International Association
for Cryptologic Research

The notion of aggregate signatures allows for combining signatures from different parties into a short certificate that attests that *all* parties signed a message. In this work, we lift this notion to capture different, more expressive signing policies. For example, we can certify that a message was signed by a (weighted) threshold of signers. We present the first constructions of aggregate signatures for monotone policies based on standard polynomial-time cryptographic assumptions. The aggregate signatures in our schemes are succinct, i.e., their size is *independent* of the number of signers. Moreover, verification is also succinct if all parties sign the same message (or if the messages have a succinct representation). All prior work requires either interaction between the parties or non-standard assumptions (that imply SNARKs for NP). Our signature schemes are based on non-interactive batch arguments (BARGs) for monotone policies [Brakerski-Brodsky-Kalai-Lombardi-Paneth, Crypto'23]. In contrast to previous constructions, our BARGs satisfy a new notion of *adaptive* security which is instrumental to our application. Our new BARGs for monotone policies can be constructed from standard BARGs and other standard assumptions.

A homomorphic secret sharing (HSS) scheme allows a client to delegate a computation to a group of untrusted servers while achieving input privacy as long as at least one server is honest. In recent years, many HSS schemes have been constructed that have, in turn, found numerous applications to cryptography. Prior work on HSS focuses on the setting where the servers are semi-honest. In this work we lift HSS to the setting of malicious evaluators. We propose the notion of *HSS with verifiable evaluation* (ve-HSS) that guarantees correctness of output *even when all the servers are corrupted*. ve-HSS retains all the attractive features of HSS and adds the new feature of succinct (public) verification of output. We present *black-box* constructions of ve-HSS by devising generic transformations for semi-honest HSS schemes (with negligible error). This provides a new non-interactive method for verifiable and private outsourcing of computation.

We provide the first constructions of SNARGs for Batch-NP and P based solely on the sub-exponential Decisional Diffie Hellman (DDH) assumption. Our schemes achieve poly-logarithmic proof sizes. We obtain our results by following the correlation-intractability framework for secure instantiation of the Fiat-Shamir paradigm. The centerpiece of our results and of independent interest is a new construction of correlation-intractable hash functions for ``small input'' product relations verifiable in TC0, based on sub-exponential DDH.

One of the most fundamental results in game theory is that every game has a Nash equilibrium, an assignment of (randomized) strategies to players with the stability property that no individual player can benefit from deviating from the assigned strategy. It is not known how to efficiently *compute* such a Nash equilibrium --- the computational complexity of this task is characterized by the class PPAD, but the relation of PPAD to other problems and well-known complexity classes is not precisely understood. In recent years there has been mounting evidence, based on cryptographic tools and techniques, showing the hardness of PPAD. We continue this line of research by showing that PPAD is as hard as *learning with errors* and the *iterated squaring* problem, two standard problems in cryptography. Our work improves over prior hardness results that relied either on (1) sub-exponential assumptions, or (2) relied on ``obfustopia,'' which can currently be based on a particular combination of three assumptions. Our work additionally establishes *public-coin* hardness for PPAD (computational hardness for a publicly sampleable distribution of instances) that seems out of reach of the obfustopia approach. Following the work of Choudhuri et al. (STOC 2019) and subsequent works, our hardness result is obtained by constructing an *unambiguous and incrementally-updateable* succinct non-interactive argument for IS, whose soundness relies on polynomial hardness of LWE. The result also implies a verifiable delay function with unique proofs, which may be of independent interest.

Existing approaches to secure multiparty computation (MPC) require all participants to commit to the entire duration of the protocol. As interest in MPC continues to grow, it is inevitable that there will be a desire to use it to evaluate increasingly complex functionalities, resulting in computations spanning several hours or days. Such scenarios call for a *dynamic* participation model for MPC where participants have the flexibility to go offline as needed and (re)join when they have available computational resources. Such a model would also democratize access to privacy-preserving computation by facilitating an ``MPC-as-a-service'' paradigm --- the deployment of MPC in volunteer-operated networks (such as blockchains, where dynamism is inherent) that perform computation on behalf of clients. In this work, we initiate the study of *fluid MPC*, where parties can dynamically join and leave the computation. The minimum commitment required from each participant is referred to as *fluidity*, measured in the number of rounds of communication that it must stay online. Our contributions are threefold: - We provide a formal treatment of fluid MPC, exploring various possible modeling choices. - We construct information-theoretic fluid MPC protocols in the honest-majority setting. Our protocols achieve *maximal fluidity*, meaning that a party can exit the computation after receiving and sending messages in one round. - We implement our protocol and test it in multiple network settings.

