International Association
for Cryptologic Research

This paper formalizes the notion of server-aided anonymous credentials (SAACs), a new model for anonymous credentials (ACs) where, in the process of showing a credential, the holder is helped by additional auxiliary information generated in an earlier (anonymous) interaction with the issuer. This model enables lightweight instantiations of publicly verifiable and multi-use ACs from pairing-free elliptic curves, which is important for compliance with existing national standards. A recent candidate for the EU Digital Identity Wallet, BBS#, roughly adheres to the SAAC model we have developed; however, it lacks formal security definitions and proofs. In this paper, we provide rigorous definitions of security for SAACs, and show how to realize SAACs from the weaker notion of key-verification ACs (KVACs) and special types of oblivious issuance protocols for zero-knowledge proofs. We instantiate this paradigm to obtain two constructions: one achieves statistical anonymity with unforgeability under the Gap q-SDH assumption, and the other achieves computational anonymity and unforgeability under the DDH assumption.

The eIDAS 2.0 regulation aims to develop interoperable digital identities for European citizens, and it has recently become law. One of its requirements is that credentials be unlinkable. Anonymous credentials (AC) allow holders to prove statements about their identity in a way that does not require to reveal their identity and does not enable linking different usages of the same credential. As a result, they are likely to become the technology that provides digital identity for Europeans. Any digital credential system, including anonymous credentials, needs to be secured against identity theft and fraud. In this work, we introduce the notion of a multi-holder anonymous credential scheme that allows issuing shares of credentials to different authentication factors (or "holders"). To present the credential, the user's authentication factors jointly run a threshold presentation protocol. Our definition of security requires that the scheme provide unforgeability: the adversary cannot succeed in presenting a credential with identity attributes that do not correspond to an identity for which the adversary controls at least t shares; this is true even if the adversary can obtain credentials of its choice and cause concurrent executions of the presentation protocol. Further, our definition requires that the presentation protocol provide security with identifiable abort. Finally, presentations generated by all honest holders must be unlinkable and must not reveal the user's secret identity attributes even to an adversary that controls some of the user's authentication factors. We design and prove the (concurrent) security of a multi-holder version of the BBS anonymous credential scheme. In our construction, each holder is issued a secret share of a BBS credential. Using these shares, the holders jointly compute a credential presentation that is identical to (and therefore compatible with) the traditional, single-holder variant (due to Tessaro and Zhu, Eurocrypt'23) of a BBS credential presentation.

Anonymous credentials, first proposed by Chaum in 1985, enable individuals to prove attributes about themselves without revealing personal information. For example, they can prove that they live in Ontario without revealing their full home address. The award celebrates a sequence of results, starting in 2001, that developed the first efficient and fully anonymous credential schemes. This is an active area of research with many beautiful results by many talented cryptographers. We hope that this recognition will encourage further adoption of this technology.

<p>To be useful and widely accepted, automated contact tracing schemes (also called exposure notification) need to solve two seemingly contradictory problems at the same time: they need to protect the anonymity of honest users while also preventing malicious users from creating false alarms. In this paper, we provide, for the first time, an exposure notification construction that guarantees the same levels of privacy and integrity as existing schemes but with a fully malicious database (notably similar to Auerbach et al. CT-RSA 2021) without special restrictions on the adversary. We construct a new definition so that we can formally prove our construction secure. Our definition ensures the following integrity guarantees: no malicious user can cause exposure warnings in two locations at the same time and that any uploaded exposure notifications must be recent and not previously uploaded. Our construction is efficient, requiring only a single message to be broadcast at contact time no matter how many recipients are nearby. To notify contacts of potential infection, an infected user uploads data with size linear in the number of notifications, similar to other schemes. Linear upload complexity is not trivial with our assumptions and guarantees (a naive scheme would be quadratic). This linear complexity is achieved with a new primitive: zero knowledge subset proofs over commitments which is used by our "no cloning" proof protocol. We also introduce another new primitive: set commitments on equivalence classes, which makes each step of our construction more efficient. Both of these new primitives are of independent interest. </p>

