International Association
for Cryptologic Research

Succinct non-interactive arguments of knowledge (SNARKs) have found numerous applications in the blockchain setting and elsewhere. The most efficient SNARKs require a distributed ceremony protocol to generate public parameters, also known as a structured reference string (SRS). Our contributions are two-fold: \begin{compactitem} \item We give a security framework for non-interactive zero-knowledge arguments with a ceremony protocol. \item We revisit the ceremony protocol of Groth's SNARK [Bowe et al., 2017]. We show that the original construction can be simplified and optimized, and then prove its security in our new framework. Importantly, our construction avoids the random beacon model used in the original work. \end{compactitem}

Trusted execution enviroments (TEEs) enable secure execution of program on untrusted hosts and cryptographically attest the correctness of outputs. As these are complex systems, it is hard to capture the exact security achieved by protocols employing TEEs. Crucially TEEs are typically employed in multiple protocols at the same time, thus composable security (with global subroutines) is a natural goal for such systems. We show that under an attested execution setup $\Gatt$ we can realise cryptographic functionalities that are unrealizable in the standard model. We propose a new primitive of Functional Encryption for Stateful and Randomised functionalities (FESR) and an associated protocol, Steel, that realizes it. We show that Steel UC-realises FESR in the universal composition with global subroutines model (TCC 2020). Our work is also a validation of the compositionality of earlier work (Iron}, CCS 2017) capturing (non-stateful) hardware-based functional encryption. As the existing functionality for attested execution of Pass et al. (Eurocrypt 2017) is too strong for real world use, we propose a weaker functionality that allows the adversary to conduct rollback and forking attacks. We show that the stateful variant of $\Steel$, contrary to the stateless variant corresponding to Iron, is not secure in this setting and propose several mitigation techniques.

Zero-knowledge succinct non-interactive arguments (zk-SNARKs) rely on knowledge assumptions for their security. Meanwhile, as the complexity and scale of cryptographic systems continues to grow, the composition of secure protocols is of vital importance. The current gold standards of composable security, the Universal Composability and Constructive Cryptography frameworks cannot capture knowledge assumptions, as their core proofs of composition prohibit white-box extraction. In this paper, we present a formal model allowing the composition of knowledge assumptions. Despite showing impossibility for the general case, we demonstrate the model’s usefulness when limiting knowledge assumptions to few instances of protocols at a time. We finish by providing the first instance of a simultaneously succinct and composable zk-SNARK, by using existing results within our framework.

Multi-client functional encryption (MCFE) is a more flexible variant of functional encryption whose functional decryption involves multiple ciphertexts from different parties. Each party holds a different secret key and can independently and adaptively be corrupted by the adversary. We present two compilers for MCFE schemes for the inner-product functionality, both of which support encryption labels. Our first compiler transforms any scheme with a special key-derivation property into a decentralized scheme, as defined by Chotard et al. (ASIACRYPT 2018), thus allowing for a simple distributed way of generating functional decryption keys without a trusted party. Our second compiler allows to lift an unnatural restriction present in existing (decentralized) MCFE schemes, which requires the adversary to ask for a ciphertext from each party. We apply our compilers to the works of Abdalla et al. (CRYPTO 2018) and Chotard et al. (ASIACRYPT 2018) to obtain schemes with hitherto unachieved properties. From Abdalla et al., we obtain instantiations of DMCFE schemes in the standard model (from DDH, Paillier, or LWE) but without labels. From Chotard et al., we obtain a DMCFE scheme with labels still in the random oracle model, but without pairings.

In structure-preserving signatures, public keys, messages, and signatures are all collections of source group elements of some bilinear groups. In this paper, we introduce fully structure-preserving signature schemes, with the additional requirement that even secret keys are group elements. This strong property allows efficient non-interactive proofs of knowledge of the secret key, which is useful in designing cryptographic protocols under simulation-based security where online extraction of the secret key is needed. We present efficient constructions under simple standard assumptions and pursue even more efficient constructions with the extra property of randomizability based on the generic bilinear group model. An essential building block for our efficient standard model construction is a shrinking structure-preserving trapdoor commitment scheme, which is by itself an important primitive and of independent interest as it appears to contradict a known impossibility result that structure-preserving commitments cannot be shrinking. We argue that a relaxed binding property lets us circumvent the impossibility while still retaining the usefulness of the primitive in important applications as mentioned above.

By design, existing (pre-processing) zk-SNARKs embed a secret trapdoor in a relation-dependent common reference strings (CRS). The trapdoor is exploited by a (hypothetical) simulator to prove the scheme is zero knowledge, and the secret-dependent structure facilitates a linear-size CRS and linear-time prover computation. If known by a real party, however, the trapdoor can be used to subvert the security of the system. The structured CRS that makes zk-SNARKs practical also makes deploying zk-SNARKS problematic, as it is difficult to argue why the trapdoor would not be available to the entity responsible for generating the CRS. Moreover, for pre-processing zk-SNARKs a new trusted CRS needs to be computed every time the relation is changed.In this paper, we address both issues by proposing a model where a number of users can update a universal CRS. The updatable CRS model guarantees security if at least one of the users updating the CRS is honest. We provide both a negative result, by showing that zk-SNARKs with private secret-dependent polynomials in the CRS cannot be updatable, and a positive result by constructing a zk-SNARK based on a CRS consisting only of secret-dependent monomials. The CRS is of quadratic size, is updatable, and is universal in the sense that it can be specialized into one or more relation-dependent CRS of linear size with linear-time prover computation.

