Comparing proofs of security for lattice-based encryption

This paper describes the limits of various security proofs , using 36 lattice-based KEMs as case studies. This description allows the limits to be systematically compared across these KEMs; shows that some previous claims are incorrect; and provides an explicit framework for thorough security reviews of these KEMs

Efficient signature verification and key revocation using identity based cryptography

Cryptography deals with the development and evaluation of procedures for securing digital information. It is essential whenever multiple entities want to communicate safely. One task of cryptography concerns digital signatures and the verification of a signer’s legitimacy requires trustworthy authentication and authorization. This is achieved by deploying cryptographic keys. When dynamic membership behavior and identity theft come into play, revocation of keys has to be addressed. Additionally, in use cases with limited networking, computational, or storage resources, efficiency is a key requirement for any solution. In this work we present a solution for signature verification and key revocation in constraned environments, e.g., in the Internet of Things (IoT). Where other mechanisms generate expensive overheads, we achieve revocation through a single multicast message without significant computational or storage overhead. Exploiting Identity Based Cryptography (IBC) complements the approach with efficient creation and verification of signatures. Our solution offers a framework for transforming a suitable signature scheme to a so-called Key Updatable Signature Scheme (KUSS) in three steps. Each step defines mathematical conditions for transformation and precise security notions. Thereby, the framework allows a novel combination of efficient Identity Based Signature (IBS) schemes with revocation mechanisms originally designed for confidentiality in group communications. Practical applicability of our framework is demonstrated by transforming four well-established IBS schemes based on Elliptic Curve Cryptography (ECC). The security of the resulting group Identity Based Signature (gIBS) schemes is carefully analyzed with techniques of Provable Security. We design and implement a testbed for evaluating these kind of cryptographic schemes on different computing- and networking hardware, typical for constrained environments. Measurements on this testbed provide evidence that the transformations are practicable and efficient. The revocation complexity in turn is significantly reduced compared to existing solutions. Some of our new schemes even outperform the signing process of the widely used Elliptic Curve Digital Signature Algorithm (ECDSA). The presented transformations allow future application on schemes beyond IBS or ECC. This includes use cases dealing with Post-Quantum Cryptography, where the revocation efficiency is similarly relevant. Our work provides the basis for such solutions currently under investigation.Die Kryptographie ist ein Instrument der Informationssicherheit und beschäftigt sich mit der Entwicklung und Evaluierung von Algorithmen zur Sicherung digitaler Werte. Sie ist für die sichere Kommunikation zwischen mehreren Entitäten unerlässlich. Ein Bestandteil sind digitale Signaturen, für deren Erstellung man kryptographische Schlüssel benötigt. Bei der Verifikation muss zusätzlich die Authentizität und die Autorisierung des Unterzeichners gewährleistet werden. Dafür müssen Schlüssel vertrauensvoll verteilt und verwaltet werden. Wenn sie in Kommunikationssystemen mit häufig wechselnden Teilnehmern zum Einsatz kommen, müssen die Schlüssel auch widerruflich sein. In Anwendungsfällen mit eingeschränkter Netz-, Rechen- und Speicherkapazität ist die Effizienz ein wichtiges Kriterium. Diese Arbeit liefert ein Rahmenwerk, mit dem Schlüssel effizient widerrufen und Signaturen effizient verifiziert werden können. Dabei fokussieren wir uns auf Szenarien aus dem Bereich des Internets der Dinge (IoT, Internet of Things). Im Gegensatz zu anderen Lösungen ermöglicht unser Ansatz den Widerruf von Schlüsseln mit einer einzelnen Nachricht innerhalb einer Kommunikationsgruppe. Dabei fällt nur geringer zusätzlicher Rechen- oder Speicheraufwand an. Ferner vervollständigt die Verwendung von Identitätsbasierter Kryptographie (IBC, Identity Based Cryptography) unsere Lösung mit effizienter Erstellung und Verifikation der Signaturen. Hierfür liefert die Arbeit eine dreistufige mathematische Transformation von geeigneten Signaturverfahren zu sogenannten Key Updatable Signature Schemes (KUSS). Neben einer präzisen Definition der Sicherheitsziele werden für jeden Schritt mathematische Vorbedingungen zur Transformation festgelegt. Dies ermöglicht die innovative Kombination von Identitätsbasierten Signaturen (IBS, Identity Based Signature) mit effizienten und sicheren Mechanismen zum Schlüsselaustausch, die ursprünglich für vertrauliche Gruppenkommunikation entwickelt wurden. Wir zeigen die erfolgreiche Anwendung der Transformationen auf vier etablierten IBSVerfahren. Die ausschließliche Verwendung von Verfahren auf Basis der Elliptic Curve Cryptography (ECC) erlaubt es, den geringen Kapazitäten der Zielgeräte gerecht zu werden. Eine Analyse aller vier sogenannten group Identity Based Signature (gIBS) Verfahren mit Techniken aus dem Forschungsgebiet der Beweisbaren Sicherheit zeigt, dass die zuvor definierten Sicherheitsziele erreicht werden. Zur praktischen Evaluierung unserer und ähnlicher kryptographischer Verfahren wird in dieser Arbeit eine Testumgebung entwickelt und mit IoT-typischen Rechen- und Netzmodulen bestückt. Hierdurch zeigt sich sowohl die praktische Anwendbarkeit der Transformationen als auch eine deutliche Reduktion der Komplexität gegenüber anderen Lösungsansätzen. Einige der von uns vorgeschlagenen Verfahren unterbieten gar die Laufzeiten des meistgenutzten Elliptic Curve Digital Signature Algorithm (ECDSA) bei der Erstellung der Signaturen. Die Systematik der Lösung erlaubt prinzipiell auch die Transformation von Verfahren jenseits von IBS und ECC. Dadurch können auch Anwendungsfälle aus dem Bereich der Post-Quanten-Kryptographie von unseren Ergebnissen profitieren. Die vorliegende Arbeit liefert die nötigen Grundlagen für solche Erweiterungen, die aktuell diskutiert und entwickelt werden

