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

Practical Delegatable Anonymous Credentials From Equivalence Class Signatures

Anonymous credentials systems (ACs) are a powerful cryptographic tool for privacy-preserving applications and provide strong user privacy guarantees for authentication and access control. ACs allow users to prove possession of attributes encoded in a credential without revealing any information beyond them. A delegatable AC (DAC) system is an enhanced AC system that allows the owners of credentials to delegate the obtained credential to other users. This allows to model hierarchies as usually encountered within public-key infrastructures (PKIs). DACs also provide stronger privacy guarantees than traditional AC systems since the identities of issuers and delegators are also hidden. A credential issuer\u27s identity may convey information about a user\u27s identity even when all other information about the user is protected. We present a novel delegatable anonymous credential scheme that supports attributes, provides anonymity for delegations, allows the delegators to restrict further delegations, and also comes with an efficient construction. In particular, our DAC credentials do not grow with delegations, i.e., are of constant size. Our approach builds on a new primitive that we call structure-preserving signatures on equivalence classes on updatable commitments (SPSEQ-UC). The high-level idea is to use a special signature scheme that can sign vectors of set commitments which can be extended by additional set commitments. Signatures additionally include a user\u27s public key, which can be switched. This allows us to efficiently realize delegation in the DAC. Similar to conventional SPSEQ signatures, the signatures and messages can be publicly randomized and thus allow unlinkable showings in the DAC system. We present further optimizations such as cross-set commitment aggregation that, in combination, enable selective, efficient showings in the DAC without using costly zero-knowledge proofs. We present an efficient instantiation that is proven to be secure in the generic group model and finally demonstrate the practical efficiency of our DAC by presenting performance benchmarks based on an implementation

Signatures courtes sur chiffrés randomizables

International audienceRandomizable encryption lets anyone randomize a ciphertext so it is distributed like a fresh encryption of the same plaintext. Signatures on randomizable cipher-texts (SoRC), introduced by Blazy et al. (PKC'11), let one adapt a signature on a ciphertext to a randomization of the latter. Since signatures can only be adapted to ciphertexts that encrypt the same message as the signed ciphertext, signatures obliviously authenticate plaintexts. SoRC have been used as a building block in e-voting, blind signatures and (delegatable) anonymous credentials. We observe that SoRC can be seen as signatures on equivalence classes (JoC'19), another primitive with many applications to anonymous authentication, and that SoRC provide better anonymity guarantees. We first strengthen the unforgeability notion for SoRC and then give a scheme that provably achieves it in the generic group model. Signatures in our scheme consist of 4 bilinear-group elements, which is considerably more efficient than prior schemes

With a Little Help from My Friends: Constructing Practical Anonymous Credentials

Anonymous credentials (ACs) are a powerful cryptographic tool for the secure use of digital services, when simultaneously aiming for strong privacy guarantees of users combined with strong authentication guarantees for providers of services. They allow users to selectively prove possession of attributes encoded in a credential without revealing any other meaningful information about themselves. While there is a significant body of research on AC systems, modern use-cases of ACs such as mobile applications come with various requirements not sufficiently considered so far. These include preventing the sharing of credentials and coping with resource constraints of the platforms (e.g., smart cards such as SIM cards in smartphones). Such aspects are typically out of scope of AC constructions, and, thus AC systems that can be considered entirely practical have been elusive so far. In this paper we address this problem by introducing and formalizing the notion of core/helper anonymous credentials (CHAC). The model considers a constrained core device (e.g., a SIM card) and a powerful helper device (e.g., a smartphone). The key idea is that the core device performs operations that do not depend on the size of the credential or the number of attributes, but at the same time the helper device is unable to use the credential without its help. We present a provably secure generic construction of CHACs using a combination of signatures with flexible public keys (SFPK) and the novel notion of aggregatable attribute-based equivalence class signatures (AAEQ) along with a concrete instantiation. The key characteristics of our scheme are that the size of showing tokens is independent of the number of attributes in the credential(s) and that the core device only needs to compute a single elliptic curve scalar multiplication, regardless of the number of attributes. We confirm the practical efficiency of our CHACs with an implementation of our scheme on a Multos smart card as the core and an Android smartphone as the helper device. A credential showing requires less than 500 ms on the smart card and around 200 ms on the smartphone (even for a credential with 1000 attributes)

Aggregate Signatures with Versatile Randomization and Issuer-Hiding Multi-Authority Anonymous Credentials

