New approaches to privacy preserving signatures

In this thesis we advance the theory and practice of privacy preserving digital signatures. Privacy preserving signatures such as group and ring signatures enable signers to hide in groups of potential signers. We design a cryptographic primitive called signatures with flexible public keys, which allows for modular construction of privacy preserving signatures. Its core is an equivalence relation between verification keys, such that key representatives can be transformed in their class to obscures their origin. The resulting constructions are more efficient than the state of the art, under the same or weaker assumptions. We show an extension of the security model of fully dynamic group signatures, which are those where members may join and leave the group over time. Our contribution here, which is facilitated by the new primitive, is the treatment of membership status as potentially sensitive information. In the theory of ring signatures, we show a construction of ring signatures which is the first in the literature with logarithmic signature size in the size of the ring without any trusted setup or reliance on non-standard assumptions. We show how to extend our techniques to the derived setting of linkable ring signatures, where different signatures of the same origin may be publicly linked. Here, we further revisit the notion of linkable anonymity, offering a significant strengthening compared to previous definitions.Diese Arbeit treibt die Theorie und Praxis der privatsphärewahrenden digitalen Signa- turen voran. Privatsphärewahrende Signaturen, wie Gruppen- oder Ringsignaturen erlauben es Zeichnern sich in einer Gruppe potenzieller Zeichner zu verstecken. Wir entwerfen mit Signatures with Flexible Public Keys einen kryptografischen Baustein zur modularen Konstruktion von privatsphärewahrenden Signaturen. Dessen Kern ist eine Äquivalenzrelation zwischen den Schlüsseln, sodass ein Schlüsselvertreter in seiner Klasse bewegt werden kann, um seinen Ursprung zu verschleiern. Darauf auf- bauende Konstruktionen sind effizienter als der Stand der Technik, unter gleichen oder schwächeren Annahmen. Wir erweitern das Sicherheitsmodell vollständig dynami- scher Gruppensignaturen, die es Mitgliedern erlauben der Gruppe beizutreten oder sie zu verlassen: Durch das neue Primitiv, wird die Behandlung der Mitgliedschaft als potenziell sensibel ermöglicht. In der Theorie der Ringsignaturen geben wir die erste Konstruktion, welche über eine logarithmische Signaturgröße verfügt, ohne auf eine Vorkonfiguration oder unübliche Annahmen vertrauen zu müssen. Wir übertragen unsere Ergebnisse auf das Feld der verknüpfbaren Ringsignaturen, die eine öffentliche Verknüpfung von zeichnergleichen Signaturen ermöglichen. Unsere Neubetrachtung des Begriffs der verknüpfbaren Anonymität führt zu einer signifikanten Stärkung im Vergleich zu früheren Definitionen

Membership Privacy for Fully Dynamic Group Signatures

Group signatures present a compromise between the traditional goals of digital signatures and the need for signer privacy, allowing for the creation of unforgeable signatures in the name of a group which reveal nothing about the actual signer's identity beyond their group membership. An important consideration that is absent in prevalent models is that group membership itself may be sensitive information, especially if group membership is dynamic, i.e. membership status may change over time. We address this issue by introducing formal notions of membership privacy for fully dynamic group signature schemes, which can be easily integrated into the most expressive models of group signature security to date. We then propose a generic construction for a fully dynamic group signature scheme with membership privacy that is based on signatures with flexible public key (SFPK) and signatures on equivalence classes (SPSEQ). Finally, we devise novel techniques for SFPK to construct a highly efficient standard model scheme (i.e. without random oracles) that provides shorter signatures than even the non-private state-of-the-art from standard assumptions. This shows that, although the strictly stronger security notions we introduce have been completely unexplored in the study of fully dynamic group signatures so far, they do not come at an additional cost in practice

