International Association
for Cryptologic Research

A cryptographic accumulator is a succinct set commitment scheme with efficient (non-)membership proofs that typically supports updates (additions and deletions) on the accumulated set. When elements are added to or deleted from the set, an update message is issued. The collection of all the update messages essentially leaks the underlying accumulated set which in certain applications is not desirable. In this work, we define oblivious accumulators, a set commitment with concise membership proofs that hides the elements and the set size from every entity: an outsider, a verifier or other element holders. We formalize this notion of privacy via two properties: element hiding and add-delete indistinguishability. We also define almost-oblivious accumulators, that only achieve a weaker notion of privacy called add-delete unlinkability. Such accumulators hide the elements but not the set size. We consider the trapdoorless, decentralized setting where different users can add and delete elements from the accumulator and compute membership proofs. We then give a generic construction of an oblivious accumulator based on key-value commitments (KVC). We also show a generic way to construct KVCs from an accumulator and a vector commitment scheme. Finally, we give lower bounds on the communication (size of update messages) required for oblivious accumulators and almost-oblivious accumulators.

We revisit the alternating moduli paradigm for constructing symmetric key primitives with a focus on constructing highly efficient protocols to evaluate them using secure multi-party computation (MPC). The alternating moduli paradigm of Boneh et al. (TCC 2018) enables the construction of various symmetric key primitives with the common characteristic that the inputs are multiplied by two linear maps over different moduli, first over F_2 and then over F_3. The first contribution focuses on efficient two-party evaluation of alternating moduli PRFs, effectively building an oblivious pseudorandom function. We present a generalization of the PRF proposed by Boneh et al. (TCC 18) along with methods to lower the communication and computation. We then provide several variants of our protocols, with different computation and communication tradeoffs, for evaluating the PRF. Most are in the OT/VOLE hybrid model while one is based on specialized garbling. Our most efficient protocol effectively is about 3x faster and requires 1.3x lesser communication. Our next contribution is the efficient evaluation of the OWF f(x) = B *_3 (A *_2 x) proposed by Dinur et al. (CRYPTO 21) where A \in F^{m x n}_2, B \in F^{t x m}_3 and *_p is multiplication mod p. This surprisingly simple OWF can be evaluated within MPC by secret sharing [x] over F_2, locally computing [v] = A *_2 [x], performing a modulus switching protocol to F_3 shares, followed by locally computing the output shares [y] = B *_3 [v]. We design a bespoke MPC-in-the-Head (MPCitH) signature scheme that evaluates the OWF, achieving state of art performance. The resulting signature has a size ranging from 4.0-5.5 KB, achieving between 2-3x reduction compared to Dinur et al. To the best of our knowledge, this is only 5% larger than the smallest signature based on symmetric key primitives, including the latest NIST PQC competition submissions. We additionally show that our core techniques can be extended to build very small post-quantum ring signatures for small-medium sized rings that are competitive with state-of-the-art lattice based schemes. Our techniques are in fact more generally applicable to set membership in MPCitH.

We present the first round-optimal and plausibly quantum-safe oblivious transfer (OT) and multi-party computation (MPC) protocols from the computational CSIDH assumption - the weakest and most widely studied assumption in the CSIDH family of isogeny-based assumptions. We obtain the following results: - The first round-optimal maliciously secure OT and MPC protocols in the plain model that achieve (black-box) simulation-based security while relying on the computational CSIDH assumption. - The first round-optimal maliciously secure OT and MPC protocols that achieves Universal Composability (UC) security in the presence of a trusted setup (common reference string plus random oracle) while relying on the computational CSIDH assumption. Prior plausibly quantum-safe isogeny-based OT protocols (with/without setup assumptions) are either not round-optimal, or rely on potentially stronger assumptions. We also build a 3-round maliciously-secure OT extension protocol where each base OT protocol requires only 4 isogeny computations. In comparison, the most efficient isogeny-based OT extension protocol till date due to Lai et al. [Eurocrypt 2021] requires 12 isogeny computations and 4 rounds of communication, while relying on the same assumption as our construction, namely the reciprocal CSIDH assumption.

