Publications

We introduce \(\mathsf Z\mathsf i\mathsf n\mathsf c\), a hash-based succinct argument for integer arithmetic. \(\mathsf Z\mathsf i\mathsf n\mathsf c\)’s goal is to provide a practically efficient scheme that bypasses the arithmetization overheads that many succinct arguments present. These overheads can be of orders of magnitude in many applications. By enabling proving statements over the integers, we are able to arithmetize many operations of interest with almost no overhead. This includes modular operations involving any moduli, not necessarily prime, and possibly involving multiple moduli in the same statement. In particular, \(\mathsf Z\mathsf i\mathsf n\mathsf c\,\)allows to prove statements for the ring \(\mathbb Z/n\mathbb Z\,\)for arbitrary \(n≥1\). Importantly, and departing from prior work, our schemes are purely code and hash-based, and do not require hidden order groups. In its final form, \(\mathsf Z\mathsf i\mathsf n\mathsf c\,\)operates similarly to other hash-based schemes using Brakedown as their PCS, and at the same time it benefits from the arithmetization perks brought by working over \(\mathbb Z\) (and \(\mathbb Q\)) natively. At its core, \(\mathsf Z\mathsf i\mathsf n\mathsf c\,\)is a succinct argument for proving relations over the rational numbers \(\mathbb Q\), even though when applied to integer statements, an honest prover and verifier will only operate with small integers. \(\mathsf Z\mathsf i\mathsf n\mathsf c\,\)consists of two main components: 1) \(\mathsf Z\mathsf i\mathsf n\mathsf c\)-\(\mathsf P\mathsf I\mathsf O\mathsf P\), a framework for proving algebraic statements over the rationals by reducing modulo a randomly chosen prime \(q\), followed by running a suitable PIOP over \(\mathbb F_q\) (this is similar to the approach taken in prior works, with the difference that we use localizations of \(\mathbb Q\,\)to enable prime modular projection); and 2) \(\mathsf Z\mathsf i\mathsf p\), a Brakedown-type polynomial commitment scheme built from an IOP of proximity to the integers, a novel primitive that we introduce. The latter primitive guarantees that a prover is using a polynomial with coefficients close to being integral. With these two primitives in place, one can use a lookup argument over the rationals to ensure that the witness contains only integer elements.

A central direction of research in secure multiparty computation with dishonest majority has been to achieve three main goals: 1. reduce the total number of rounds of communication (to four, which is optimal); 2. use only polynomial-time hardness assumptions, and 3. rely solely on cryptographic assumptions in a black-box manner. This is especially challenging when we do not allow a trusted setup assumption of any kind. While protocols achieving two out of three goals in this setting have been designed in recent literature, achieving all three simultaneously remained an elusive open question. Specifically, it was answered positively only for a restricted class of functionalities. In this paper, we completely resolve this long-standing open question. Specifically, we present a protocol for all polynomial-time computable functions that does not require any trusted setup assumptions and achieves all three of the above goals simultaneously.

Efficient realizations of succinct non-interactive arguments of knowledge (SNARKs) have gained popularity due to their practical applications in various domains. Among existing schemes, those based on error-correcting codes are of particular interest because of their good concrete efficiency, transparent setup, and plausible post-quantum security. However, many existing code-based SNARKs suffer from the disadvantage that they only work over specific finite fields. In this work, we construct a code-based SNARK that does not rely on any specific underlying field; i.e., it is field-agnostic. Our construction follows the framework of Brakedown (CRYPTO ’23) and builds a polynomial commitment scheme (and hence a SNARK) based on recently introduced expand-accumulate codes. Our work generalizes these codes to arbitrary finite fields; our main technical contribution is showing that, with high probability, these codes have constant rate and constant relative distance (crucial properties for building efficient SNARKs), solving an open problem from prior work. As a result of our work we obtain a SNARK where, for a statement of size \(M\), the prover time is \(O(M\log M)\)and the proof size is \(O(\sqrt M)\). We demonstrate the concrete efficiency of our scheme empirically via experiments. Proving ECDSA verification on the secp256k1 curve requires only 0.23s for proof generation, 2 orders of magnitude faster than SNARKs that are not field-agnostic. Compared to the original Brakedown result (which is also field-agnostic), we obtain proofs that are 1.9–2.8\(\times\)smaller due to the good concrete distance of our underlying error-correcting code, while introducing only a small overhead of 1.2\(\times\)in the prover time.

