Lattice-Based Group Signatures: Achieving Full Dynamicity (and Deniability) with Ease

In this work, we provide the first lattice-based group signature that offers full dynamicity (i.e., users have the flexibility in joining and leaving the group), and thus, resolve a prominent open problem posed by previous works. Moreover, we achieve this non-trivial feat in a relatively simple manner. Starting with Libert et al.'s fully static construction (Eurocrypt 2016) - which is arguably the most efficient lattice-based group signature to date, we introduce simple-but-insightful tweaks that allow to upgrade it directly into the fully dynamic setting. More startlingly, our scheme even produces slightly shorter signatures than the former, thanks to an adaptation of a technique proposed by Ling et al. (PKC 2013), allowing to prove inequalities in zero-knowledge. Our design approach consists of upgrading Libert et al.'s static construction (EUROCRYPT 2016) - which is arguably the most efficient lattice-based group signature to date - into the fully dynamic setting. Somewhat surprisingly, our scheme produces slightly shorter signatures than the former, thanks to a new technique for proving inequality in zero-knowledge without relying on any inequality check. The scheme satisfies the strong security requirements of Bootle et al.'s model (ACNS 2016), under the Short Integer Solution (SIS) and the Learning With Errors (LWE) assumptions. Furthermore, we demonstrate how to equip the obtained group signature scheme with the deniability functionality in a simple way. This attractive functionality, put forward by Ishida et al. (CANS 2016), enables the tracing authority to provide an evidence that a given user is not the owner of a signature in question. In the process, we design a zero-knowledge protocol for proving that a given LWE ciphertext does not decrypt to a particular message

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