The recent development of pseudorandom correlation generators (PCG) holds tremendous promise for highly efficient MPC protocols. Among other correlations, PCGs allow for the efficient generation of oblivious transfer (OT) and vector oblivious linear evaluations (VOLE) with sublinear communication and concretely good computational overhead. This type of PCG makes use of a so-called LPN-friendly error-correcting code. That is, for large dimensions the code should have very efficient encoding and have high minimum distance. We investigate existing LPN-friendly codes and find that several candidates are less secure than was believed. Beginning with the recent expand-accumulate codes, we find that for their aggressive parameters, aimed at good concrete efficiency, they achieve a smaller minimum distance than conjectured. This decreases the resulting security parameter of the PCG but it remains unclear by how much. We additionally show that the recently proposed and extremely efficient silver codes achieve only very small minimum distance and result in concretely efficient attacks on the resulting PCG protocol. As such, silver codes should not be used. We introduce a new LPN-friendly code which we call expand-convolute. These codes have provably high minimum distance and faster encoding time than suitable alternatives, e.g. expand-accumulate. The main contribution of these codes is the introduction of a convolution step that dramatically increases the minimum distance. This in turn allows for a more efficient parameter selection which results in improved concrete performance. In particular, we observe a 2 times improvement in running time.

Fitzi, Garay, Maurer, and Ostrovsky (J.\ Cryptology 2005) showed that in the presence of a dishonest majority, no primitive of cardinality $n - 1$ is complete for realizing an arbitrary $n$-party functionality with {\em guaranteed output delivery}. In this work, we introduce a new $2$-party primitive $\mathcal{F}_{\mathsf{SyX}}$ (``synchronizable fair exchange'') and show that it is complete for realizing any $n$-party functionality with {\em fairness} in a setting where all parties are pairwise connected by instances of $\mathcal{F}_{\mathsf{SyX}}$. In the $\mathcal{F}_{\mathsf{SyX}}$-hybrid model, the two parties {\em load} $\mathcal{F}_{\mathsf{SyX}}$ with some input, and following this, either party can {\em trigger} $\mathcal{F}_{\mathsf{SyX}}$ with a ``witness'' at a later time to receive the output from $\mathcal{F}_{\mathsf{SyX}}$. Crucially the other party also receives output from $\mathcal{F}_{\mathsf{SyX}}$ when $\mathcal{F}_{\mathsf{SyX}}$ is triggered. The trigger witnesses allow us to {\em synchronize} the trigger phases of multiple instances of $\mathcal{F}_{\mathsf{SyX}}$, thereby aiding in the design of fair multiparty protocols. Additionally, a pair of parties may {\em reuse} a single {\em a priori} loaded instance of $\mathcal{F}_{\mathsf{SyX}}$ in any number of multiparty protocols (involving different sets of parties).

Fitzi, Garay, Maurer, and Ostrovsky (J. Cryptology 2005) showed that in the presence of a dishonest majority, no primitive of cardinality n − 1 is complete for realizing an arbitrary n-party functionality with guaranteed output delivery. In this work, we show that in the presence of n − 1 corrupt parties, no unreactive primitive of cardinality n − 1 is complete for realizing an arbitrary n-party functionality with fairness. We show more generally that for t > n/2, in the presence of t malicious parties, no unreactive primitive of cardinality t is complete for realizing an arbitrary n-party functionality with fairness. We complement this result by noting that (t + 1)-wise fair exchange is complete for realizing an arbitrary n-party functionality with fairness. In order to prove our results, we utilize the primitive of fair coin tossing and the notion of predictability. While this notion has been considered in some form in past works, we come up with a novel and non-trivial framework to employ it, one that readily generalizes from the setting of two parties to multiple parties, and also to the setting of unreactive functionalities.