Improvements and New Constructions of Digital Signatures

Ein digitales Signaturverfahren, oft auch nur digitale Signatur genannt, ist ein wichtiger und nicht mehr wegzudenkender Baustein in der Kryptographie. Es stellt das digitale Äquivalent zur klassischen handschriftlichen Signatur dar und liefert darüber hinaus noch weitere wünschenswerte Eigenschaften. Mit solch einem Verfahren kann man einen öffentlichen und einen geheimen Schlüssel erzeugen. Der geheime Schlüssel dient zur Erstellung von Signaturen zu beliebigen Nachrichten. Diese können mit Hilfe des öffentlichen Schlüssels von jedem überprüft und somit verifiziert werden. Desweiteren fordert man, dass das Verfahren "sicher" sein soll. Dazu gibt es in der Literatur viele verschiedene Begriffe und Definitionen, je nachdem welche konkreten Vorstellungen beziehungsweise Anwendungsgebiete man hat. Vereinfacht gesagt, sollte es für einen Angreifer ohne Kenntnis des geheimen Schlüssels nicht möglich sein eine gültige Signatur zu einer beliebigen Nachricht zu fälschen. Ein sicheres Signaturverfahren kann somit verwendet werden um die folgenden Ziele zu realisieren: - Authentizität: Jeder Empfänger kann überprüfen, ob die Nachricht von einem bestimmten Absender kommt. - Integrität der Nachricht: Jeder Empfänger kann feststellen, ob die Nachricht bei der Übertragung verändert wurde. - Nicht-Abstreitbarkeit: Der Absender kann nicht abstreiten die Signatur erstellt zu haben. Damit ist der Einsatz von digitalen Signaturen für viele Anwendungen in der Praxis sehr wichtig. Überall da, wo es wichtig ist die Authentizität und Integrität einer Nachricht sicherzustellen, wie beim elektronischen Zahlungsverkehr, Softwareupdates oder digitalen Zertifikaten im Internet, kommen digitale Signaturen zum Einsatz. Aber auch für die kryptographische Theorie sind digitale Signaturen ein unverzichtbares Hilfsmittel. Sie ermöglichen zum Beispiel die Konstruktion von stark sicheren Verschlüsselungsverfahren. Eigener Beitrag: Wie bereits erwähnt gibt es unterschiedliche Sicherheitsbegriffe im Rahmen von digitalen Signaturen. Ein Standardbegriff von Sicherheit, der eine recht starke Form von Sicherheit beschreibt, wird in dieser Arbeit näher betrachtet. Die Konstruktion von Verfahren, die diese Form der Sicherheit erfüllen, ist ein vielschichtiges Forschungsthema. Dazu existieren unterschiedliche Strategien in unterschiedlichen Modellen. In dieser Arbeit konzentrieren wir uns daher auf folgende Punkte. - Ausgehend von vergleichsweise realistischen Annahmen konstruieren wir ein stark sicheres Signaturverfahren im sogenannten Standardmodell, welches das realistischste Modell für Sicherheitsbeweise darstellt. Unser Verfahren ist das bis dahin effizienteste Verfahren in seiner Kategorie. Es erstellt sehr kurze Signaturen und verwendet kurze Schlüssel, beides unverzichtbar für die Praxis. - Wir verbessern die Qualität eines Sicherheitsbeweises von einem verwandten Baustein, der identitätsbasierten Verschlüsselung. Dies hat unter anderem Auswirkung auf dessen Effizienz bezüglich der empfohlenen Schlüssellängen für den sicheren Einsatz in der Praxis. Da jedes identitätsbasierte Verschlüsselungsverfahren generisch in ein digitales Signaturverfahren umgewandelt werden kann ist dies auch im Kontext digitaler Signaturen interessant. - Wir betrachten Varianten von digitalen Signaturen mit zusätzlichen Eigenschaften, sogenannte aggregierbare Signaturverfahren. Diese ermöglichen es mehrere Signaturen effizient zu einer zusammenzufassen und dabei trotzdem alle zugehörigen verschiedenen Nachrichten zu verifizieren. Wir geben eine neue Konstruktion von solch einem aggregierbaren Signaturverfahren an, bei der das Verfahren eine Liste aller korrekt signierten Nachrichten in einer aggregierten Signatur ausgibt anstatt, wie bisher üblich, nur gültig oder ungültig. Wenn eine aggregierte Signatur aus vielen Einzelsignaturen besteht wird somit das erneute Berechnen und eventuell erneute Senden hinfällig und dadurch der Aufwand erheblich reduziert

Research Philosophy of Modern Cryptography

Proposing novel cryptography schemes (e.g., encryption, signatures, and protocols) is one of the main research goals in modern cryptography. In this paper, based on more than 800 research papers since 1976 that we have surveyed, we introduce the research philosophy of cryptography behind these papers. We use ``benefits and ``novelty as the keywords to introduce the research philosophy of proposing new schemes, assuming that there is already one scheme proposed for a cryptography notion. Next, we introduce how benefits were explored in the literature and we have categorized the methodology into 3 ways for benefits, 6 types of benefits, and 17 benefit areas. As examples, we introduce 40 research strategies within these benefit areas that were invented in the literature. The introduced research strategies have covered most cryptography schemes published in top-tier cryptography conferences

A Note on Post-Quantum Authenticated Key Exchange from Supersingular Isogenies

In this work, we study several post-quantum authenticated key exchange protocols in the setting of supersingular isogenies. Leveraging the design of the well-studied schemes by Krawczyk (2003), Boyd et al. (2008), Fujioka et al. (2013), Krawczyk and Wee (2015), and others, we show how to use the Supersingular Isogeny Diffie-Hellman (SIDH) and Supersingular Isogeny Key Encapsulation (SIKE) protocols as basic building blocks to construct efficient and flexible authenticated key exchange schemes featuring different functionalities and levels of security. This note is also intended to be a ``gentle\u27\u27 introduction to supersingular isogeny based cryptography, and its most relevant constructions, for protocol designers and cryptographers

Foundations of Fully Dynamic Group Signatures

Group signatures allow members of a group to anonymously sign on behalf of the group. Membership is administered by a designated group manager. The group manager can also reveal the identity of a signer if and when needed to enforce accountability and deter abuse. For group signatures to be applicable in practice, they need to support fully dynamic groups, i.e., users may join and leave at any time. Existing security definitions for fully dynamic group signatures are informal, have shortcomings, and are mutually incompatible. We fill the gap by providing a formal rigorous security model for fully dynamic group signatures. Our model is general and is not tailored toward a specific design paradigm and can therefore, as we show, be used to argue about the security of different existing constructions following different design paradigms. Our definitions are stringent and when possible incorporate protection against maliciously chosen keys. We consider both the case where the group management and tracing signatures are administered by the same authority, i.e., a single group manager, and also the case where those roles are administered by two separate authorities, i.e., a group manager and an opening authority. We also show that a specialization of our model captures existing models for static and partially dynamic schemes. In the process, we identify a subtle gap in the security achieved by group signatures using revocation lists. We show that in such schemes new members achieve a slightly weaker notion of traceability. The flexibility of our security model allows to capture such relaxation of traceability

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

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