Delegatable anonymous credentials (DACs) enable a root issuer to delegate credential-issuing power, allowing a delegatee to take a delegator role. To preserve privacy, credential recipients and verifiers should not learn anything about intermediate issuers in the delegation chain. One particularly efficient approach to constructing DACs is due to Crites and Lysyanskaya (CT-RSA '19). In contrast to previous approaches, it is based on mercurial signatures (a type of equivalence-class signature), offering a conceptually simple design that does not require extensive use of zero-knowledge proofs. Unfortunately, current constructions of ``CL-type'' DACs only offer a weak form of privacy-preserving delegation: if an adversarial issuer (even an honest-but-curious one) is part of a user's delegation chain, they can detect when the user shows its credential. This is because the underlying mercurial signature schemes allows a signer to identify his public key in a delegation chain. We propose CL-type DACs that overcome the above limitation based on a new mercurial signature scheme that provides adversarial public key class hiding which ensures that adversarial signers who participate in a user's delegation chain cannot exploit that fact to trace users. We achieve this introducing structured public parameters for each delegation level. Since the related setup produces critical trapdoors, we discuss techniques from updatable structured reference strings in zero-knowledge proof systems (Groth et al. CRYPTO '18) to guarantee the required privacy needs. In addition, we propose a simple way to realize revocation for CL-type DACs via the concept of revocation tokens. While we showcase this approach to revocation using our DAC scheme, it is generic and can be applied to any CL-type DAC system. Revocation is a vital feature that is largely unexplored and notoriously hard to achieve for DACs, thus providing it can help to make DAC schemes more attractive in practical applications.

In onion routing, a message travels through the network via a series of intermediaries, wrapped in layers of encryption to make it difficult to trace. Onion routing is an attractive approach to realizing anonymous channels because it is simple and fault tolerant. Onion routing protocols provably achieving anonymity in realistic adversary models are known for the synchronous model of communication so far. In this paper, we give the first onion routing protocol that achieves anonymity in the asynchronous model of communication. The key tool that our protocol relies on is the novel cryptographic object that we call bruisable onion encryption. The idea of bruisable onion encryption is that even though neither the onion's path nor its message content can be altered in transit, an intermediate router on the onion's path that observes that the onion is delayed can nevertheless slightly damage, or bruise it. An onion that is chronically delayed will have been bruised by many intermediaries on its path and become undeliverable. This prevents timing attacks and, as we show, yields a provably secure onion routing protocol in the asynchronous setting.

<jats:title>Abstract</jats:title><jats:p>A two-input function is a dual PRF if it is a PRF when keyed by either of its inputs. Dual PRFs are assumed in the design and analysis of numerous primitives and protocols including HMAC, AMAC, TLS 1.3 and MLS. But, not only do we not know whether particular functions on which the assumption is made really are dual PRFs; we do not know if dual PRFs even exist. What if the goal is impossible? This paper addresses this with a foundational treatment of dual PRFs, giving constructions based on standard assumptions. This provides what we call a generic validation of the dual PRF assumption. Our approach is to introduce and construct symmetric PRFs, which imply dual PRFs and may be of independent interest. We give a general construction of a symmetric PRF based on a function having a weak form of collision resistance coupled with a leakage hardcore function, a strengthening of the usual notion of hardcore functions we introduce. We instantiate this general construction in two ways to obtain two specific symmetric and dual PRFs, the first assuming any collision-resistant hash function and the second assuming any one-way permutation. A construction based on any one-way function evades us and is left as an intriguing open problem. </jats:p>

In a blind signature scheme, a user can obtain a digital signature on a message of her choice without revealing anything about the message or the resulting signature to the signer. Blind signature schemes have recently found applications for privacy-preserving web browsing and ad ecosystems, and as such, are ripe for standardization. In this paper, we show that the recent proposed standard of Denis, Jacobs and Wood constitutes a strongly one-more-unforgeable blind signature scheme in the random-oracle model under the one-more-RSA assumption. Further, we show that the blind version of RSA-FDH proposed and analyzed by Bellare, Namprempre, Pointcheval and Semanko does not satisfy blindness when the public key is chosen maliciously, but satisfies a weaker notion of a blind token.