We study the problem of verifiably outsourcing computation in a model where the verifier has black-box access to the function being computed. We introduce the problem of oracle-aided batch verification of computation (OBVC) for a function class F. This allows a verifier to efficiently verify the correctness of any f \in F evaluated on a batch of n instances x_1, ...., x_n, while only making \lambda calls to an oracle for f (along with O(n \lambda) calls to low-complexity helper oracles), where \lambda denotes a security parameter. We obtain the following positive and negative results: 1. We build OBVC protocols for the class F of all functions that admit random-self-reductions. Some of our protocols rely on homomorphic encryption schemes. 2. We show that there cannot exist OBVC schemes for the class F of all functions mapping \lambda-bit inputs to \lambda-bit outputs, for any n = \poly(\lambda).

The OCB mode of operation for block ciphers has three variants, OCB1, OCB2 and OCB3. OCB1 and OCB3 can be used as secure authenticated encryption schemes whereas OCB2 has been shown to be classically insecure (Inoue et al., Crypto 2019). Even further, in the presence of quantum queries to the encryption functionality, a series of works by Kaplan et al. (Crypto 2016), Bhaumik et al. (Asiacrypt 2021) and Bonnetain et al. (Asiacrypt 2021) have shown how to break the unforgeability of the OCB modes. However, these works did not consider the confidentiality of OCB in the presence of quantum queries.We fill this gap by presenting the first formal analysis of the IND-qCPA security of OCB. In particular, we show the first attacks breaking the IND-qCPA security of the OCB modes. Surprisingly, we are able to prove that OCB2 is IND-qCPA secure when used without associated data, while relying on the assumption that the underlying block cipher is a quantum-secure pseudorandom permutation. Additionally, we present new quantum attacks breaking the universal unforgeability of OCB. Our analysis of OCB has implications for the post-quantum security of XTS, a well-known disk encryption standard, that was considered but mostly left open by Anand et al. (PQCrypto 2016).

Seminal works by Cohn-Gordon, Cremers, Dowling, Garratt, and Stebila [Journal of Cryptology 2020] and Alwen, Coretti, and Dodis [EUROCRYPT 2019] provided the first formal frameworks for studying the widely-used Signal Double Ratchet (DR for short) algorithm. In this work, we develop a new Universally Composable (UC) definition F_DR that we show is provably achieved by the DR protocol. Our definition captures not only the security and correctness guarantees of the DR already identified in the prior state-of-the-art analyses of Cohn-Gordon et al. and Alwen et al., but also more guarantees that are absent from one or both of these works. In particular, we construct six different modified versions of the DR protocol, all of which are insecure according to our definition F_DR, but remain secure according to one (or both) of their definitions. For example, our definition is the first to capture CCA-style attacks possible immediately after a compromise — attacks that, as we show, the DR protocol provably resists, but were not captured by prior definitions. We additionally show that multiple compromises of a party in a short time interval, which the DR should be able to withstand, as we understand from its whitepaper, nonetheless introduce a new non-trivial (albeit minor) weakness of the DR. Since the definitions in the literature (including our F_DR above) do not capture security against this more nuanced scenario, we define a new stronger definition F_TR that does. Finally, we provide a minimalistic modification to the DR (that we call the Triple Ratchet, or TR for short) and show that the resulting protocol securely realizes the stronger functionality F_TR. Remarkably, the modification incurs no additional communication cost and virtually no additional computational cost. We also show that these techniques can be used to improve communication costs in other scenarios, e.g. practical Updatable Public Key Encryption schemes and the re-randomized TreeKEM protocol of Alwen et al. [CRYPTO 2020] for Secure Group Messaging.

In multi-party threshold private set intersection (PSI), $n$ parties each with a private set wish to compute the intersection of their sets if the intersection is sufficiently large. Previously, Ghosh and Simkin (CRYPTO 2019) studied this problem for the two-party case and demonstrated interesting lower and upper bounds on the communication complexity. In this work, we investigate the communication complexity of the multi-party setting $(n\geq 2)$. We consider two functionalities for multi-party threshold PSI. In the first, parties learn the intersection if each of their sets and the intersection differ by at most $T$. In the second functionality, parties learn the intersection if the union of all their sets and the intersection differ by at most $T$. For both functionalities, we show that any protocol must have communication complexity $\Omega(nT)$. We build protocols with a matching upper bound of $O(nT)$ communication complexity for both functionalities assuming threshold FHE. We also construct a computationally more efficient protocol for the second functionality with communication complexity $\widetilde{O}(nT)$ under a weaker assumption of threshold additive homomorphic encryption. As a direct implication, we solve one of the open problems in the work of Ghosh and Simkin (CRYPTO 2019) by designing a two-party protocol with communication cost $\widetilde{O}(T)$ from assumptions weaker than FHE. As a consequence of our results, we achieve the first "regular" multi-party PSI protocol where the communication complexity only grows with the size of the set difference and does not depend on the size of the input sets.

