We present a new construction of two-party, threshold ECDSA, building on a 2017 scheme of Lindell and improving his scheme in several ways. ECDSA signing is notoriously hard to distribute securely, due to non-linearities in the signing function. Lindell's scheme uses Paillier encryption to encrypt one party's key share and handle these non-linearities homomorphically, while elegantly avoiding any expensive zero knowledge proofs over the Paillier group during the signing process. However,...

Succinct randomized encodings allow encoding the input $x$ of a time-$t$ uniform computation $M(x)$ in sub-linear time $o(t)$. The resulting encoding $\tilde{x}$ allows recovering the result of the computation $M(x)$, but hides any other information about $x$. Such encodings are known to have powerful applications such as reducing communication in MPC, bootstrapping advanced encryption schemes, and constructing time-lock puzzles. Until not long ago, the only known constructions were...

In this paper we introduce the notion of encrypted RAM delegation. In an encrypted RAM delegation scheme, the prover creates a succinct proof for a group of two input strings $x_\mathsf{pb}$ and $x_\mathsf{pr}$, where $x_\mathsf{pb}$ corresponds to a large \emph{public} input and $x_\mathsf{pr}$ is a \emph{private} input. A verifier can check correctness of computation of $\mathcal{M}$ on $(x_\mathsf{pb}, x_\mathsf{pr})$, given only the proof $\pi$ and $x_\mathsf{pb}$. We design encrypted...

Zero-knowledge Succinct Non-interactive Argument of Knowledge (zkSNARK) is a powerful cryptographic primitive, in which a prover convinces a verifier that a given statement is true without leaking any additional information. However, existing zkSNARKs suffer from high computation overhead in the proof generation. This limits the applications of zkSNARKs, such as private payments, private smart contracts, and anonymous credentials. Private delegation has become a prominent way to accelerate...

We propose a privacy-preserving multiparty search protocol using threshold-level homomorphic encryption, which we prove correct and secure to honest but curious adversaries. Unlike existing approaches, our protocol maintains a constant circuit depth. This feature enhances its suitability for practical applications involving dynamic underlying databases.

\textit{Federated Learning} (FL) is a distributed machine learning paradigm that allows multiple clients to train models collaboratively without sharing local data. Numerous works have explored security and privacy protection in FL, as well as its integration with blockchain technology. However, existing FL works still face critical issues. \romannumeral1) It is difficult to achieving \textit{poisoning robustness} and \textit{data privacy} while ensuring high \textit{model accuracy}....

Adaptor signatures (AS) extend the functionality of traditional digital signatures by enabling the generation of a pre-signature tied to an instance of a hard NP relation, which can later be turned (adapted) into a full signature upon revealing a corresponding witness. The recent work by Liu et al. [ASIACRYPT 2024] devised a generic AS scheme that can be used for any NP relation---which here we will refer to as universal adaptor signatures scheme, in short UAS---from any one-way function....

Distributed mean estimation (DME) is a fundamental and important task as it serves as a subroutine in convex optimization, aggregate statistics, and, more generally, federated learning. The inputs for distributed mean estimation (DME) are provided by clients (such as mobile devices), and these inputs often contain sensitive information. Thus, protecting privacy and mitigating the influence of malicious adversaries are critical concerns in DME. A surge of recent works has focused on building...

In many multi-round public-coin interactive proof systems, challenges in different rounds serve different roles, but a formulation that actively utilizes this aspect has not been studied extensively. In this paper, we propose new notions called critical-round special honest verifier zero-knowledge and critical-round special soundness. Our notions are simple, intuitive, easy to apply, and capture several practical multi-round proof protocols including, but not limited to, those from the...

Privacy-preserving graph analysis allows performing computations on graphs that store sensitive information while ensuring all the information about the topology of the graph, as well as data associated with the nodes and edges, remains hidden. The current work addresses this problem by designing a highly scalable framework, $\mathsf{Graphiti}$, that allows securely realising any graph algorithm. $\mathsf{Graphiti}$ relies on the technique of secure multiparty computation (MPC) to design a...

We present an asynchronous secure multi-party computation (MPC) protocol that is practically efficient. Our protocol can evaluate any arithmetic circuit with linear communication in the number of parties per multiplication gate, while relying solely on computationally lightweight cryptography such as hash function and symmetric encryption. Our protocol is optimally resilient and tolerates $t$ malicious parties among $n = 3t+1$ parties. At the technical level, we manage to apply the...

Fully asynchronous multi-party computation (AMPC) has superior robustness in realizing privacy and guaranteed output delivery (G.O.D.) against asynchronous adversaries that can arbitrarily delay communications. However, none of these protocols are truly practical, as they either have sub-optimal resilience, incur cumbersome communication cost, or suffer from an online phase with extra cryptographic overhead. The only attempting implementation---HoneyBadgerMPC (hbMPC)---merely ensures G.O.D....

