On the Security Notions for Homomorphic Signatures

Homomorphic signature schemes allow anyone to perform computation on signed data in such a way that the correctness of computation’s results is publicly certified. In this work we analyze the security notions for this powerful primitive considered in previous work, with a special focus on adaptive security. Motivated by the complications of existing security models in the adaptive setting, we consider a simpler and (at the same time) stronger security definition inspired to that proposed by Gennaro and Wichs (ASIACRYPT’13) for homomorphic MACs. In addition to strength and simplicity, this definition has the advantage to enable the adoption of homomorphic signatures in dynamic data outsourcing scenarios, such as delegation of computation on data streams. Then, since no existing homomorphic signature satisfies this stronger notion, our main technical contribution are general compilers which turn a homomorphic signature scheme secure under a weak definition into one secure under the new stronger notion. Our compilers are totally generic with respect to the underlying scheme. Moreover, they preserve two important properties of homomorphic signatures: context-hiding (i.e. signatures on computation’s output do not reveal information about the input) and efficient verification (i.e. verifying a signature against a program P can be made faster, in an amortized, asymptotic sense, than recomputing P from scratch)

An Efficient Homomorphic Aggregate Signature Scheme Based on Lattice

Homomorphic aggregate signature (HAS) is a linearly homomorphic signature (LHS) for multiple users, which can be applied for a variety of purposes, such as multi-source network coding and sensor data aggregation. In order to design an efficient postquantum secure HAS scheme, we borrow the idea of the lattice-based LHS scheme over binary field in the single-user case, and develop it into a new lattice-based HAS scheme in this paper. The security of the proposed scheme is proved by showing a reduction to the single-user case and the signature length remains invariant. Compared with the existing lattice-based homomorphic aggregate signature scheme, our new scheme enjoys shorter signature length and high efficiency

Bounded Fully Homomorphic Signature Schemes

Homomorphic signatures enable anyone to publicly perform computations on signed data and produce a compact tag to authenticate the results. In this paper, we construct two bounded fully homomorphic signature schemes, as follows. \begin{itemize} \item For any two polynomials $d=d(\lambda), s=s(\lambda)$, where $\lambda$ is the security parameter. Our first scheme is able to evaluate any circuit on the signatures, as long as the depth and size of the circuit are bounded by $d$ and $s$, respectively. The construction relies on indistinguishability obfuscation and injective (or polynomially bounded pre-image size) one-way functions. \medskip \item The second scheme, removing the restriction on the size of the circuits, is an extension of the first one, with succinct verification and evaluation keys. More specifically, for an a-prior polynomial $d=d(\lambda)$, the scheme allows to evaluate any circuit on the signatures, as long as the depth of the circuit is bounded by $d$. This scheme is based on differing-inputs obfuscation and collision-resistant hash functions and relies on a technique called recording hash of circuits. \end{itemize} Both schemes enjoy the composition property. Namely, outputs of previously derived signatures can be re-used as inputs for new computations. The length of derived signatures in both schemes is independent of the size of the data set. Moreover, both constructions satisfy a strong privacy notion, we call {\em semi-strong context hiding}, which requires that the derived signatures of evaluating any circuit on the signatures of two data sets are {\em identical} as long as the evaluations of the circuit on these two data sets are the same

Structure-Preserving Signatures on Equivalence Classes and Constant-Size Anonymous Credentials

Structure-preserving signatures (SPS) are a powerful building block for cryptographic protocols. We introduce SPS on equivalence classes (SPS-EQ), which allow joint randomization of messages and signatures. Messages are projective equivalence classes defined on group element vectors, so multiplying a vector by a scalar yields a different representative of the same class. Our scheme lets one adapt a signature for one representative to a signature for another representative without knowledge of any secret. Moreover, given a signature, an adapted signature for a different representative is indistinguishable from a fresh signature on a random message. We propose a definitional framework for SPS-EQ and an efficient construction in Type-3 bilinear groups, which we prove secure against generic forgers. We also introduce set-commitment schemes that let one open subsets of the committed set. From this and SPS-EQ we then build an efficient multi-show attribute-based anonymous credential system for an arbitrary number of attributes. Our ABC system avoids costly zero-knowledge proofs and only requires a short interactive proof to thwart replay attacks. It is the first credential system whose bandwidth required for credential showing is independent of the number of its attributes, i.e., constant-size. We propose strengthened game-based security definitions for ABC and prove our scheme anonymous against malicious organizations in the standard model; finally, we discuss a concurrently secure variant in the CRS model

