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,...

Secure aggregation is the distributed task of securely computing a sum of values (or a vector of values) held by a set of parties, revealing only the output (i.e., the sum) in the computation. Existing protocols, such as Prio (NDSI’17), Prio+ (SCN’22), Elsa (S&P’23), and Whisper (S&P’24), support secure aggregation with input validation to ensure inputs belong to a specified domain. However, when malicious servers are present, these protocols primarily guarantee privacy but not input...

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...

\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}....

Aaronson, Atia, and Susskind [Aaronson et al., 2020] established that efficiently mapping between quantum states $\ket{\psi}$ and $\ket{\phi}$ is computationally equivalent to distinguishing their superpositions $\frac{1}{\sqrt{2}}(|\psi\rangle + |\phi\rangle)$ and $\frac{1}{\sqrt{2}}(|\psi\rangle - |\phi\rangle)$. We generalize this insight into a broader duality principle in quantum computation, wherein manipulating quantum states in one basis is equivalent to extracting their value in a...

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...

Falcon is a winner of NIST's six-year post-quantum cryptography standardisation competition. Based on the celebrated full-domain-hash framework of Gentry, Peikert and Vaikuntanathan (GPV) (STOC'08), Falcon leverages NTRU lattices to achieve the most compact signatures among lattice-based schemes. Its security hinges on a Rényi divergence-based argument for Gaussian samplers, a core element of the scheme. However, the GPV proof, which uses statistical distance to argue closeness of...

Cloud storage offers convenient data access and sharing, but security concerns remain. Existing secure cloud storage solutions often lack essential features like data integrity, multi-cloud support, user-friendly file sharing, and efficient search. This paper proposes a novel secure cloud storage system that addresses these limitations. Our system uses distributed storage and attribute-based encryption to enhance data availability, access control, and user experience. It also enables private...

Random classical codes have good error correcting properties, and yet they are notoriously hard to decode in practice. Despite many decades of extensive study, the fastest known algorithms still run in exponential time. The Learning Parity with Noise (LPN) problem, which can be seen as the task of decoding a random linear code in the presence of noise, has thus emerged as a prominent hardness assumption with numerous applications in both cryptography and learning theory. Is there a...

Evaluation of cryptographic implementations with respect to side-channels has been mandated at high security levels nowadays. Typically, the evaluation involves four stages: detection, modeling, certification and secret recovery. In pursuit of specific goal at each stage, inherently different techniques used to be considered necessary. However, since the recent works of Eurocrypt2022 and Eurocrypt2024, linear regression analysis (LRA) has uniquely become the technique that is well-applied...

Proof-Carrying Data (PCD) is a foundational tool for ensuring the correctness of incremental distributed computations that has found numerous applications in theory and practice. The state-of-the-art PCD constructions are obtained via accumulation or folding schemes. Unfortunately, almost all known constructions of accumulation schemes rely on homomorphic vector commitments (VCs), which results in relatively high computational costs and insecurity in the face of quantum adversaries. A recent...

Non-interactive zero-knowledge proofs (NIZK) are essential building blocks in threshold cryptosystems like multiparty signatures, distributed key generation, and verifiable secret sharing, allowing parties to prove correct behavior without revealing secrets. Furthermore, universally composable (UC) NIZKs enable seamless composition in the larger cryptosystems. A popular way to construct NIZKs is to compile interactive protocols using the Fiat-Shamir transform. Unfortunately, Fiat-Shamir...

We reconsider Cleve's famous 1986 impossibility result on coin-flipping without an honest majority. Recently proposed constructions have circumvented this limit by using cryptographic delay functions. We show that this is necessary: a (weak) notion of delay functions is in fact implied by the existence of a protocol circumventing Cleve's impossibility. However, such delay functions are weaker than those used in existing constructions. We complete our result by showing an equivalence, that...

We construct a quantum oracle relative to which $\mathbf{BQP}=\mathbf{QCMA}$ but quantum-computation-classical-communication (QCCC) key exchange, QCCC commitments, and two-round quantum key distribution exist. We also construct an oracle relative to which $\mathbf{BQP}=\mathbf{QMA}$, but quantum lightning (a stronger variant of quantum money) exists. This extends previous work by Kretschmer [Kretschmer, TQC22], which showed that there is a quantum oracle relative to which...

This work conducts a comprehensive investigation on determining the entropic hardness of (R/M)LWR under polynomial modulus. Particularly, we establish the hardness of (M)LWR for general entropic secret distributions from (Module) LWE assumptions based on a new conceptually simple framework called rounding lossiness. By combining this hardness result and a trapdoor inversion algorithm with asymptotically the most compact parameters, we obtain a compact lossy trapdoor function (LTF) with...

The Leftover Hash Lemma (LHL) is a powerful tool for extracting randomness from an entropic distribution, with numerous applications in cryptography. LHLs for discrete Gaussians have been explored in both integer settings by Gentry et al. (GPV, STOC'08) and algebraic ring settings by Lyubashevsky et al. (LPR, Eurocrypt'13). However, the existing LHLs for discrete Gaussians have two main limitations: they require the Gaussian parameter to be larger than certain smoothing parameters, and they...