Privacy-preserving payment systems face the difficult task of balancing privacy and accountability: on one hand, users should be able to transact privately and anonymously, on the other hand, no illegal activities should be tolerated. The challenging question of finding the right balance lies at the core of the research on accountable privacy that stipulates the use of cryptographic techniques for policy enforcement. Current state-of-the-art systems are only able to enforce rather limited policies, such as spending or transaction limits, or assertions about single participants, but are unable to enforce more complex policies that for example jointly evaluate both, the private credentials of sender and recipient, such as admissible cross-border payments, let alone to do this without auditors in the loop during payment. This severely limits the cases where decentralized virtual assets can be used in accordance with regulatory compliance such as the Financial Action Task Force (FATF) travel rule, while further retaining strong privacy features. We present unlinkable Policy-Compliant Signatures (ul-PCS), an enhanced cryptographic primitive extending the work of Badertscher et al. (TCC 21). We give rigorous definitions, formally proven constructions, and benchmarks using our prototype developed using CharmCrypto. Unlinkable PCS has the following unique combination of features: 1. It is an enhanced signature scheme where the public key encodes in a privacy-preserving way the user’s verifiable credentials (obtained from a credential authority). 2. Signatures can be created (and later publicly verified) by additionally specifying a recipient’s public key aside of the to-be-signed message. A valid signature can only ever be created if the attributes x_S of the signer and the attributes x_R of the receiver fulfill some global policy F(x_S,x_R). 3. The signature can be created by the signer just knowing the recipient’s public key; there is no further interaction needed no attributes are leaked (beyond the validity of the policy). 4. Once credentials are obtained, a user can generate fresh public keys without interacting with the credential authority. By merging the act of signing a transaction with the act of providing an assurance about the involved participants being compliant with complex policies, yet retain that participants are able to change addresses without the involvement of an authority, we show how ul-PCS constitutes a crucial step towards achieving a technology that improves regulatory compliance of privacy coins such as Monero or Zcash.

Policy-compliant signatures (PCS) are a recently introduced primitive by Badertscher et al. [TCC 2021] in which a central authority distributes secret and public keys associated with sets of attributes (e.g., nationality, affiliation with a specific department, or age) to its users. The authority also enforces a policy determining which senders can sign messages for which receivers based on a joint check of their attributes. For example, senders and receivers must have the same nationality, or only senders that are at least 18 years old can send to members of the computer science department. PCS further requires attribute-privacy – nothing about the users’ attributes is revealed from their public keys and signatures apart from whether the attributes satisfy the policy or not. The policy in a PCS scheme is fixed once and for all during the setup. Therefore, a policy update requires a redistribution of all keys. This severely limits the practicality of PCS. In this work, we introduce the notion of updatable policy-compliant signatures (UPCS) extending PCS with a mechanism to efficiently update the policy without redistributing keys to all participants. We define the notion of UPCS and provide the corresponding security definitions. We then provide a generic construction of UPCS based on digital signatures, a NIZK proof system, and a so-called secret-key two-input partially-hiding predicate encryption (2-PHPE) scheme. Unfortunately, the only known way to build the latter for general two-input predicates is using indistinguishability obfuscation. We show that the reliance on the heavy tool of 2-PHPE is inherent to build UPCS by proving that non-interactive UPCS implies 2-PHPE. To circumvent the reliance on 2-PHPE, we consider interactive UPCS, which allows the sender and receiver to interact during the message signing procedure. In this setting, we present two schemes: the first one requires only a digital signature scheme, a NIZK proof system, and secure two-party computation. This scheme works for arbitrary policies, but requires sender and receiver to engage in a two-party computation protocol for each policy update. Our second scheme additionally requires a (single-input) predicate-encryption scheme but, in turn, only requires a single interaction between sender and receiver, independent of the updates. In contrast to 2-PHPE, single-input predicate encryption for certain predicate classes is known to exist (e.g., from pairings) under more concrete and well-understood assumptions.