Anonymous credentials (AC) have emerged as a promising privacy-preserving solu- tion for user-centric identity management. They allow users to authenticate in an anonymous and unlinkable way such that only required information (i.e., attributes) from their credentials are re- vealed. With the increasing push towards decentralized systems and identity, e.g., self-sovereign identity (SSI) and the concept of verifiable credentials, this also necessitates the need for suit- able AC systems. For instance, when relying on existing AC systems, obtaining credentials from different issuers requires the presentation of independent credentials, which can become cum- bersome. Consequently, it is desirable for AC systems to support the so-called multi-authority (MA) feature. It allows a compact and efficient showing of multiple credentials from different is- suers. Another important property is called issuer hiding (IH). This means that showing a set of credentials is not revealed which issuer has issued which credentials but only whether a verifier- defined policy on the acceptable set of issuers is satisfied. This issue becomes particularly acute in the context of MA, where a user could be uniquely identified by the combination of issuers in their showing. Unfortunately, there are no AC schemes that satisfy both these properties simul- taneously. To close this gap, we introduce the concept of Issuer-Hiding Multi-Authority Anonymous Cre- dentials (IhMA). Our proposed solution involves the development of two new signature primi- tives with versatile randomization features which are independent of interest: 1) Aggregate Sig- natures with Randomizable Tags and Public Keys (AtoSa) and 2) Aggregate Mercurial Signatures (ATMS), which extend the functionality of AtoSa to additionally support the randomization of messages and yield the first instance of an aggregate (equivalence-class) structure-preserving sig- nature. These primitives can be elegantly used to obtain IhMA with different trade-offs but have applications beyond. We formalize all notations and provide rigorous security definitions for our proposed primi- tives. We present provably secure and efficient instantiations of the two primitives as well as corresponding IhMA systems. Finally, we provide benchmarks based on an implementation to demonstrate the practical efficiency of our construction

Structure-Preserving Signatures on Equivalence Classes From Standard Assumptions

Structure-preserving signatures on equivalence classes (SPS-EQ) introduced at ASIACRYPT 2014 are a variant of SPS where a message is considered as a projective equivalence class, and a new representative of the same class can be obtained by multiplying a vector by a scalar. Given a message and corresponding signature, anyone can produce an updated and randomized signature on an arbitrary representative from the same equivalence class. SPS-EQ have proven to be a very versatile building block for many cryptographic applications. In this paper, we present the first EUF-CMA secure SPS-EQ scheme under standard assumptions. So far only constructions in the generic group model are known. One recent candidate under standard assumptions are the weakly secure equivalence class signatures by Fuchsbauer and Gay (PKC\u2718), a variant of SPS-EQ satisfying only a weaker unforgeability and adaption notion. Fuchsbauer and Gay show that this weaker unforgeability notion is sufficient for many known applications of SPS-EQ. Unfortunately, the weaker adaption notion is only proper for a semi-honest (passive) model and as we show in this paper, makes their scheme unusable in the current models for almost all of their advertised applications of SPS-EQ from the literature. We then present a new EUF-CMA secure SPS-EQ scheme with a tight security reduction under the SXDH assumption providing the notion of perfect adaption (under malicious keys). To achieve the strongest notion of perfect adaption under malicious keys, we require a common reference string (CRS), which seems inherent for constructions under standard assumptions. However, for most known applications of SPS-EQ we do not require a trusted CRS (as the CRS can be generated by the signer during key generation). Technically, our construction is inspired by a recent work of Gay et al. (EUROCRYPT\u2718), who construct a tightly secure message authentication code and translate it to an SPS scheme adapting techniques due to Bellare and Goldwasser (CRYPTO\u2789)

SoK: Signatures With Randomizable Keys

Digital signature schemes with specific properties have recently seen various real-world applications with a strong emphasis on privacy-enhancing technologies. They have been extensively used to develop anonymous credentials schemes and to achieve an even more comprehensive range of functionalities in the decentralized web. Substantial work has been done to formalize different types of signatures where an allowable set of transformations can be applied to message-signature pairs to obtain new related pairs. Most of the previous work focused on transformations with respect to the message being signed, but little has been done to study what happens when transformations apply to the signing keys. A first attempt to thoroughly formalize such aspects was carried by Derler and Slamanig (ePrint \u2716, Designs, Codes and Cryptography \u2719), followed by the more recent efforts by Backes et. al (ASIACRYPT \u2718) and Eaton et. al (ePrint \u2723). However, the literature on the topic is vast and different terminology is used across contributions, which makes it difficult to compare related works and understand the range of applications covered by a given construction. In this work, we present a unified view of signatures with randomizable keys and revisit their security properties. We focus on state-of-the-art constructions and related applications, identifying existing challenges. Our systematization allows us to highlight gaps, open questions and directions for future research on signatures with randomizable keys

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