Composable & Modular Anonymous Credentials: Definitions and Practical Constructions

It takes time for theoretical advances to get used in practical schemes. Anonymous credential schemes are no exception. For instance, existing schemes suited for real-world use lack formal, composable definitions, partly because they do not support straight-line extraction and rely on random oracles for their security arguments. To address this gap, we propose unlinkable redactable signatures (URS), a new building block for privacy-enhancing protocols, which we use to construct the first efficient UC-secure anonymous credential system that supports multiple issuers, selective disclosure of attributes, and pseudonyms. Our scheme is one of the first such systems for which both the size of a credential and its presentation proof are independent of the number of attributes issued in a credential. Moreover, our new credential scheme does not rely on random oracles. As an important intermediary step, we address the problem of building a functionality for a complex credential system that can cover many different features. Namely, we design a core building block for a single issuer that supports credential issuance and presentation with respect to pseudonyms and then show how to construct a full-fledged credential system with multiple issuers in a modular way. We expect this flexible definitional approach to be of independent interest

Signature Schemes with Efficient Protocols and Dynamic Group Signatures from Lattice Assumptions

International audienceA recent line of works – initiated by Gordon, Katz and Vaikuntanathan (Asiacrypt 2010) – gave lattice-based realizations of privacy-preserving protocols allowing users to authenticate while remaining hidden in a crowd. Despite five years of efforts, known constructions remain limited to static populations of users, which cannot be dynamically updated. For example, none of the existing lattice-based group signatures seems easily extendable to the more realistic setting of dynamic groups. This work provides new tools enabling the design of anonymous authen-tication systems whereby new users can register and obtain credentials at any time. Our first contribution is a signature scheme with efficient protocols, which allows users to obtain a signature on a committed value and subsequently prove knowledge of a signature on a committed message. This construction, which builds on the lattice-based signature of Böhl et al. (Eurocrypt'13), is well-suited to the design of anonymous credentials and dynamic group signatures. As a second technical contribution, we provide a simple, round-optimal joining mechanism for introducing new members in a group. This mechanism consists of zero-knowledge arguments allowing registered group members to prove knowledge of a secret short vector of which the corresponding public syndrome was certified by the group manager. This method provides similar advantages to those of structure-preserving signatures in the realm of bilinear groups. Namely, it allows group members to generate their public key on their own without having to prove knowledge of the underlying secret key. This results in a two-round join protocol supporting concurrent enrollments, which can be used in other settings such as group encryption

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

Efficient Zero-Knowledge Proof of Algebraic and Non-Algebraic Statements with Applications to Privacy Preserving Credentials

Practical anonymous credential systems are generally built around sigma-protocol ZK proofs. This requires that credentials be based on specially formed signatures. Here we ask whether we can instead use a standard (say, RSA, or (EC)DSA) signature that includes formatting and hashing messages, as a credential, and still provide privacy. Existing techniques do not provide efficient solutions for proving knowledge of such a signature: On the one hand, ZK proofs based on garbled circuits (Jawurek et al. 2013) give efficient proofs for checking formatting of messages and evaluating hash functions. On the other hand they are expensive for checking algebraic relations such as RSA or discrete-log, which can be done efficiently with sigma protocols. We design new constructions obtaining the best of both worlds: combining the efficiency of the garbled circuit approach for non-algebraic statements and that of sigma protocols for algebraic ones. We then discuss how to use these as building-blocks to construct privacy-preserving credential systems based on standard RSA and (EC)DSA signatures. Other applications of our techniques include anonymous credentials with more complex policies, the ability to efficiently switch between commitments (and signatures) in different groups, and secure two-party computation on committed/signed inputs

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

Anonymous Point Collection - Improved Models and Security Definitions

This work is a comprehensive, formal treatment of anonymous point collection. The proposed definition does not only provide a strong notion of security and privacy, but also covers features which are important for practical use. An efficient realization is presented and proven to fulfill the proposed definition. The resulting building block is the first one that allows for anonymous two-way transactions, has semi-offline capabilities, yields constant storage size, and is provably secure

Anonymous Point Collection - Improved Models and Security Definitions

This work is a comprehensive, formal treatment of anonymous point collection. The proposed definition does not only provide a strong notion of security and privacy, but also covers features which are important for practical use. An efficient realization is presented and proven to fulfill the proposed definition. The resulting building block is the first one that allows for anonymous two-way transactions, has semi-offline capabilities, yields constant storage size, and is provably secure

Foundations of Anonymous Signatures: Formal Definitions, Simplified Requirements, and a Construction Based on General Assumptions

In today\u27s systems, privacy is often at odds with utility: users that reveal little information about themselves get restricted functionality, and service providers mistrust them. In practice, systems tip to either full anonymity (e.g. Monero), or full utility (e.g. Bitcoin). Well-known cryptographic primitives for bridging this gap exist: anonymous credentials (AC) let users disclose a subset of their credentials\u27 attributes, revealing to service providers just what they need ; group signatures (GS) allow users to authenticate anonymously, to be de-anonymized just when deemed necessary . However, these primitives are hard to deploy. Current AC and GS variants reach specific points in the privacy-utility tradeoff, which we point as counter-productive engineering-wise, as it requires full and error-prone re-engineering to adjust the tradeoff. Also, so far, GS and AC have been studied separately by theoretical research. We take the first steps toward unifying and generalizing both domains, with the goal of bringing their benefits to practice, in a flexible way. We give a common model capturing their core properties, and use functional placeholders to subsume intermediate instantiations of the privacy-utility tradeoff under the same model. To prove its flexibility, we show how concrete variants of GS, AC (and others, like ring signatures) can be seen as special cases of our scheme – to which we refer as universal anonymous signatures (UAS). In practice, this means that instantiations following our construction can be configured to behave as variant X of a GS scheme, or as variant Y of an AC scheme, by tweaking a few functions