Transciphering (or Hybrid-Homomorphic Encryption, HHE) is an es- tablished technique for avoiding ciphertext expansion in HE applications, saving communication and storage resources. Recently, it has also been shown to be a fundamental component in the practical construction of HE-based multi-party computation (MPC) protocols, being used both for input data and intermediary results (Smart, IMACC 2023). In these protocols, however, ciphers are used with keys that are jointly generated by...

This document provides a specification guide for the Multi-party Computation (MPC) setup ceremony for the Tokamak zk-SNARK scheme. It begins by revisiting the MMORPG protocol proposed in BGM17 for Groth16 setup generation, which leverages a random beacon to ensure public randomness. Additionally, it explores the alternative design approach presented in the ``Snarky Ceremonies" paper KMSV21, which removes the need for a random beacon. The document includes a detailed pseudocode and workflow...

The seminal work of Rabin and Ben-Or (STOC'89) showed that the problem of secure $n$-party computation can be solved for $t<n/2$ corruptions with guaranteed output delivery and statistical security. This holds in the traditional static model where the set of parties is fixed throughout the entire protocol execution. The need to better capture the dynamics of large scale and long-lived computations, where compromised parties may recover and the set of parties can change over time, has...

The Multi-Party Computation in the Head (MPCitH) paradigm has proven to be a versatile tool to design proofs of knowledge (PoK) based on variety of computationally hard problems. For instance, many post-quantum signatures have been designed from MPC based proofs combined with the Fiat-Shamir transformation. Over the years, MPCitH has evolved significantly with developments based on techniques such as threshold computing and other optimizations. Recently, Vector Oblivious Linear Evaluation...

We consider the setting of asynchronous multi-party computation (AMPC) with optimal resilience $n=3t+1$ and linear communication complexity, and employ only ``lightweight'' cryptographic primitives, such as random oracle hash. In this model, we introduce two concretely efficient AMPC protocols for a circuit with $|C|$ multiplication gates: a protocol achieving fairness with $\mathcal{O}(|C|\cdot n + n^3)$ field elements of communication, and a protocol achieving guaranteed output delivery...

Recent advances in differentially private federated learning (DPFL) algorithms have found that using correlated noise across the rounds of federated learning (DP-FTRL) yields provably and empirically better accuracy than using independent noise (DP-SGD). While DP-SGD is well-suited to federated learning with a single untrusted central server using lightweight secure aggregation protocols, secure aggregation is not conducive to implementing modern DP-FTRL techniques without assuming a trusted...

Traditional secure multiparty computation (MPC) protocols presuppose a fixed set of participants throughout the computational process. To address this limitation, Fluid MPC [CRYPTO 2021] presents a dynamic MPC model that allows parties to join or exit during circuit evaluation dynamically. However, existing dynamic MPC protocols can guarantee safety but not liveness within asynchronous networks. This paper introduces ΠAD-MPC, a fully asynchronous dynamic MPC protocol. ΠAD-MPC ensures both...

In this paper, we introduce a novel approach to Multi-Key Fully Homomorphic Encryption (MK-FHE) that enhances both efficiency and security beyond the capabilities of traditional MK-FHE and MultiParty Computation (MPC) systems. Our method generates a unified key structure, enabling constant ciphertext size and constant execution time for encrypted computations, regardless of the number of participants involved. This approach addresses critical limitations such as ciphertext size expansion,...

We address the problem of detecting and punishing shareholder collusion in secret-sharing schemes. We do it in the recently proposed cryptographic model called individual cryptography (Dziembowski, Faust, and Lizurej, Crypto 2023), which assumes that there exist tasks that can be efficiently computed by a single machine but distributing this computation across multiple (mutually distrustful devices) is infeasible. Within this model, we introduce a novel primitive called secret sharing...

The MPC-in-the-Head framework has been pro- posed as a solution for Non-Interactive Zero-Knowledge Arguments of Knowledge (NIZKAoK) due to its efficient proof generation. However, most existing NIZKAoK constructions using this approach require multiple MPC evaluations to achieve negligible soundness error, resulting in proof size and time that are asymptotically at least λ times the size of the circuit of the NP relation. In this paper, we propose a novel method to eliminate the need for...

Vessels can be recognised by their navigation radar due to the characteristics of the emitted radar signal. This is particularly useful if one wants to build situational awareness without revealing one's own presence. Most countries maintain databases of radar fingerprints but will not readily share these due to national security regulations. Sharing of such information will generally require some form of information exchange agreement. However, all parties in a coalition benefit from...

We propose a new cryptographic primitive called "batched identity-based encryption" (Batched IBE) and its thresholdized version. The new primitive allows encrypting messages with specific identities and batch labels, where the latter can represent, for example, a block number on a blockchain. Given an arbitrary subset of identities for a particular batch, our primitive enables efficient issuance of a single decryption key that can be used to decrypt all ciphertexts having identities that are...

Cryptographic proof systems have a plethora of applications: from building other cryptographic tools (e.g., malicious security for MPC protocols) to concrete settings such as private transactions or rollups. In several settings it is important for proof systems to be non-malleable: an adversary should not to be able to modify a proof they have observed into another for a statement for which they do not know the witness. Proof systems that have been deployed in practice should arguably...