We study the problem of designing *non-interactive batch arguments* for NP. Such an argument system allows an efficient prover to prove multiple $\npol$ statements, with size much smaller than the combined witness length. We provide the first construction of such an argument system for NP in the common reference string model based on standard cryptographic assumptions. Prior works either require non-falsifiable assumptions (or the random oracle model) or can only support private verification. At the heart of our result is a new *dual mode* interactive batch argument system for NP. We show how to apply the correlation-intractability framework for Fiat-Shamir -- that has primarily been applied to proof systems -- to such interactive arguments.

Oblivious transfer (OT) is a foundational primitive within cryptography owing to its connection with secure computation. One of the oldest constructions of oblivious transfer was from certified trapdoor permutations (TDPs). However several decades later, we do not know if a similar construction can be obtained from TDPs in general. In this work, we study the problem of constructing round optimal oblivious transfer from trapdoor permutations. In particular, we obtain the following new results (in the plain model) relying on TDPs in a black-box manner: – Three-round oblivious transfer protocol that guarantees indistinguishability-security against malicious senders (and semi-honest receivers). – Four-round oblivious transfer protocol secure against malicious adversaries with black-box simulation-based security. By combining our second result with an already known compiler we obtain the first round-optimal 2-party computation protocol that relies in a black-box way on TDPs. A key technical tool underlying our results is a new primitive we call dual witness encryption (DWE) that may be of independent interest.

We construct a four round secure multiparty computation (MPC) protocol in the plain model that achieves security against any dishonest majority. The security of our protocol relies only on the existence of four round oblivious transfer. This culminates the long line of research on constructing round-efficient MPC from minimal assumptions (at least w.r.t. black-box simulation).

Randomness is typically thought to be essential for zero knowledge protocols. Following this intuition, Goldreich and Oren (Journal of Cryptology 94) proved that auxiliary-input zero knowledge cannot be achieved with a deterministic prover. On the other hand, positive results are only known in the honest-verifier setting, or when the prover is given at least a restricted source of entropy. We prove that removing (or just bounding) the verifier's auxiliary input, deterministic-prover zero knowledge becomes feasible: - Assuming non-interactive witness-indistinguishable proofs and subexponential indistinguishability obfuscation and one-way functions, we construct deterministic-prover zero-knowledge arguments for $\NP\cap \coNP$ against verifiers with bounded non-uniform auxiliary input. - Assuming also keyless hash functions that are collision-resistant against bounded-auxiliary-input quasipolynomial-time attackers, we construct similar arguments for all of $\NP$. Together with the result of Goldreich and Oren, this characterizes when deterministic-prover zero knowledge is feasible. We also demonstrate the necessity of strong assumptions, by showing that deterministic prover zero knowledge arguments for a given language imply witness encryption for that language. We further prove that such arguments can always be collapsed to two messages and be made laconic. These implications rely on a more general connection with the notion of predictable arguments by Faonio, Nielsen, and Venturi (PKC 17).

Reducing the rounds of interaction in secure multiparty computation (MPC) protocols has been the topic of study of many works. One popular approach to reduce rounds is to construct {\em round compression compilers}. A round compression compiler is one that takes a highly interactive protocol and transforms it into a protocol with far fewer rounds. The design of round compression compilers has traditionally focused on preserving the security properties of the underlying protocol and in particular, not much attention has been given towards preserving their computational and communication efficiency. Indeed, the recent round compression compilers that yield round-optimal MPC protocols incur large computational and communication overhead. In this work, we initiate the study of {\em efficiency-preserving} round compression compilers, i.e. compilers that translate the efficiency benefits of the underlying highly interactive protocols to the fewer round setting. Focusing on the honest majority setting (with near-optimal corruption threshold $\frac{1}{2} - \varepsilon$, for any $\varepsilon > 0$), we devise a new compiler that yields two round (i.e., round optimal) semi-honest MPC with similar communication efficiency as the underlying (arbitrary round) protocol. By applying our compiler on the most efficient known MPC protocols, we obtain a two-round semi-honest protocol based on one-way functions, with total communication (and per-party computation) cost $\widetilde{O}(s+n^4)$ -- a significant improvement over prior two-round protocols with cost $\widetilde{O}(n^\tau s+n^{\tau+1}d)$, where $\tau\geq 2$, $s$ is the size of the circuit computing the function and $d$ the corresponding depth. Our result can also be extended to handle malicious adversaries, either using stronger assumptions in the public key infrastructure (PKI) model, or in the plain model using an extra round. An artifact of our approach is that the resultant protocol is ``unbalanced'' in the amount of computation performed by different parties. We give evidence that this is {\em necessary} in our setting. Our impossibility result makes novel use of the ``MPC-in-the-head" paradigm which has typically been used to demonstrate feasibility results.