In this work we study the problem of minimizing the round complexity for securely evaluating multiparty functionalities while making black-box use of polynomial time assumptions. In Eurocrypt 2016, Garg et al. showed that assuming all parties have access to a broadcast channel, then at least four rounds of communication are required to securely realize non-trivial functionalities in the plain model. A sequence of results follow-up the result of Garg et al. matching this lower bound under a variety of assumptions. Unfortunately, none of these works make black-box use of the underlying cryptographic primitives. In Crypto 2021, Ishai, Khurana, Sahai, and Srinivasan came closer to matching the four-round lower bound, obtaining a five-round protocol that makes black-box use of oblivious transfer and PKE with pseudorandom public keys. In this work, we show how to realize any input-less functionality (e.g., coin-tossing, generation of key-pairs, and so on) in four rounds while making black-box use of two-round oblivious transfer. As an additional result, we construct the first four-round MPC protocol for generic functionalities that makes black-box use of the underlying primitives, achieving security against non-aborting adversaries. Our protocols are based on a new primitive called list two-party computation. This primitive offers relaxed security compared to the standard notion of secure two-party computation. Despite this relaxation, we argue that this tool suffices for our applications. List two-party computation is of independent interest, as we argue it can also be used for the generation of setups, like oblivious transfer correlated randomness, in three rounds. Prior to our work, generating such a setup required at least four rounds of interactions or a trusted third party.

We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a random oracle: (a) BPP^QNC^BPP≠BQP. This refutes Jozsa’s conjecture [QIP 05] in the random oracle model. As a result, this gives the first instantiatable separation between the classes by replacing the oracle with a cryptographic hash function, yielding a resolution to one of Aaronson’s ten semi-grand challenges in quantum computing. (b) BPP^QNC⊈QNC^BPP and QNC^BPP⊈BPP^QNC. This shows that there is a subtle interplay between classical computation and shallow quantum computation. In fact, for the second separation, we establish that, for some problems, the ability to perform adaptive measurements in a single shallow quantum circuit, is more useful than the ability to perform polynomially many shallow quantum circuits without adaptive measurements. (c) There exists a 2-message proof of quantum depth protocol. Such a protocol allows a classical verifier to efficiently certify that a prover must be performing a computation of some minimum quantum depth. Our proof of quantum depth can be instantiated using the recent proof of quantumness construction by Yamakawa and Zhandry [STOC 22].

Secure multi-party computation (MPC) protocols that are resilient to a dishonest majority allow the adversary to get the output of the computation while, at the same time, forcing the honest parties to abort. Aumann and Lindell introduced the enhanced notion of security with identifiable abort, which still allows the adversary to trigger an abort but, at the same time, it enables the honest parties to agree on the identity of the party that led to the abort. More recently, in Eurocrypt 2016, Garg et al. showed that, assuming access to a simultaneous message exchange channel for all the parties, at least four rounds of communication are required to securely realize non-trivial functionalities in the plain model. Following Garg et al., a sequence of works has matched this lower bound, but none of them achieved security with identifiable abort. In this work, we close this gap and show that four rounds of communication are also sufficient to securely realize any functionality with identifiable abort using standard and generic polynomial-time assumptions. To achieve this result we introduce the new notion of bounded-rewind secure MPC that guarantees security even against an adversary that performs a mild form of reset attacks. We show how to instantiate this primitive starting from any MPC protocol and by assuming trapdoor-permutations. The notion of bounded-rewind secure MPC allows for easier parallel composition of MPC protocols with other (interactive) cryptographic primitives. Therefore, we believe that this primitive can be useful in other contexts in which it is crucial to combine multiple primitives with MPC protocols while keeping the round complexity of the final protocol low.