In this paper, we introduce a new method to construct a signature scheme based on the subfield bilinear collision problem published at Crypto 2024. We use techniques based on vector oblivious linear evaluation (VOLE) to significantly improve the running time and signature size of the scheme compared to the MPC-in-the-head version.

We present a new and efficient method to obtain circuit privacy for lattice-based linearly homomorphic encryptions (LHE). In particular, our method does not involve noise-flooding with exponetially large errors or iterative bootstrapping. As a direct result, we obtain a semi-honest oblivious linear evaluation (OLE) protocol with the same efficiency, reducing the communication cost of the prior state of the art by 50%. Consequently, the amortized time of our protocol improves the prior work...

In decentralized finance (DeFi), the public availability of pending transactions presents significant privacy concerns, enabling market manipulation through miner extractable value (MEV). MEV occurs when block proposers exploit the ability to reorder, omit, or include transactions, causing financial loss to users from frontrunning. Recent research has focused on encrypting pending transactions, hiding transaction data until block finalization. To this end, Choudhuri et al. (USENIX '24)...

The SPDZ protocol family is a popular choice for secure multi-party computation (MPC) in a dishonest majority setting with active adversaries. Over the past decade, a series of studies have focused on improving its offline phase, where special additive shares, called authenticated triples, are generated. However, to accommodate recent demands for matrix operations in secure machine learning and big integer arithmetic in distributed RSA key generation, updates to the offline phase are...

The problem of reliable/secure all-to-all communication over low-degree networks has been essential for communication-local (CL) n-party MPC (i.e., MPC protocols where every party directly communicates only with a few, typically polylogarithmic in n, parties) and more recently for communication over ad hoc networks, which are used in blockchain protocols. However, a limited number of adaptively secure solutions exist, and they all make relatively strong assumptions on the ability of parties...

In the context of secure multiparty computation (MPC) protocols with guaranteed output delivery (GOD) for the honest majority setting, the state-of-the-art in terms of communication is the work of (Goyal et al. CRYPTO'20), which communicates O(n|C|) field elements, where |C| is the size of the circuit being computed and n is the number of parties. Their round complexity, as usual in secret-sharing based MPC, is proportional to O(depth(C)), but only in the optimistic case where there is no...

We consider the graph-theoretic problem of removing (few) nodes from a directed acyclic graph in order to reduce its depth. While this problem is intractable in the general case, we provide a variety of algorithms in the case where the graph is that of a circuit of fan-in (at most) two, and explore applications of these algorithms to secure multiparty computation with low communication. Over the past few years, a paradigm for low-communication secure multiparty computation has found success...

Distributed training that enables multiple parties to jointly train a model on their respective datasets is a promising approach to address the challenges of large volumes of diverse data for training modern machine learning models. However, this approach immedi- ately raises security and privacy concerns; both about each party wishing to protect its data from other parties during training and preventing leakage of private information from the model after training through various...

We witness an increase in applications like cryptocurrency wallets, which involve users issuing signatures using private keys. To protect these keys from loss or compromise, users commonly outsource them to a custodial server. This creates a new point of failure, because compromise of such a server leaks the user’s key, and if user authentication is implemented with a password then this password becomes open to an offline dictionary attack (ODA). A better solution is to secret-share the key...

In this work, we study constant round multiparty computation (MPC) for Boolean circuits against a fully malicious adversary who may control up to $n-1$ out of $n$ parties. Without relying on fully homomorphic encryption (FHE), the best-known results in this setting are achieved by Wang et al. (CCS 2017) and Hazay et al. (ASIACRYPT 2017) based on garbled circuits, which require a quadratic communication in the number of parties $O(|C|\cdot n^2)$. In contrast, for non-constant round MPC, the...

Many of the currently best actively secure Multi-Party Computation (MPC) protocols like SPDZ (Damgård et al., CRYPTO 2012) and improvements thereof use correlated randomness to speed up the time-critical online phase. Although many of these protocols still rely on classical Beaver triples, recent results show that more complex correlations like matrix or convolution triples lead to more efficient evaluations of the corresponding operations, i.e. matrix multiplications or tensor convolutions....

Secure Multi-party Computation (MPC) provides a promising solution for privacy-preserving multi-source data analytics. However, existing MPC-based collaborative analytics systems (MCASs) have unsatisfying performance for scenarios with dynamic databases. Naively running an MCAS on a dynamic database would lead to significant redundant costs and raise performance concerns, due to the substantial duplicate contents between the pre-updating and post-updating databases. In this paper, we...

Garbled circuits are a powerful and important cryptographic primitive, introduced by Yao [FOCS 1986] for secure two-party computation. Beaver, Micali and Rogaway (BMR) [STOCS 1990] extended the garbled circuit technique to construct the first constant-round secure multiparty computation (MPC) protocol. In the BMR protocol, the garbled circuit size grows linearly and the online computation time grows quadratically with the number of parties. Previous solutions to avoid this relied on...