In a world where everyone uses anonymous credentials for all access control needs, it is impossible to trace wrongdoers, by design. This makes legitimate controls, such as tracing illicit trade and terror suspects, impossible to carry out. Here, we propose a privacy-preserving blueprint capability that allows an auditor to publish an encoding pk_A of the function f(x, . ) for a publicly known function f and a secret input x. For example, x may be a secret watchlist, and f(x,y) may return y if y in x. On input her data y and the auditor's pk_A, a user can compute an escrow Z such that anyone can verify that Z was computed correctly from the user's credential attributes, and moreover, the auditor can recover f(x,y) from Z. Our contributions are: -- We define secure f-blueprint systems; our definition is designed to provide a modular extension to anonymous credential systems. -- We show that secure f-blueprint systems can be constructed for all functions $f$ from fully homomorphic encryption and NIZK proof systems. This result is of theoretical interest but is not efficient enough for practical use. -- We realize an optimal blueprint system under the DDH assumption in the random-oracle model for the watchlist function.

Blind signature schemes are one of the best-studied tools for privacy-preserving authentication. Unfortunately, known constructions of provably secure blind signatures either rely on non-standard hardness assumptions, or require parameters that grow linearly with the number of concurrently issued signatures, or involve prohibitively inefficient general techniques such as general secure two-party computation. Recently, Katz, Loss and Rosenberg (ASIACRYPT'21) gave a technique that, for the security parameter n, transforms blind signature schemes secure for O(log n) concurrent executions of the blind signing protocol into ones that are secure for any poly(n) concurrent executions. This transform has two drawbacks that we eliminate in this paper: 1) the communication complexity of the resulting blind signing protocol grows linearly with the number of signing interactions; 2) the resulting schemes inherit a very loose security bound from the underlying scheme and, as a result, require impractical parameter sizes. In this work, we give an improved transform for obtaining a secure blind signing protocol tolerating any poly(n) concurrent executions from one that is secure for O(log n) concurrent executions. While preserving the advantages of the original transform, the communication complexity of our new transform only grows logarithmically with the number of interactions. Under the CDH and RSA assumptions, we improve on this generic transform in terms of concrete efficiency and give (1) a BLS-based blind signature scheme over a standard-sized group where signatures are of size roughly 3 KB and communication per signature is roughly 120 KB; and (2) an Okamoto-Guillou-Quisquater-based blind signature scheme with signatures and communication of roughly 9 KB and 8 KB, respectively.

Onion routing is a popular approach towards anonymous communication. Practical implementations are widely used (for example, Tor has millions of users daily), but are vulnerable to various traffic correlation attacks, and the theoretical foundations, despite recent progress, still lag behind. In particular, all works that model onion routing protocols and prove their security only address a single run, where each party sends and receives a single message of fixed length, once. Moreover, they all assume a static network setting, where the parties are stable throughout the lifetime of the protocol. In contrast, real networks have a high rate of churn (nodes joining and exiting the network), real users want to send multiple messages, and realistic adversaries may observe multiple runs of the protocol. We initiate a formal treatment of onion routing in a setting with multiple runs over a dynamic network with churn. We provide definitions of both security and anonymity in this setting, and constructions that satisfy them. In particular, we define a new cryptographic primitive called \emph{Poly Onions} and show that it can be used to realize our definitions.