Structure-preserving signatures from type II pairings

We investigate structure-preserving signatures in asymmetric bilinear groups with an efficiently computable homomorphism from one source group to the other, i.e., the Type II setting. It has been shown that in the Type I and Type III settings, structure-preserving signatures need at least 2 verification equations and 3 group elements. It is therefore natural to conjecture that this would also be required in the intermediate Type II setting, but surprisingly this turns out not to be the case. We construct structure-preserving signatures in the Type II setting that only require a single verification equation and consist of only 2 group elements. This shows that the Type II setting with partial asymmetry is different from the other two settings in a way that permits the construction of cryptographic schemes with unique properties. We also investigate lower bounds on the size of the public verification key in the Type II setting. Previous work on structure-preserving signatures has explored lower bounds on the number of verification equations and the number of group elements in a signature but the size of the verification key has not been investigated before.We show that in the Type II setting it is necessary to have at least 2 group elements in the public verification key in a signature scheme with a single verification equation. Our constructions match the lower bounds so they are optimal with respect to verification complexity, signature sizes and verification key sizes. In fact, in terms of verification complexity, they are the most efficient structure preserving signature schemes to date. We give two structure-preserving signature schemes with a single verification equation where both the signatures and the public verification keys consist of two group elements each. One signature scheme is strongly existentially unforgeable, the other is fully randomizable. Having such simple and elegant structure-preserving signatures may make the Type II setting the easiest to use when designing new structure-preserving cryptographic schemes, and lead to schemes with the greatest conceptual simplicity

Unified, Minimal and Selectively Randomizable Structure-Preserving Signatures

Abstract. We construct a structure-preserving signature scheme that is selectively randomizable and works in all types of bilinear groups. We give matching lower bounds showing that our structure-preserving signature scheme is optimal with respect to both signature size and public verification key size. State of the art structure-preserving signatures in the asymmetric setting consist of 3 group elements, which is known to be optimal. Our construc-tion preserves the signature size of 3 group elements and also at the same time minimizes the verification key size to 1 group element. Depending on the application, it is sometimes desirable to have strong unforgeability and in other situations desirable to have randomizable signatures. To get the best of both worlds, we introduce the notion of selective randomizability where the signer may for specific signatures provide randomization tokens that enable randomization. Our structure-preserving signature scheme unifies the different pairing-based settings since it can be instantiated in both symmetric and asym-metric groups. Since previously optimal structure-preserving signatures had only been constructed in asymmetric bilinear groups this closes an important gap in our knowledge. Having a unified signature scheme that works in all types of bilinear groups is not just conceptually nice but also gives a hedge against future cryptanalytic attacks. An instantiation of our signature scheme in an asymmetric bilinear group may remain secure even if cryptanalysts later discover an efficiently computable homomorphism between the source groups

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

Declarative design and enforcement for secure cloud applications

The growing demands of users and industry have led to an increase in both size and complexity of deployed software in recent years. This tendency mainly stems from a growing number of interconnected mobile devices and from the huge amounts of data that is collected every day by a growing number of sensors and interfaces. Such increase in complexity imposes various challenges -- not only in terms of software correctness, but also with respect to security. This thesis addresses three complementary approaches to cope with the challenges: (i) appropriate high-level abstractions and verifiable translation methods to executable applications in order to guarantee flawless implementations, (ii) strong cryptographic mechanisms in order to realize the desired security goals, and (iii) convenient methods in order to incentivize the correct usage of existing techniques and tools. In more detail, the thesis presents two frameworks for the declarative specification of functionality and security, together with advanced compilers for the verifiable translation to executable applications. Moreover, the thesis presents two cryptographic primitives for the enforcement of cloud-based security properties: homomorphic message authentication codes ensure the correctness of evaluating functions over data outsourced to unreliable cloud servers; and efficiently verifiable non-interactive zero-knowledge proofs convince verifiers of computation results without the verifiers having access to the computation input.Die wachsenden Anforderungen von Seiten der Industrie und der Endbenutzer verlangen nach immer komplexeren Softwaresystemen -- größtenteils begründet durch die stetig wachsende Zahl mobiler Geräte und die damit wachsende Zahl an Sensoren und erfassten Daten. Mit wachsender Software-Komplexität steigen auch die Herausforderungen an Korrektheit und Sicherheit. Die vorliegende Arbeit widmet sich diesen Herausforderungen in Form dreier komplementärer Ansätze: (i) geeignete Abstraktionen und verifizierbare Übersetzungsmethoden zu ausführbaren Anwendungen, die fehlerfreie Implementierungen garantieren, (ii) starke kryptographische Mechanismen, um die spezifizierten Sicherheitsanforderungen effizient und korrekt umzusetzen, und (iii) zweckmäßige Methoden, die eine korrekte Benutzung existierender Werkzeuge und Techniken begünstigen. Diese Arbeit stellt zwei neuartige Abläufe vor, die verifizierbare Übersetzungen von deklarativen Spezifikationen funktionaler und sicherheitsrelevanter Ziele zu ausführbaren Cloud-Anwendungen ermöglichen. Darüber hinaus präsentiert diese Arbeit zwei kryptographische Primitive für sichere Berechnungen in unzuverlässigen Cloud-Umgebungen. Obwohl die Eingabedaten der Berechnungen zuvor in die Cloud ausgelagert wurden und zur Verifikation der Berechnungen nicht mehr zur Verfügung stehen, ist es möglich, die Korrektheit der Ergebnisse in effizienter Weise zu überprüfen