Efficient Batch Zero-Knowledge Arguments for Low Degree Polynomials

Bootle et al. (EUROCRYPT 2016) construct an extremely efficient zero-knowledge argument for arithmetic circuit satisfiability in the discrete logarithm setting. However, the argument does not treat relations involving commitments, and furthermore, for simple polynomial relations, the complex machinery employed is unnecessary. In this work, we give a framework for expressing simple relations between commitments and field elements, and present a zero-knowledge argument which, by contrast with Bootle et al., is constant-round and uses fewer group operations, in the case where the polynomials in the relation have low degree. Our method also directly yields a batch protocol, which allows many copies of the same relation to be proved and verified in a single argument more efficiently with only a square-root communication overhead in the number of copies. We instantiate our protocol with concrete polynomial relations to construct zero-knowledge arguments for membership proofs, polynomial evaluation proofs, and range proofs. Our work can be seen as a unified explanation of the underlying ideas of these protocols. In the instantiations of membership proofs and polynomial evaluation proofs, we also achieve better efficiency than the state of the art

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

Multi-Party Revocation in Sovrin: Performance through Distributed Trust

Accumulators provide compact representations of large sets and compact membership witnesses. Besides constant-size witnesses, public-key accumulators provide efficient updates of both the accumulator itself and the witness. However, bilinear group based accumulators come with drawbacks: they require a trusted setup and their performance is not practical for real-world applications with large sets. In this paper, we introduce multi-party public-key accumulators dubbed dynamic (threshold) secret-shared accumulators. We present an instantiation using bilinear groups having access to more efficient witness generation and update algorithms that utilize the shares of the secret trapdoors sampled by the parties generating the public parameters. Specifically, for the q-SDH-based accumulators, we provide a maliciously-secure variant sped up by a secure multi-party computation (MPC) protocol (IMACC\u2719) built on top of SPDZ and a maliciously secure threshold variant built with Shamir secret sharing. For these schemes, a performant proof-of-concept implementation is provided, which substantiates the practicability of public-key accumulators in this setting. We explore applications of dynamic (threshold) secret-shared accumulators to revocation schemes of group signatures and credentials system. In particular, we consider it as part of Sovrin\u27s system for anonymous credentials where credentials are issued by the foundation of trusted nodes

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

Blacklistable Anonymous Credentials: Blocking Misbehaving Users without TTPs (Extended Version)

Several credential systems have been proposed in which users can authenticate to services anonymously. Since anonymity can give users the license to misbehave, some variants allow the selective deanonymization (or linking) of misbehaving users upon a complaint to a trusted third party (TTP). The ability of the TTP to revoke a user\u27s privacy at any time, however, is too strong a punishment for misbehavior. To limit the scope of deanonymization, systems such as ``e-cash\u27\u27 have been proposed in which users are deanonymized under only certain types of well-defined misbehavior such as ``double spending.\u27\u27 While useful in some applications, it is not possible to generalize such techniques to more subjective definitions of misbehavior. We present the first anonymous credential system in which services can ``blacklist\u27\u27 misbehaving users without contacting a TTP. Since blacklisted users remain anonymous, misbehaviors can be judged subjectively without users fearing arbitrary deanonymization by a TTP

PPAA: Peer-to-Peer Anonymous Authentication (Extended Version)

In the pursuit of authentication schemes that balance user privacy and accountability, numerous anonymous credential systems have been constructed. However, existing systems assume a client-server architecture in which only the clients, but not the servers, care about their privacy. In peer-to-peer (P2P) systems where both clients and servers are peer users with privacy concerns, no existing system correctly strikes that balance between privacy and accountability. In this paper, we provide this missing piece: a credential system in which peers are {\em pseudonymous} to one another (that is, two who interact more than once can recognize each other via pseudonyms) but are otherwise anonymous and unlinkable across different peers. Such a credential system finds applications in, e.g., Vehicular Ad-hoc Networks (VANets) and P2P networks. We formalize the security requirements of our proposed credential system, provide a construction for it, and prove the security of our construction. Our solution is efficient: its complexities are independent of the number of users in the system