The security analysis of real-world protocols involves reduction steps that are conceptually simple but still have to account for many protocol complications found in standards and implementations. Taking inspiration from universal composability, abstract cryptography, process algebras, and type-based verification frameworks, we propose a method to simplify large reductions, avoid mistakes in carrying them out, and obtain concise security statements.Our method decomposes monolithic games into collections of stateful packages representing collections of oracles that call one another using well-defined interfaces. Every component scheme yields a pair of a real and an ideal package. In security proofs, we then successively replace each real package with its ideal counterpart, treating the other packages as the reduction. We build this reduction by applying a number of algebraic operations on packages justified by their state separation. Our method handles reductions that emulate the game perfectly, and leaves more complex arguments to existing game-based proof techniques such as the code-based analysis suggested by Bellare and Rogaway. It also facilitates computer-aided proofs, inasmuch as the perfect reductions steps can be automatically discharged by proof assistants.We illustrate our method on two generic composition proofs: a proof of self-composition using a hybrid argument; and the composition of keying and keyed components. For concreteness, we apply them to the KEM-DEM proof of hybrid-encryption by Cramer and Shoup and to the composition of forward-secure game-based key exchange protocols with symmetric-key protocols.

We construct an efficient delegatable anonymous credential system. Users can anonymously and unlinkably obtain credentials from any authority, delegate their credentials to other users, and prove possession of a credential $L$ levels away from the given authority. The size of the proof (and time to compute it) is $O(Lk)$, where $k$ is the security parameter. The only other construction of delegatable anonymous credentials (Chase and Lysyanskaya, Crypto 2006) relies on general non-interactive proofs for NP-complete languages of size $k \Omega(2^{L})$. We revise the entire approach to constructing anonymous credentials and identify \emph{randomizable} zero-knowledge proof of knowledge systems as the key building block. We formally define the notion of randomizable non-interactive zero-knowledge proofs, and give the first construction by showing how to appropriately rerandomize Groth and Sahai (Eurocrypt 2008) proofs. We show that such proof systems, in combination with an appropriate authentication scheme and a few other protocols, allow us to construct delegatable anonymous credentials. Finally, we instantiate these building blocks under appropriate assumptions about groups with bilinear maps.

The success of electronic authentication systems, be it e-ID card systems or Internet authentication systems such as CardSpace, highly depends on the provided level of user-privacy. Thereby, an important requirement is an efficient means for revocation of the authentication credentials. In this paper we consider the problem of revocation for certificate-based privacy-protecting authentication systems. To date, the most efficient solutions for revocation for such systems are based on cryptographic accumulators. Here, an accumulate of all currently valid certificates is published regularly and each user holds a {\em witness} enabling her to prove the validity of her (anonymous) credential while retaining anonymity. Unfortunately, the users' witnesses must be updated at least each time a credential is revoked. For the know solutions, these updates are computationally very expensive for users and/or certificate issuers which is very problematic as revocation is a frequent event as practice shows. In this paper, we propose a new dynamic accumulator scheme based on bilinear maps and show how to apply it to the problem of revocation of anonymous credentials. In the resulting scheme, proving a credential's validity and updating witnesses both come at (virtually) no cost for credential owners and verifiers. In particular, updating a witness requires the issuer to do only one multiplication per addition or revocation of a credential and can also be delegated to untrusted entities from which a user could just retrieve the updated witness. We believe that thereby we provide the first authentication system offering privacy protection suitable for implementation with electronic tokens such as eID cards or drivers' licenses.

In this paper, we introduce P-signatures. A P-signature scheme consists of a signature scheme, a commitment scheme, and (1) an interactive protocol for obtaining a signature on a committed value; (2) a non-interactive proof system for proving that the contents of a commitment has been signed; (3) a non-interactive proof system for proving that a pair of commitments are commitments to the same value. We give a definition of security for P-signatures and show how they can be realized under appropriate assumptions about groups with bilinear map. Namely, we make extensive use of the powerful suite of non-interactive proof techniques due to Groth and Sahai. Our P-signatures enable, for the first time, the design of a practical non-interactive anonymous credential system whose security does not rely on the random oracle model. In addition, they may serve as a useful building block for other privacy-preserving authentication mechanisms.

We create a credential system that lets a user anonymously authenticate at most $n$ times in a single time period. A user withdraws a dispenser of $n$ e-tokens. She shows an e-token to a verifier to authenticate herself; each e-token can be used only once, however, the dispenser automatically refreshes every time period. The only prior solution to this problem, due to Damg{\aa}rd et al.~[DDP05], uses protocols that are a factor of $k$ slower for the user and verifier, where $k$ is the security parameter. Damg{\aa}rd et al. also only support one authentication per time period, while we support $n$. Because our construction is based on e-cash, we can use existing techniques to identify a cheating user, trace all of her e-tokens, and revoke her dispensers. We also offer a new anonymity service: glitch protection for basically honest users who (occasionally) reuse e-tokens. The verifier can always recognize a reused e-token; however, we preserve the anonymity of users who do not reuse e-tokens too often.