments.When the mobile nodes of a MANET are embedded in cars, such a network is called Vehicular Ad hoc Network (VANET). This kind of networks can be very useful to increase the road traffic safety and they will be deployed for real use in the forthcoming years. As a proof of that, eight important European vehicle manufacturers have founded the CAR 2 CAR Communication Consortium. This non-profit organisation is dedicated to the objective of further increasing traffic safety and efficiency by means of inter-vehicle communications.Social networks differ from the special-purpose networks commented above in that they are not physical networks. Social networks are applications that work through classic networks. They can be defined as a community of web users where each user can publish and share information and services. Social networks have become an object of study both in computer and social sciences, with even dedicated journals and conferences.The special-purpose networks described above provide a wide range of new services and applications. Even though they are expected to improve the society in several ways, these innovative networks and their related applications bring also security and privacy issues that must be addressed.This thesis solves some security and privacy issues related to such new applications and services. More specifically, it focuses on:·Secure information transmission in many-to-one scenarios with resource-constrained devices such as sensor networks.·Secure and private information sharing in MANETs.·Secure and private information spread in VANETs.·Private resource access in social networks.Results presented in this thesis include four contributions published in ISI JCR journals (IEEE Transactions on Vehicular Technology, Computer Networks (2) and Computer Communications) and two contributions published in two international conferences (Lecture Notes in Computer Science).Esta tesis trata diversos problemas de seguridad y privacidad que surgen al implantar en escenarios reales novedosas aplicaciones basadas en nuevos y emergentes modelos de red. Estos nuevos modelos de red difieren significativamente de las redes de computadores clásicas y son catalogadas como redes de propósito especial. Específicamente, en este trabajo se estudian diferentes aspectos relacionados con la seguridad de la información y la privacidad de los usuarios en redes de sensores, redes ad hoc móviles (MANETs), redes ad hoc vehiculares (VANETs) y redes sociales.Las redes de sensores están formadas por dispositivos inalámbricos muy limitados a nivel de recursos (capacidad de computación y batería) que detectan eventos o condiciones del entorno donde se instalan. Esta tecnología tiene una amplia variedad de aplicaciones entre las que destacan la detección de emergencias o la creación de perímetros de seguridad. Una MANET esta formada por nodos móviles conectados entre ellos mediante conexiones inalámbricas y de forma auto-organizada. Este tipo de redes se constituye sin la ayuda de infraestructuras, por ello son especialmente útiles en situaciones donde implantar una infraestructura es inviable por ser su coste demasiado elevado o por cualquier otra razón. Una de las muchas aplicaciones de las MANETs es proporcionar servicio en situaciones críticas (por ejemplo desastres naturales) donde la infraestructura de comunicaciones ha sido destruida y proporcionar conectividad rápidamente es crucial. Otra aplicación directa aparece en escenarios sin sistemas de comunicación fijos donde existe la necesidad de realizar algún tipo de computación colaborativa entre diversas máquinas. Esta situación se da tanto en ámbitos empresariales como militares.Cuando los nodos móviles de una MANET se asocian a vehículos (coches, camiones.), dicha red se denomina red ad hoc vehicular o VANET. Este tipo de redes pueden ser muy útiles para incrementar la seguridad vial y se espera su implantación para uso real en los próximos años. Como prueba de la gran importancia que tiene esta tecnología, los ocho fabricantes europeos más importantes han fundado la CAR 2 CAR Communication Consortium. Esta organización tiene como objetivo incrementar la seguridad y la eficiencia del tráfico mediante el uso de comunicaciones entre los vehículos.Las redes sociales se diferencian de las redes especiales descritas anteriormente en que éstas no son redes físicas. Las redes sociales son aplicaciones que funcionan a través de las redes de computadores clásicas. Una red de este tipo puede ser definida como una comunidad de usuarios web en donde dichos usuarios pueden publicar y compartir información y servicios. En la actualidad, las redes sociales han adquirido gran importancia ofreciendo un amplio abanico de posibilidades a sus usuarios: trabajar de forma colaborativa, compartir ficheros, búsqueda de nuevos amigos, etc.A continuación se resumen las aplicaciones en las que esta tesis se centra según el tipo de red asociada:·Transmisión segura de información en escenarios muchos-a-uno (múltiples emisores y un solo receptor) donde los dispositivos en uso poseen recursos muy limitados. Este escenario es el habitual en redes de sensores.·Distribución de información de forma segura y preservando la privacidad de los usuarios en redes ad hoc móviles.·Difusión de información (con el objeto de incrementar la seguridad vial) fidedigna preservando la privacidad de los usuarios en redes ad hoc vehiculares.·Acceso a recursos en redes sociales preservando la privacidad de los usuarios. Los resultados de la tesis incluyen cuatro publicaciones en revistas ISI JCR (IEEE Transactions on Vehicular Technology, Computer Networks (2) y Computer Communications) y dos publicaciones en congresos internacionales(Lecture Notes in Computer Science)