Zero-Knowledge (ZK) protocols allow a prover to demonstrate the truth of a statement without disclosing additional information about the underlying witness. Code-based cryptography has a long history but did suffer from periods of slow development. Recently, a prominent line of research have been contributing to designing efficient code-based ZK from MPC-in-the-head (Ishai et al., STOC 2007) and VOLE-in-the head (VOLEitH) (Baum et al., Crypto 2023) paradigms, resulting in quite efficient...

Multiparty computation (MPC) is an important field of cryptography that deals with protecting the privacy of data, while allowing to do computation on that data. A key part of MPC is the parties involved having correlated randomness that they can use to make the computation or the communication between themselves more efficient, while still preserving the privacy of the data. Examples of these correlations include random oblivious transfer (OT) correlations, oblivious linear-function...

Achieving malicious security with high efficiency in dishonest-majority secure multiparty computation is a formidable challenge. The milestone works SPDZ and TinyOT have spawn a large family of protocols in this direction. For boolean circuits, state-of-the-art works (Cascudo et. al, TCC 2020 and Escudero et. al, CRYPTO 2022) have proposed schemes based on reverse multiplication-friendly embedding (RMFE) to reduce the amortized cost. However, these protocols are theoretically described and...

Privacy-Preserving Machine Learning is one of the most relevant use cases for Secure Multiparty Computation (MPC). While private training of large neural networks such as VGG-16 or ResNet-50 on state-of-the-art datasets such as Imagenet is still out of reach, given the performance overhead of MPC, private inference is starting to achieve practical runtimes. However, we show that in contrast to plaintext machine learning, the usage of GPU acceleration for both linear and nonlinear neural...

Secure multiparty computation (MPC) protocols enable $n$ parties, each with private inputs, to compute a given function without leaking information beyond the outputs. One of the main approaches to designing efficient MPC protocols is to use secret sharing. In general, secret sharing based MPC contains three phases: input sharing, circuit evaluation, and output recovery. If the adversary corrupts at most $t$ parties, the protocol typically uses $(t,n)$ threshold secret sharing to share the...

Secure multi-party computation (MPC) enables multiple distrusting parties to jointly compute a function while keeping their inputs private. Computing the AES block cipher in MPC, where the key and/or the input are secret-shared among the parties is important for various applications, particularly threshold cryptography. In this work, we propose a family of dedicated, high-performance MPC protocols to compute the non-linear S-box part of AES in the honest majority setting. Our protocols...

In the last fifteen years, there has been a steady stream of works combining differential privacy with various other cryptographic disciplines, particularly that of multi-party computation, yielding both practical and theoretical unification. As a part of that unification, due to the rich definitional nature of both fields, there have been many proposed definitions of differential privacy adapted to the given use cases and cryptographic tools at hand, resulting in computational and/or...

We consider protocols for secure multi-party computation (MPC) built from FHE under honest majority, i.e., for $n=2t+1$ players of which $t$ are corrupt, that are robust. Surprisingly there exists no robust threshold FHE scheme based on BFV to design such MPC protocols. Precisely, all existing methods for generating a common relinearization key can abort as soon as one player deviates. We address this issue, with a new relinearization key (adapted from [CDKS19, CCS'19]) which we show how to...

Passwords are widely adopted for user authentication in practice, which led to the question of whether we can bootstrap a strongly-secure setting based on them. Historically, this has been extensively studied for key exchange; bootstrap from a low-entropy password to a high entropy key securing the communication. Other instances include digital lockers, signatures, secret sharing, and encryption. Motivated by a recent work on consumable tokens (Almashaqbeh et al., Eurocrypt 2022), we...

The recent VOLE-based interactive zero-knowledge (VOLE-ZK) protocols along with non-interactive zero-knowledge (NIZK) proofs based on MPC-in-the-Head (MPCitH) and VOLE-in-the-Head (VOLEitH) extensively utilize the commitment schemes, which adopt a circular correlation robust (CCR) hash function as the core primitive. Nevertheless, the state-of-the-art CCR hash construction by Guo et al. (S&P'20), building from random permutations, can only provide 128-bit security, when it is instantiated...

Non-interactive zero-knowledge (NIZK) proofs of knowledge have proven to be highly relevant for securely realizing a wide array of applications that rely on both privacy and correctness. They enable a prover to convince any party of the correctness of a public statement for a secret witness. However, most NIZKs do not natively support proving knowledge of a secret witness that is distributed over multiple provers. Previously, collaborative proofs [51] have been proposed to overcome this...

Bottleneck complexity is an efficiency measure of secure multiparty computation (MPC) protocols introduced to achieve load-balancing in large-scale networks, which is defined as the maximum communication complexity required by any one player within the protocol execution. Towards the goal of achieving low bottleneck complexity, prior works proposed MPC protocols for computing symmetric functions in the correlated randomness model, where players are given input-independent correlated...