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 New Isogeny Representation and Applications to Cryptography

International audienceThis paper focuses on isogeny representations, defined as ways to evaluate isogenies and verify membership to the language of isogenous supersingular curves (the set of triples D, E1, E2 with a cyclic isogeny of degree D between E1 and E2). The tasks of evaluating and verifying isogenies are fundamental for isogeny-based cryptography. Our main contribution is the design of the suborder representation, a new isogeny representation targetted at the case of (big) prime degree. The core of our new method is the revelation of endomorphisms of smooth norm inside a well-chosen suborder of the codomain's endomorphism ring. This new representation appears to be opening interesting prospects for isogeny-based cryptography under the hardness of a new computational problem: the SubOrder to Ideal Problem (SOIP). As an application, we introduce pSIDH, a new NIKE based on the suborder representation. Studying new assumption appears to be particularly crucial in the light of the recent attacks against isogeny-based cryptography. In order to manipulate efficiently the suborder representation, we develop several heuristic algorithmic tools to solve norm equations inside a new family of quaternion orders. These new algorithms may be of independent interest

End-to-End Encrypted Group Messaging with Insider Security

Our society has become heavily dependent on electronic communication, and preserving the integrity of this communication has never been more important. Cryptography is a tool that can help to protect the security and privacy of these communications. Secure messaging protocols like OTR and Signal typically employ end-to-end encryption technology to mitigate some of the most egregious adversarial attacks, such as mass surveillance. However, the secure messaging protocols deployed today suffer from two major omissions: they do not natively support group conversations with three or more participants, and they do not fully defend against participants that behave maliciously. Secure messaging tools typically implement group conversations by establishing pairwise instances of a two-party secure messaging protocol, which limits their scalability and makes them vulnerable to insider attacks by malicious members of the group. Insiders can often perform attacks such as rendering the group permanently unusable, causing the state of the group to diverge for the other participants, or covertly remaining in the group after appearing to leave. It is increasingly important to prevent these insider attacks as group conversations become larger, because there are more potentially malicious participants. This dissertation introduces several new protocols that can be used to build modern communication tools with strong security and privacy properties, including resistance to insider attacks. Firstly, the dissertation addresses a weakness in current two-party secure messaging tools: malicious participants can leak portions of a conversation alongside cryptographic proof of authorship, undermining confidentiality. The dissertation introduces two new authenticated key exchange protocols, DAKEZ and XZDH, with deniability properties that can prevent this type of attack when integrated into a secure messaging protocol. DAKEZ provides strong deniability in interactive settings such as instant messaging, while XZDH provides deniability for non-interactive settings such as mobile messaging. These protocols are accompanied by composable security proofs. Secondly, the dissertation introduces Safehouse, a new protocol that can be used to implement secure group messaging tools for a wide range of applications. Safehouse solves the difficult cryptographic problems at the core of secure group messaging protocol design: it securely establishes and manages a shared encryption key for the group and ephemeral signing keys for the participants. These keys can be used to build chat rooms, team communication servers, video