Linking-Based Revocation for Group Signatures: A Pragmatic Approach for Efficient Revocation Checks

Group signature schemes (GSS) represent an important privacy-enhancing technology. However, their practical applicability is restricted due to inefficiencies of existing membership revocation mechanisms that often place a too large computational burden and communication overhead on the involved parties. Moreover, it seems that the general belief (or unwritten law) of avoiding online authorities by all means artificially and unnecessarily restricts the efficiency and practicality of revocation mechanisms in GSSs. While a mindset of preventing online authorities might have been appropriate more than 10 years ago, today the availability of highly reliable cloud computing infrastructures could be used to solve open challenges. More specifically, in order to overcome the inefficiencies of existing revocation mechanisms, we propose an alternative approach denoted as linking-based revocation (LBR) which is based on the concept of controllable linkability. The novelty of LBR is its transparency for signers and verifiers that spares additional computations as well as updates. We therefore introduce dedicated revocation authorities (RAs) that can be contacted for efficient (constant time) revocation checks. In order to protect these RAs and to reduce the trust in involved online authorities, we additionally introduce distributed controllable linkability. Using latter, RAs cooperate with multiple authorities to compute the required linking information, thus reducing the required trust. Besides efficiency, an appealing benefit of LBR is its generic applicability to pairing-based GSSs secure in the BSZ model as well as GSSs with controllable linkability. This includes the XSGS scheme, and the GSSs proposed by Hwang et al., one of which has been standardized in the recent ISO 20008-2 standard

Traceable Identity-Based Group Signature

Group signature is a useful cryptographic primitive, which makes every group member sign messages on behalf of a group they belong to. Namely group signature allows that group member anonymously signs any message without revealing his/her specific identity. However, group signature may make the signers abuse their signing rights if there are no measures of keeping them from abusing signing rights in the group signature schemes. So, group manager must be able to trace (or reveal) the identity of the signer by the signature when the result of the signature needs to be arbitrated, and some revoked group members must fully lose their capability of signing a message on behalf of the group they belong to. A practical model meeting the requirement is verifier-local revocation, which supports the revocation of group member. In this model, the verifiers receive the group member revocation messages from the trusted authority when the relevant signatures need to be verified. With the rapid development of identity-based cryptography, several identity-based group signature (IBGS) schemes have been proposed. Compared with group signature based on public key cryptography, IBGS can simplify key management and be used for more applications. Although some identity-based group signature schemes have been proposed, few identity-based group signature schemes are constructed in the standard model and focus on the traceability of signature. In this paper, we present a fully traceable (and verifier-local revocation) identity-based group signature (TIBGS) scheme, which has a security reduction to the computational Diffie–Hellman (CDH) assumption. Also, we give a formal security model for traceable identity-based group signature and prove that the proposed scheme has the properties of traceability and anonymity

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

Efficient Batch Zero-Knowledge Arguments for Low Degree Polynomials

The work of Bootle et al. (EUROCRYPT 2016) constructs an extremely efficient zero-knowledge argument for arithmetic circuit satisfiability in the discrete logarithm setting. However, the argument does not treat relations involving commitments, and furthermore, for simple polynomial relations, the complex machinery employed is unnecessary. In this work, we give a framework for expressing simple relations between commitments and field elements, and present a zero-knowledge argument which is considerably more efficient than Bootle et al. in the case where the polynomials in the relation have low degree. Our method also directly yields a batch protocol, which allows many copies of the same relation to be more efficiently proved and verified in a single argument. We instantiate our protocol with concrete polynomial relations to construct zero-knowledge arguments for membership proofs, polynomial evaluation proofs, and range proofs. Our work can be seen as a unified explanation of the underlying ideas of these protocols. In some of these instantiations we also achieve better efficiency than the state of the art