Model quantization has become a common practice in machine learning (ML) to improve efficiency and reduce computational/communicational overhead. However, adopting quantization in privacy-preserving machine learning (PPML) remains challenging due to the complex internal structure of quantized operators, which leads to inefficient protocols under the existing PPML frameworks. In this work, we propose a new PPML paradigm that is tailor-made for and can benefit from quantized models. Our...

Recent advancements in transformers have revolutionized machine learning, forming the core of Large language models (LLMs). However, integrating these systems into everyday applications raises privacy concerns as client queries are exposed to model owners. Secure multiparty computation (MPC) allows parties to evaluate machine learning applications while keeping sensitive user inputs and proprietary models private. Due to inherent MPC costs, recent works introduce model-specific optimizations...

Oblivious transfer (OT) is a fundamental cryptographic protocol that plays a crucial role in secure multi-party computation (MPC). Most practical OT protocols by, e.g., Naor and Pinkas (SODA'01) or Chou and Orlandi (Latincrypt'15), are based on Diffie-Hellman (DH)-like assumptions and not post-quantum secure. In contrast, many other components of MPC protocols, including garbled circuits and secret sharings, are post-quantum secure. The reliance on non-post-quantum OT protocols presents a...

Proving the security of a Multiparty Computation (MPC) protocol is a difficult task. Under the current simulation-based definition of MPC, a security proof consists of a simulator, which is usually specific to the concrete protocol and requires to be manually constructed, together with a theoretical analysis of the output distribution of the simulator and corrupted parties' views in the real world. This presents an obstacle in verifying the security of a given MPC protocol. Moreover, an...

Decision trees are an important class of supervised learning algorithms. When multiple entities contribute data to train a decision tree (e.g. for fraud detection in the financial sector), data privacy concerns necessitate the use of a privacy-enhancing technology such as secure multi-party computation (MPC) in order to secure the underlying training data. Prior state-of-the-art (Hamada et al.) construct an MPC protocol for decision tree training with a communication of $\mathcal{O}(hmN\log...

NIST started the standardization of additional post-quantum signatures in 2022. Among 40 candidates, a few of them showed their stronger security than existential unforgeability, strong existential unforgeability and BUFF (beyond unforgeability features) securities. Recently, Aulbach, Düzlü, Meyer, Struck, and Weishäupl (PQCrypto 2024) examined the BUFF securities of 17 out of 40 candidates. Unfortunately, on the so-called MPC-in-the-Head (MPCitH) signature schemes, we have no knowledge of...

A threshold signature scheme distributes the ability to generate signatures through distributed key generation and signing protocols. A threshold signature scheme should be functionally interchangeable, meaning that a signature produced by a threshold scheme should be verifiable by the same algorithm used for non-threshold signatures. To resist future attacks from quantum adversaries, lattice-based threshold signatures are desirable. However, the performance of existing lattice-based...

Researchers across various fields seek to understand causal relationships but often find controlled experiments impractical. To address this, statistical tools for causal discovery from naturally observed data have become crucial. Non-linear regression models, such as Gaussian process regression, are commonly used in causal inference but have limitations due to high costs when adapted for secure computation. Support vector regression (SVR) offers an alternative but remains costly in an...

We develop a distributed service for generating correlated randomness (e.g. permutations) for multiple parties, where each party’s output is private but publicly verifiable. This service provides users with a low-cost way to play online poker in real-time, without a trusted party. Our service is backed by a committee of compute providers, who run a multi-party computation (MPC) protocol to produce an (identity-based) encrypted permutation of a deck of cards, in an offline phase well ahead...

The problem of minimizing the share size of threshold secret-sharing schemes is a basic research question that has been extensively studied. Ideally, one strives for schemes in which the share size equals the secret size. While this is achievable for large secrets (Shamir, CACM '79), no similar solutions are known for the case of binary, single-bit secrets. Current approaches often rely on so-called ramp secret sharing that achieves a constant share size at the expense of a slight gap...

Secure merge refers to the problem of merging two sorted lists. The problem appears in different settings where each list is held by one of two parties, or the lists are themselves shared among two or more parties. The output of a secure merge protocol is secret shared. Each variant of the problem offers many useful applications. The difficulty in designing secure merge protocols vis-a-vis insecure merge protocols (which work in linear time with a single pass over the lists) has to do...

Machine learning is widely used for a range of applications and is increasingly offered as a service by major technology companies. However, the required massive data collection raises privacy concerns during both training and inference. Privacy-preserving machine learning aims to solve this problem. In this setting, a collection of servers secret share their data and use secure multi-party computation to train and evaluate models on the joint data. All prior work focused on the scenario...

An oblivious pseudorandom function (OPRF) is a two-party protocol in which a party holds an input and the other party holds the PRF key, such that the party having the input only learns the PRF output and the party having the key would not learn the input. Now, in a threshold oblivious pseudorandom function (TOPRF) protocol, a PRF key K is initially shared among T servers. A client can obtain a PRF value by interacting with t(≤ T) servers but is unable to compute the same with up to (t − 1)...