We study the foundations of secure computation in the blockchain-hybrid model, where a blockchain – modeled as a global functionality – is available as an Oracle to all the participants of a cryptographic protocol. We demonstrate both destructive and constructive applications of blockchains:We show that classical rewinding-based simulation techniques used in many security proofs fail against blockchain-active adversaries that have read and post access to a global blockchain. In particular, we show that zero-knowledge (ZK) proofs with black-box simulation are impossible against blockchain-active adversaries.Nevertheless, we show that achieving security against blockchain-active adversaries is possible if the honest parties are also blockchain active. We construct an $$\omega (1)$$-round ZK protocol with black-box simulation. We show that this result is tight by proving the impossibility of constant-round ZK with black-box simulation.Finally, we demonstrate a novel application of blockchains to overcome the known impossibility results for concurrent secure computation in the plain model. We construct a concurrent self-composable secure computation protocol for general functionalities in the blockchain-hybrid model based on standard cryptographic assumptions. We develop a suite of techniques for constructing secure protocols in the blockchain-hybrid model that we hope will find applications to future research in this area.

We provide the first constructions of two round information-theoretic (IT) secure multiparty computation (MPC) protocols in the plain model that tolerate any $$t<n/2$$t<n/2 malicious corruptions. Our protocols satisfy the strongest achievable standard notions of security in two rounds in different communication models.Previously, IT-MPC protocols in the plain model either required a larger number of rounds, or a smaller minority of corruptions.

We study the exact round complexity of secure multiparty computation (MPC) in the honest majority setting. We construct several round-optimaln-party protocols, tolerating any $$t<\frac{n}{2}$$ corruptions. 1.Security with abort: We give the first construction of two round MPC for general functions that achieves security with abort against malicious adversaries in the plain model. The security of our protocol only relies on one-way functions.2.Guaranteed output delivery: We also construct protocols that achieve security with guaranteed output delivery: (i) Against fail-stop adversaries, we construct two round MPC either in the (bare) public-key infrastructure model with no additional assumptions, or in the plain model assuming two-round semi-honest oblivious transfer. In three rounds, however, we can achieve security assuming only one-way functions. (ii) Against malicious adversaries, we construct three round MPC in the plain model, assuming public-key encryption and Zaps.Previously, such protocols were only known based on specific learning assumptions and required the use of common reference strings. All of our results are obtained via general compilers that may be of independent interest.

ChaCha and Salsa are two software oriented stream ciphers that have attracted serious attention in academic as well as commercial domain. The most important cryptanalysis of reduced versions of these ciphers was presented by Aumasson et al. in FSE 2008. One part of their attack was to apply input difference(s) to investigate biases after a few rounds. So far there have been certain kind of limited exhaustive searches to obtain such biases. For the first time, in this paper, we show how to theoretically choose the combinations of the output bits to obtain significantly improved biases. The main idea here is to consider the multi-bit differentials as extension of suitable single-bit differentials with linear approximations, which is essentially a differential-linear attack. As we consider combinations of many output bits (for example 19 for Salsa and 21 for ChaCha), exhaustive search is not possible here. By this method we obtain very high biases for linear combinations of bits in Salsa after 6 rounds and in ChaCha after 5 rounds. These are clearly two rounds of improvement for both the ciphers over the existing works. Using these biases we obtain several significantly improved cryptanalytic results for reduced round Salsa and ChaCha that could not b obtained earlier. In fact, with our results it is now possible to cryptanalyse 6-round Salsa and 5-round ChaCha in practical time.