Numerous cryptographic applications require efficient non-interactive zero-knowledge proofs of knowledge (NIZKPoK) as a building block. Typically they rely on the Fiat-Shamir heuristic to do so, as security in the random-oracle model is considered good enough in practice. However, there is a troubling disconnect between the stand-alone security of such a protocol and its security as part of a larger, more complex system where several protocols may be running at the same time. Provable security in the general universal composition model (GUC model) of Canetti et al. is the best guarantee that nothing will go wrong when a system is part of a larger whole, even when all parties share a common random oracle. In this paper, we prove the minimal necessary properties of generally universally composable (GUC) NIZKPoK in any global random-oracle model, and show how to achieve efficient and GUC NIZKPoK in both the restricted programmable and restricted observable (non-programmable) global random-oracle models.

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Onion routing is a popular, efficient, and scalable method for enabling anonymous communications. To send a message m to Bob via onion routing, Alice picks several intermediaries, wraps m in multiple layers of encryption --- a layer per intermediary --- and sends the resulting “onion” to the first intermediary. Each intermediary “peels off'”a layer of encryption and learns the identity of the next entity on the path and what to send along; finally Bob learns that he is the recipient and recovers the message m. Despite its wide use in the real world (e.g., Mixminion), the foundations of onion routing have not been thoroughly studied. In particular, although two-way communication is needed in most instances, such as anonymous Web browsing or anonymous access to a resource, until now no definitions or provably secure constructions have been given for two-way onion routing. Moreover, the security definitions that existed even for one-way onion routing were found to have significant flaws. In this paper, we (1) propose an ideal functionality for a repliable onion encryption scheme; (2) give a game-based definition for repliable onion encryption and show that it is sufficient to realize our ideal functionality; and finally (3), our main result is a construction of repliable onion encryption that satisfies our definitions.

In this work, we define and construct fully homomorphic non-interactive zero knowledge (FH-NIZK) and non-interactive witness-indistinguishable (FH-NIWI) proof systems.     We focus on the NP complete language L, where, for a boolean circuit C and a bit b, the pair $$(C,b)\in L$$ if there exists an input $$\mathbf {w}$$ such that $$C(\mathbf {w})=b$$. For this language, we call a non-interactive proof system fully homomorphic if, given instances $$(C_i,b_i)\in L$$ along with their proofs $$\varPi _i$$, for $$i\in \{1,\ldots ,k\}$$, and given any circuit $$D:\{0,1\}^k\rightarrow \{0,1\}$$, one can efficiently compute a proof $$\varPi $$ for $$(C^*,b)\in L$$, where $$C^*(\mathbf {w}^{(1)},\ldots ,\mathbf {w}^{(k)})=D(C_1(\mathbf {w}^{(1)}),\ldots ,C_k(\mathbf {w}^{(k)}))$$ and $$D(b_1,\ldots ,b_k)=b$$. The key security property is unlinkability: the resulting proof $$\varPi $$ is indistinguishable from a fresh proof of the same statement.     Our first result, under the Decision Linear Assumption (DLIN), is an FH-NIZK proof system for L in the common random string model. Our more surprising second result (under a new decisional assumption on groups with bilinear maps) is an FH-NIWI proof system that requires no setup.

A recent line of work has explored the use of physically unclonable functions (PUFs) for secure computation, with the goals of (1) achieving universal composability without additional setup and/or (2) obtaining unconditional security (i.e., avoiding complexity-theoretic assumptions). Initial work assumed that all PUFs, even those created by an attacker, are honestly generated. Subsequently, researchers have investigated models in which an adversary can create malicious PUFs with arbitrary behavior. Researchers have considered both malicious PUFs that might be stateful , as well as malicious PUFs that can have arbitrary behavior but are guaranteed to be stateless . We settle the main open questions regarding secure computation in the malicious-PUF model: We prove that unconditionally secure oblivious transfer is impossible, even in the stand-alone setting, if the adversary can construct (malicious) stateful PUFs. We show that if the attacker is limited to creating (malicious) stateless PUFs, then universally composable two-party computation is possible, unconditionally.