Secure multi-party computation (MPC) in a three-party, honest majority scenario is currently the state-of-the-art for running machine learning algorithms in a privacy-preserving manner. For efficiency reasons, fixed-point arithmetic is widely used to approximate computation over decimal numbers. After multiplication in fixed-point arithmetic, truncation is required to keep the result's precision. In this paper, we present an efficient three-party truncation protocol secure in the presence of...

Neural network inference as a service enables a cloud server to provide inference services to clients. To ensure the privacy of both the cloud server's model and the client's data, secure neural network inference is essential. Binarized neural networks (BNNs), which use binary weights and activations, are often employed to accelerate inference. However, achieving secure BNN inference with secure multi-party computation (MPC) is challenging because MPC protocols cannot directly operate on...

MPC-in-the-Head (MPCitH) has recently gained traction as a foundation for post-quantum signature schemes, offering robust security without trapdoors. Despite its strong security profile, MPCitH-based schemes suffer from high computational overhead and large signature sizes, limiting their practical application. This work addresses these inefficiencies by relaxing vector commitments within MPCitH-based schemes. We introduce the concept of vector semi-commitment, which relaxes the binding...

We study network-agnostic secure multiparty computation with perfect security. Traditionally MPC is studied assuming the underlying network is either synchronous or asynchronous. In a network-agnostic setting, the parties are unaware of whether the underlying network is synchronous or asynchronous. The feasibility of perfectly-secure MPC in synchronous and asynchronous networks has been settled a long ago. The landmark work of [Ben-Or, Goldwasser, and Wigderson, STOC'88] shows that $n...

Given a graph $G(V,E)$, represented as a secret-sharing of an adjacency list, we show how to obliviously convert it into an alternative, MPC-friendly secret-shared representation, so-called $d$-normalized replicated adjacency list (which we abbreviate to $d$-normalized), where the size of our new data-structure is only 4x larger -- compared to the original (secret-shared adjacency list) representation of $G$. Yet, this new data structure enables us to execute oblivious graph algorithms that...

Multi-party computation (\textsf{MPC}) is a major research interest in modern cryptography, and Privacy Set Intersection (\textsf{PSI}) is an important research topic within \textsf{MPC}. Its main function is to allow two parties to compute the intersection of their private sets without revealing any other information. Therefore, \textsf{PSI} can be applied to various real-world scenarios, such as the Industrial Internet of Things (\textsf{IIOT}). Chase and Miao presented a paper on...

Key blinding produces pseudonymous digital identities by rerandomizing public keys of a digital signature scheme. It is used in anonymous networks to provide the seemingly contradictory goals of anonymity and authentication. Current key blinding schemes are based on the discrete log assumption. Eaton, Stebila and Stracovsky (LATINCRYPT 2021) proposed the first key blinding schemes from lattice assumptions. However, the large public keys and lack of QROM security means they are not ready to...

Collaborative zk-SNARK (USENIX'22) allows multiple parties to jointly create a zk-SNARK proof over distributed secrets (also known as the witness). It provides a promising approach to proof outsourcing, where a client wishes to delegate the tedious task of proof generation to many servers from different locations, while ensuring no corrupted server can learn its witness (USENIX'23). Unfortunately, existing work remains a significant efficiency problem, as the protocols rely heavily on a...

A popular way to build post-quantum signature schemes is by first constructing an identification scheme (IDS) and applying the Fiat-Shamir transform to it. In this work we tackle two open questions related to the general applicability of techniques around this approach that together allow for efficient post-quantum signatures with optimal security bounds in the QROM. First we consider a recent work by Aguilar-Melchor, Hülsing, Joseph, Majenz, Ronen, and Yue (Asiacrypt'23) that showed...

The rapid development of advanced cryptographic applications like multi-party computation (MPC), fully homomorphic encryption (FHE), and zero-knowledge (ZK) proofs have motivated the designs of the so-called arithmetic-oriented (AO) primitives. Efficient AO primitives typically build over large fields and use large S-boxes. Such design philosophy brings difficulties in the cryptanalysis of these primitives as classical cryptanalysis methods do not apply well. The generally recognized attacks...

In the *Distributed Secret Sharing Generation* (DSG) problem $n$ parties wish to obliviously sample a secret-sharing of a random value $s$ taken from some finite field, without letting any of the parties learn $s$. *Distributed Key Generation* (DKG) is a closely related variant of the problem in which, in addition to their private shares, the parties also generate a public ``commitment'' $g^s$ to the secret. Both DSG and DKG are central primitives in the domain of secure multiparty...

We design and implement a novel post-quantum signature scheme based on the Legendre PRF, named Loquat. Prior to this work, efficient approaches for constructing post-quantum signatures with comparable security assumptions mainly used the MPC-in-the-head paradigm or hash trees. Our method departs from these paradigms and, notably, is SNARK-friendly, a feature not commonly found in earlier designs. Loquat requires significantly fewer computational operations for verification than other...