Primeless Factoring-Based Cryptography

Factoring-based public-key cryptosystems have an overall complexity which is dominated by the key-production algorithm, which requires the generation of prime numbers. This is most inconvenient in settings where the key-generation is not an one-off process, e.g., secure delegation of computation or EKE password-based key exchange protocols. To this end, we extend the Goldwasser-Micali (GM) cryptosystem to a provably secure system, denoted SIS, where the generation of primes is bypassed. By developing on the correct choice of the parameters of SIS, we align SIS's security guarantees (i.e., resistance to factoring of moduli, etc.) to those of other well-known factoring-based cryptosystems. Taking into consideration different possibilities to implement the fundamental operations, we explicitly compare and contrast the asymptotic complexity of well-known public-key cryptosystems (e.g., GM and/or RSA) with that of SIS's. The latter shows that once we are ready to accept an increase in the size of the moduli, SIS offers a generally lower asymptotic complexity than, e.g., GM or even RSA (when scaling correctly the number of encrypted bits). This would yield most significant speed-ups to applications like the aforementioned secure delegation of computation or protocols where a fresh key needs to be generated with every new session, e.g., EKE password-based key exchange protocols

Pairing Cryptography Meets Isogeny: A New Framework of Isogenous Pairing Groups

We put forth a new mathematical framework called Isogenous Pairing Groups (IPG) and new intractable assumptions in the framework, the Isogenous DBDH (Isog-DBDH) assumption and its variants. Three operations, i.e., exponentiation, pairing and isogeny on elliptic curves are treated under a unified notion of trapdoor homomorphisms, and combinations of the operations have potential new cryptographic applications, in which the compatibility of pairing and isogeny is a main ingredient in IPG. As an example, we present constructions of (small and large universe) key-policy attribute-based encryption (KP-ABE) schemes secure against pre-challenge quantum adversaries in the quantum random oracle model (QROM). Note that our small universe KP-ABE has asymptotically the same efficiency as Goyal et al.\u27s small universe KP-ABE, which has only classical security. As a by-product, we also propose practical (hierarchical) identity-based encryption ((H)IBE) schemes secure against pre-challenge quantum adversaries in the QROM from isogenies, which are based on the Boneh-Franklin IBE and the Gentry-Silverberg HIBE, respectively

Computational problems in supersingular elliptic curve isogenies

We present an overview of supersingular isogeny cryptography and how it fits into the broad theme of post-quantum public key crypto. The paper also gives a brief tutorial of elliptic curve isogenies and the computational problems relevant for supersingular isogeny crypto. Supersingular isogeny crypto is attracting attention due to the fact that the best attacks, both classical and quantum, require exponential time. However, the underlying computational problems have not been sufficiently studied by quantum algorithm researchers, especially since there are significant mathematical preliminaries needed to fully understand isogeny crypto. The main goal of the paper is to advertise various related computational problems, and to explain the relationships between them, in a way that is accessible to experts in quantum algorithms. This is a post-peer-review, pre-copyedit version of an article to be published as a perspective paper in the journal Quantum Information Processing