We put forth new protocols for oblivious transfer extension and vector OLE, called \emph{Silver}, for SILent Vole and oblivious transfER. Silver offers extremely high performances: generating 10 million random OTs on one core of a standard laptop requires only 300ms of computation and 122KB of communication. This represents 37% less computation and ~1300x less communication than the standard IKNP protocol, as well as ~4x less computation and ~4x less communication than the recent protocol of Yang et al. (CCS 2020). Silver is \emph{silent}: after a one-time cheap interaction, two parties can store small seeds, from which they can later \emph{locally} generate a large number of OTs \emph{while remaining offline}. Neither IKNP nor Yang et al. enjoys this feature; compared to the best known silent OT extension protocol of Boyle et al. (CCS 2019), upon which we build up, Silver has 19x less computation, and the same communication. Due to its attractive efficiency features, Silver yields major efficiency improvements in numerous MPC protocols. Our approach is a radical departure from the standard paradigm for building MPC protocols, in that we do \emph{not} attempt to base our constructions on a well-studied assumption. Rather, we follow an approach closer in spirit to the standard paradigm in the design of symmetric primitives: we identify a set of fundamental structural properties that allow us to withstand all known attacks, and put forth a candidate design, guided by our analysis. We also rely on extensive experimentations to analyze our candidate and experimentally validate their properties. In essence, our approach boils down to constructing new families of linear codes with (plausibly) high minimum distance and extremely low encoding time. While further analysis is of course warranted to confidently assess the security of Silver, we hope and believe that initiating this approach to the design of MPC primitives will pave the way to new secure primitives with extremely attractive efficiency features.

We study the problem of {\em almost-everywhere reliable message transmission}; a key component in designing efficient and secure MPC protocols for sparsely connected networks. The goal is to design low-degree networks which allow a large fraction of honest nodes to communicate reliably even while linearly many nodes can experience byzantine corruption and deviate arbitrarily from the assigned protocol.\\ \noindent In this paper, we achieve a $\log$-degree network with a polylogarithmic work complexity protocol, thereby improving over the state-of-the-art result of Chandran {\em et al.} (ICALP 2010) who required a polylogarithmic-degree network and had a linear work complexity. In addition, we also achieve: \begin{itemize} \item A work efficient version of Dwork et. al.'s (STOC 1986) butterfly network. \item An improvement upon the state of the art protocol of Ben-or and Ron (Information Processing Letters 1996) in the randomized corruption model---both in work-efficiency and in resilience.

As blockchains grow in size, validating new transactions becomes more and more resource intensive. To deal with this, there is a need to discover compact encodings of the (effective) state of a blockchain --- an encoding that allows for efficient proofs of membership and updates. In the case of account-based cryptocurrencies, the state can be represented by a key-value map, where keys are the account addresses and values consist of account balance, nonce, etc. We propose a new commitment scheme for key-value maps whose size does not grow with the number of keys, yet proofs of membership are of constant-size. In fact, both the encoding and the proofs consist of just two and three group elements respectively (in groups of unknown order like class groups). Verifying and updating proofs involves just a few group exponentiations. Additive updates to key values enjoy the same level of efficiency too. Key-value commitments can be used to build dynamic accumulators and vector commitments, which find applications in group signatures, anonymous credentials, verifiable databases, interactive oracle proofs, etc. Using our new key-value commitment, we provide the most efficient constructions of (sub)vector commitments to date.