We revisit the question of the overhead to achieve full security (i.e., guaranteed output delivery) in secure multiparty computation (MPC). Recent works have closed the gap between full security and semi-honest security, by introducing protocols where the parties first compute the circuit using a semi-honest protocol and then run a verification step with sublinear communication in the circuit size. However, in these works the number of interaction rounds in the verification step is also...

This work introduces homomorphic secret sharing (HSS) with succinct share size. In HSS, private inputs are shared between parties, who can then homomorphically evaluate a function on their shares, obtaining a share of the function output. In succinct HSS, a portion of the inputs can be distributed using shares whose size is sublinear in the number of such inputs. The parties can then locally evaluate a function $f$ on the shares, with the restriction that $f$ must be linear in the succinctly...

Keeping decrypting parties accountable in public key encryption is notoriously hard since the secret key owner can decrypt any arbitrary ciphertext. Threshold encryption aims to solve this issue by distributing the power to decrypt among a set of parties, who must interact via a decryption protocol. However, such parties can employ cryptographic tools such as Multiparty Computation (MPC) to decrypt arbitrary ciphertexts without being detected. We introduce the notion of (threshold)...

In this work we introduce PERK a compact digital signature scheme based on the hardness of a new variant of the Permuted Kernel Problem (PKP). PERK achieves the smallest signature sizes for any PKP-based scheme for NIST category I security with 6 kB, while obtaining competitive signing and verification timings. PERK also compares well with the general state-of-the-art. To substantiate those claims we provide an optimized constant-time AVX2 implementation, a detailed performance analysis and...

We design a new MPC protocol for arithmetic circuits secure against erasure-free covert adaptive adversaries with deterrence 1/2. The new MPC protocol has the same asymptotic communication cost, the number of PKE operations and the number of exponentiation operations as the most efficient MPC protocol for arithmetic circuits secure against covert static adversaries. That means, the new MPC protocol improves security from covert static security to covert adaptive adversary almost for free....

In this work we tackle privacy concerns in biometric verification systems that typically require server-side processing of sensitive data (e.g., fingerprints and Iris Codes). Concretely, we design a solution that allows us to query whether a given Iris Code is similar to one contained in a given database, while all queries and datasets are being protected using secure multiparty computation (MPC). Addressing the substantial performance demands of operational systems like World ID and aid...

Multiple works have designed or used maliciously secure honest majority MPC protocols over $\mathbb{Z}_{2^k}$ using replicated secret sharing (e.g. Koti et al. USENIX'21). A recent trend in the design of such MPC protocols is to first execute a semi-honest protocol, and then use a check that verifies the correctness of the computation requiring only sublinear amount of communication in terms of the circuit size. The so-called Galois ring extensions are needed in order to execute such checks...

Private information retrieval (PIR) is a fundamental cryptographic primitive that allows a user to fetch a database entry without revealing to the server which database entry it learns. PIR becomes non-trivial if the server communication is less than the database size. We show that building (even) very weak forms of single-server PIR protocols, without pre-processing, requires the number of public-key operations to scale linearly in the database size. This holds irrespective of the number of...

Group signatures and their variants have been widely used in privacy-sensitive scenarios such as anonymous authentication and attestation. In this paper, we present a new post-quantum group signature scheme from symmetric primitives. Using only symmetric primitives makes the scheme less prone to unknown attacks than basing the design on newly proposed hard problems whose security is less well-understood. However, symmetric primitives do not have rich algebraic properties, and this makes it...

A Verifiable Random Function (VRF) can be evaluated on an input by a prover who holds a secret key, generating a pseudorandom output and a proof of output validity that can be verified using the corresponding public key. VRFs are a central building block of committee election mechanisms that sample parties to execute tasks in cryptographic protocols, e.g. generating blocks in a Proof-of-Stake (PoS) blockchain or executing a round of MPC protocols. We propose the notion, and a matching...

We revisit the alternating-moduli paradigm for constructing symmetric-key primitives with a focus on constructing efficient protocols to evaluate them using secure multi-party computation (MPC). The alternating-moduli paradigm of Boneh, Ishai, Passelègue, Sahai, and Wu (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. The first contribution focuses on...

Private set intersection (PSI) allows two parties to compute the intersection of their sets without revealing anything else. In some applications of PSI, a server holds a large set and runs a PSI protocol with multiple clients, each with its own smaller set. In this setting, existing protocols fall short: they either achieve only semi-honest security, or else require the server to run the protocol from scratch for each execution. We design an efficient protocol for this setting with...

Despite much progress, general-purpose secure multi-party computation (MPC) with active security may still be prohibitively expensive in settings with large input datasets. This particularly applies to the secure evaluation of graph algorithms, where each party holds a subset of a large graph. Recently, Araki et al. (ACM CCS '21) showed that dedicated solutions may provide significantly better efficiency if the input graph is sparse. In particular, they provide an efficient protocol for...