Typical approaches for minimizing the round complexity of multiparty computation (MPC) come at the cost of increased communication complexity (CC) or the reliance on setup assumptions. A notable exception is the recent work of Ananth et al. [TCC 2019], which used Functional Encryption (FE) combiners to obtain a round optimal (two-round) semi-honest MPC in the plain model with a CC proportional to the depth and input-output length of the circuit being computed—we refer to such protocols as circuit scalable. This leaves open the question of obtaining communication efficient protocols that are secure against malicious adversaries in the plain model, which we present in this work. Concretely, our two main contributions are: 1) We provide a round-preserving black-box compiler that compiles a wide class of MPC protocols into circuit-scalable maliciously secure MPC protocols in the plain model, assuming (succinct) FE combiners. 2) We provide a round-preserving black-box compiler that compiles a wide class of MPC protocols into circuit-independent— i.e., with a CC that depends only on the input-output length of the circuit—maliciously secure MPC protocols in the plain model, assuming Multi-Key Fully-Homomorphic Encryption (MFHE). Our constructions are based on a new compiler that turns a wide class of MPC protocols into k-delayed-input function MPC protocols (a notion we introduce), where the function that is being computed is specified only in the k-th round of the protocol. As immediate corollaries of our two compilers, we derive (1) the first round-optimal and circuit-scalable maliciously secure MPC protocol, and (2) the first round-optimal and circuit-independent maliciously secure MPC protocol in the plain model. The latter achieves the best to-date CC for a round-optimal maliciously secure MPC protocol. In fact, it is even communication-optimal when the output size of the function being evaluated is smaller than its input size (e.g., for boolean functions). All of our results are based on standard polynomial time assumptions.

We introduce policy-compliant signatures (PCS). A PCS scheme can be used in a setting where a central authority determines a global policy and distributes public and secret keys associated with sets of attributes to the users in the system. If two users, Alice and Bob, have attribute sets that jointly satisfy the global policy, Alice can use her secret key and Bob’s public key to sign a message. Unforgeability ensures that a valid signature can only be produced if Alice’s secret key is known and if the policy is satisfied. Privacy guarantees that the public keys and produced signatures reveal nothing about the users’ attributes beyond whether they satisfy the policy or not. PCS extend the functionality provided by existing primitives such as attribute-based signatures and policy-based signatures, which do not consider a designated receiver and thus cannot include the receiver’s attributes in the policies. We describe practical applications of PCS which include controlling transactions in financial systems with strong privacy guarantees (avoiding additional trusted entities that check compliance), as well as being a tool for trust negotiations. We introduce an indistinguishability-based privacy notion for PCS and present a generic and modular scheme based on standard building blocks such as signatures, non-interactive zero-knowledge proofs, and a (predicate-only) predicate encryption scheme. We show that it can be instantiated to obtain an efficient scheme that is provably secure under standard pairing-assumptions for a wide range of policies. We further model PCS in UC by describing the goal of PCS as an enhanced ideal signature functionality which gives rise to a simulation-based privacy notion for PCS. We show that our generic scheme achieves this composable security notion under the additional assumption that the underlying predicate encryption scheme satisfies a stronger, fully adaptive, simulation-based attribute-hiding notion.

The concept of private stream aggregation (PSA) has been proposed by Shi et al. (NDSS 2011) to allow for data analysis in a privacy-preserving manner. In this work, we introduce the notion of labeled secret sharing (LaSS) schemes and show how to use it to construct PSA schemes. We also show how to realize LaSS using pseudorandom functions or alternatively with a hash function modeled as a random oracle and how it can be used to construct PSA schemes. Additionally, we revisit the security model of Becker et al. (NDSS 2018) and describe stronger security notions for PSA. We then present additional constructions achieving the stronger security notions by relying on recent results on multi-client functional encryption. For all of our constructions, we present implementations to show their practicality and the performance gains over existing solutions.