conferencing tools, and more. Safehouse enables a server to detect and reject protocol deviations, while still providing end-to-end encryption. This allows an honest server to completely prevent insider attacks launched by malicious participants. A malicious server can still perform a denial-of-service attack that renders the group unavailable or "forks" the group into subgroups that can never communicate again, but other attacks are prevented, even if the server colludes with a malicious participant. In particular, an adversary controlling the server and one or more participants cannot cause honest participants' group states to diverge (even in subtle ways) without also permanently preventing them from communicating, nor can the adversary arrange to covertly remain in the group after all of the malicious participants under its control are removed from the group. Safehouse supports non-interactive communication, dynamic group membership, mass membership changes, an invitation system, and secure property storage, while offering a variety of configurable security properties including forward secrecy, post-compromise security, long-term identity authentication, strong deniability, and anonymity preservation. The dissertation includes a complete proof-of-concept implementation of Safehouse and a sample application with a graphical client. Two sub-protocols of independent interest are also introduced: a new cryptographic primitive that can encrypt multiple private keys to several sets of recipients in a publicly verifiable and repeatable manner, and a round-efficient interactive group key exchange protocol that can instantiate multiple shared key pairs with a configurable knowledge relationship

Evaluating elliptic curve based KEMs in the light of pairings

Several efforts have been made recently to put forward a set of cryptographic primitives for public key encryption, suitable to be standardized. In two of them (in the first place the NESSIE european evaluation project, already finished, and in the second place the standardisation bodies ISO/IEC), the methodology by Victor Shoup for hybrid encryption, known as Key Encapsulation Method-Data Encapsulation Mechanism (KEM-DEM), has been accepted. In this work we re-evaluate the elliptic curve based KEMs studied to become standards, which are called ACE-KEM, ECIES-KEM and PSEC-KEM. Their security is based on di#erent assumptions related to the elliptic curve discrete logarithm (ECDL) problem on a random elliptic curve. First of all, we fix some inexact results claimed in the previous literature. As a consequence, the performance features of PSEC-KEM are dramatically affected. In second place, we analyse both their security properties and performance when elliptic curves with computable bilinear maps (pairing curves for short) are used. It turns out that these KEMs present a very tight security reduction to the same problem, namely the ECDH problem on such curves; moreover, one can even relate their security to the ECDL problem in certain curves with a small security loss. It is also argued that ECIES-KEM arises as the best option among these KEMs when pairing curves are used. This is remarkable, since NESSIE did not include ECIES-KEM over a random curve in its portfolio of recommended cryptographic primitives. It i

Actas de las VI Jornadas Nacionales (JNIC2021 LIVE)

Estas jornadas se han convertido en un foro de encuentro de los actores más relevantes en el ámbito de la ciberseguridad en España. En ellas, no sólo se presentan algunos de los trabajos científicos punteros en las diversas áreas de ciberseguridad, sino que se presta especial atención a la formación e innovación educativa en materia de ciberseguridad, y también a la conexión con la industria, a través de propuestas de transferencia de tecnología. Tanto es así que, este año se presentan en el Programa de Transferencia algunas modificaciones sobre su funcionamiento y desarrollo que han sido diseñadas con la intención de mejorarlo y hacerlo más valioso para toda la comunidad investigadora en ciberseguridad