Private set intersection (PSI) is a cryptographic functionality for two parties to learn the intersection of their input sets, without leaking any other information. Circuit-PSI is a stronger PSI functionality where the parties learn only a secret-shared form of the desired intersection, thus without revealing the intersection directly. These secret shares can subsequently serve as input to a secure multiparty computation of any function on this intersection. In this paper we consider...

Running machine learning algorithms on encrypted data is a way forward to marry functionality needs common in industry with the important concerns for privacy when working with potentially sensitive data. While there is already a growing field on this topic and a variety of protocols, mostly employing fully homomorphic encryption or performing secure multiparty computation (MPC), we are the first to propose a protocol that makes use of a specialized encryption scheme that allows to do secure...

In this work we formalize the notion of a two-party permutation correlation $(A, B), (C, \pi)$ s.t. $\pi(A)=B+C$ for a random permutation $\pi$ of $n$ elements and vectors $A,B,C\in \mathbb{F}^n$. This correlation can be viewed as an abstraction and generalization of the Chase et al. (Asiacrypt 2020) share translation protocol. We give a systematization of knowledge for how such a permutation correlation can be derandomized to allow the parties to perform a wide range of oblivious...

A distributed OPRF allows a client to evaluate a pseudorandom function on an input chosen by the client using a distributed key shared among multiple servers. This primitive ensures that the servers learn nothing about the input nor the output, and the client learns nothing about the key. We present a post-quantum OPRF in a distributed server setting, which can be computed in a single round of communication between a client and the servers. The only server-to-server communication occurs...

The MPC-in-the-Head (MPCitH) paradigm is widely used for building post-quantum signature schemes, as it provides a versatile way to design proofs of knowledge based on hard problems. Over the years, the MPCitH landscape has changed significantly, with the most recent improvements coming from VOLE-in-the-Head (VOLEitH) and Threshold-Computation-in-the-Head (TCitH). While a straightforward application of these frameworks already improve the existing MPCitH-based signatures, we show in...

With the growing adoption of cloud computing, the ability to store data and delegate computations to powerful and affordable cloud servers have become advantageous for both companies and individual users. However, the security of cloud computing has emerged as a significant concern. Particularly, Cloud Service Providers (CSPs) cannot assure data confidentiality and computations integrity in mission-critical applications. In this paper, we propose a confidential and verifiable delegation...

The Gradient Boosting Decision Tree (GBDT) is a well-known machine learning algorithm, which achieves high performance and outstanding interpretability in real-world scenes such as fraud detection, online marketing and risk management. Meanwhile, two data owners can jointly train a GBDT model without disclosing their private dataset by executing secure Multi-Party Computation (MPC) protocols. In this work, we propose NodeGuard, a highly efficient two party computation (2PC) framework for...

In recent years, there has been tremendous progress in improving the communication complexity of dishonest majority MPC. In the sub-optimal corruption threshold setting, where $t<(1-\varepsilon)\cdot n$ for some constant $0<\varepsilon\leq 1/2$, the recent works Sharing Transformation (Goyal $\textit{et al.}$, CRYPTO'22) and SuperPack (Escudero $\textit{et al.}$, EUROCRYPT'23) presented protocols with information-theoretic online phases achieving $O(1)$ communication per multiplication gate,...

The use of MPC-in-the-Head (MPCitH)-based zero-knowledge proofs of knowledge (ZKPoK) to prove knowledge of a preimage of a one-way function (OWF) is a popular approach towards constructing efficient post-quantum digital signatures. Starting with the Picnic signature scheme, many optimized MPCitH signatures using a variety of (candidate) OWFs have been proposed. Recently, Baum et al. (CRYPTO 2023) showed a fundamental improvement to MPCitH, called VOLE-in-the-Head (VOLEitH), which can...

The VOLE-in-the-Head paradigm, recently introduced by Baum et al. (Crypto 2023), is a compiler that uses SoftspokenOT (Crypto 2022) to transfer any VOLE-based designated verifier zero-knowledge protocol into a publicly verifiable zero-knowledge protocol. Together with the Fiat-Shamir transformation, a new digital signature scheme FAEST (faest.info) is proposed, and it outperforms all MPC-in-the-Head signatures. We propose a new candidate post-quantum signature scheme from the Multivariate...

We study secure multiparty computation in the asynchronous setting with perfect security and optimal resilience (less than one-fourth of the participants are malicious). It has been shown that every function can be computed in this model [Ben-OR, Canetti, and Goldreich, STOC'1993]. Despite 30 years of research, all protocols in the asynchronous setting require $\Omega(n^2C)$ communication complexity for computing a circuit with $C$ multiplication gates. In contrast, for nearly 15 years, in...

Secure Multi-party Computation (MPC) allows two or more parties to compute any public function over their privately-held inputs, without revealing any information beyond the result of the computation. Modern protocols for MPC generate a large amount of input-independent preprocessing material called multiplication triples, in an offline phase. This preprocessing can later be used by the parties to efficiently instantiate an input-dependent online phase computing the function. To date, the...