In functional encryption (FE) a sender, Alice, encrypts plaintexts that a receiver, Bob, can obtain functional evaluations of, while Charlie is responsible for initializing the encryption keys and issuing the decryption keys. Standard notions of security for FE deal with a malicious Bob and how the confidentiality of Alice’s messages can be maintained taking into account the leakage that occurs due to the functional keys that are revealed to the adversary via various forms of indistinguishability experiments that correspond to IND-CPA, IND-CCA and simulation-based security. In this work we provide a complete and systematic investigation of Consistency, a natural security property for FE, that deals with attacks that can be mounted by Alice, Charlie or a collusion of the two against Bob. We develop three main types of consistency notions according to which set of parties is corrupted and investigate their relation to the standard security properties of FE. To validate our different consistency types, we investigate FE in the universally composition setting and we show that our consistency notions naturally complement FE security by proving how they imply (and are implied by) UC security depending on which set of parties is corrupted; in this way we demonstrate a complete characterization of consistency for FE. Finally, we provide explicit constructions that achieve consistency efficiently either directly via a construction based on MDDH for specific function classes of inner products over a modulo group or generically for all the consistency types via compilers using standard cryptographic tools.

In this work, we provide a compiler that transforms a single-input functional encryption scheme for the class of polynomially bounded circuits into a multi-client functional encryption (MCFE) scheme for the class of separable functions. An n-input function f is called separable if it can be described as a list of polynomially bounded circuits f^1, ... , f^n s.t. f(x_1, ... , x_n)= f^1(x_1)+ ... + f^n(x_n) for all x_1 ,... , x_n. Our compiler extends the works of Brakerski et al. [Eurocrypt 2016] and of Komargodski et al. [Eurocrypt 2017] in which a generic compiler is proposed to obtain multi-input functional encryption (MIFE) from single-input functional encryption. Our construction achieves the stronger notion of MCFE but for the less generic class of separable functions. Prior to our work, a long line of results has been proposed in the setting of MCFE for the inner-product functionality, which is a special case of a separable function. We also propose a modified version of the notion of decentralized MCFE introduced by Chotard et al. [Asiacrypt 2018] that we call outsourceable mulit-client functional encryption (OMCFE). Intuitively, the notion of OMCFE makes it possible to distribute the load of the decryption procedure among at most n different entities, which will return decryption shares that can be combined (e.g., additively) thus obtaining the output of the computation. This notion is especially useful in the case of a very resource consuming decryption procedure, while the combine algorithm is non-time consuming. We also show how to extend the presented MCFE protocol to obtain an OMCFE scheme for the same functionality class.

Multi-client functional encryption (MCFE) is an extension of functional encryption (FE) in which the decryption procedure involves ciphertexts from multiple parties. In this paper, we consider MCFE schemes supporting encryption labels, which allow the encryptor to limit the amount of possible mix-and-match that can take place during the decryption. This is achieved by only allowing the decryption of ciphertexts that were generated with respect to the same label. This flexible form of FE was already investigated by Chotard et al. at Asiacrypt 2018 and Abdalla et al. at Asiacrypt 2019. The former provided a general construction based on different standard assumptions, but its ciphertext size grows quadratically with the number of clients. The latter gave a MCFE based on Decisional Diffie-Hellman (DDH) assumption which requires a small inner-product space. In this work, we overcome the deficiency of these works by presenting three constructions with linear-sized ciphertexts based on the Matrix-DDH (MDDH), Decisional Composite Residuosity (DCR) and Learning with Errors (LWE) assumptions in the random-oracle model. We also implement our constructions to evaluate their concrete efficiency.

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 sk_i 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 a 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.