Multi-valued validated Byzantine agreement (MVBA), a fundamental primitive of distributed computing, enables $n$ processes to agree on a valid $\ell$-bit value, despite $t$ faulty processes behaving arbitrarily. Among hash-based protocols for the asynchronous setting with adaptive faults, the state-of-the-art HMVBA protocol has optimal $O(1)$ time complexity and near-optimal $O(n \ell + n^2 \kappa \log n)$ bit complexity, but tolerates only $t < n/5$ faults. We present REDUCER, an MVBA...

Federated Learning (FL) has gained lots of traction recently, both in industry and academia. In FL, a machine learning model is trained using data from various end-users arranged in committees across several rounds. Since such data can often be sensitive, a primary challenge in FL is providing privacy while still retaining utility of the model. Differential Privacy (DP) has become the main measure of privacy in the FL setting. DP comes in two flavors: central and local. In the former, a...

This paper addresses verifiable consensus of pre-processed circuit polynomials for succinct non-interactive argument of knowledge (SNARK). More specifically, we focus on parts of circuits, referred to as wire maps, which may change based on program inputs or statements being argued. Preparing commitments to wire maps in advance is essential for certain SNARK protocols to maintain their succinctness, but it can be costly. SNARK verifiers can alternatively consider receiving wire maps from an...

Distributed point functions (DPF) are increasingly becoming a foundational tool with applications for application-specific and general secure computation. While two-party DPF constructions are readily available for those applications with satisfiable performance, the three-party ones are left behind in both security and efficiency. In this paper we close this gap and propose the first three-party DPF construction that matches the state-of-the-art two-party DPF on all metrics. Namely, it...

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...

For Password-Based Authenticated Key Exchange (PAKE), an idealized setup such as random oracle (RO) or a trusted setup such as common reference string (CRS) is a must in the universal composability (UC) framework (Canetti, FOCS 2001). Given the potential failure of a CRS or RO setup, it is natural to consider distributing trust among the two setups, resulting a CRS-or-RO-setup (i.e., CoR-setup). However, the infeasibility highlighted by Katz et al. (PODC 2014) suggested that it is...

Cryptographic group actions are a leading contender for post-quantum cryptography, and have also been used in the development of quantum cryptographic protocols. In this work, we explore quantum group actions, which consist of a group acting on a set of quantum states. We show the following results: 1. In certain settings, statistical (even query bounded) security is impossible, analogously to post-quantum classical group actions. 2. We construct quantum state group actions and prove that...

Threshold signatures are one of the most important cryptographic primitives in distributed systems. The threshold Schnorr signature scheme, an efficient and pairing-free scheme, is a popular choice and is included in NIST's standards and recent call for threshold cryptography. Despite its importance, most threshold Schnorr signature schemes assume a static adversary in their security proof. A recent scheme proposed by Katsumata et al. (Crypto 2024) addresses this issue. However, it requires...

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...

We describe a fully distributed KZG-based Snark instantiable with any pairing-friendly curve with a sufficiently large scalar field. In particular, the proof system is compatible with Cocks-Pinch or Brezing-Weng outer curves to the the widely used curves such as secp256k1, ED25519, BLS12-381 and BN254. This allows us to retain the fully parallelizable nature and the O(1) communication complexity of Pianist ([LXZ+23]) in conjunction with circumventing the huge overhead of non-native...

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...

In classical cryptography, one-way functions (OWFs) are the minimal assumption, while recent active studies have demonstrated that OWFs are not necessarily the minimum assumption in quantum cryptography. Several new primitives have been introduced such as pseudorandom unitaries (PRUs), pseudorandom function-like state generators (PRFSGs), pseudorandom state generators (PRSGs), one-way state generators (OWSGs), one-way puzzles (OWPuzzs), and EFI pairs. They are believed to be weaker than...

In this paper, we introduce the notion of relaxed lattice-based programmable hash function (RPHF), which is a novel variant of lattice-based programmable hash functions (PHFs). Lattice-based PHFs, together with preimage trapdoor functions (TDFs), have been widely utilized (implicitly or explicitly) in the construction of adaptively secure identity-based encryption (IBE) schemes. The preimage length and the output length of the underlying PHF and TDF together determine the user secret key and...

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...

Although one-way functions are well-established as the minimal primitive for classical cryptography, a minimal primitive for quantum cryptography is still unclear. Universal extrapolation, first considered by Impagliazzo and Levin (1990), is hard if and only if one-way functions exist. Towards better understanding minimal assumptions for quantum cryptography, we study the quantum analogues of the universal extrapolation task. Specifically, we put forth the classical$\rightarrow$quantum...

The planted random subgraph detection conjecture of Abram et al. (TCC 2023) asserts the pseudorandomness of a pair of graphs $(H, G)$, where $G$ is an Erdos-Renyi random graph on $n$ vertices, and $H$ is a random induced subgraph of $G$ on $k$ vertices. Assuming the hardness of distinguishing these two distributions (with two leaked vertices), Abram et al. construct communication-efficient, computationally secure (1) 2-party private simultaneous messages (PSM) and (2) secret sharing for...

Frontrunning is rampant in blockchain ecosystems, yielding attackers profits that have already soared into several million. Most existing frontrunning attacks focus on manipulating transaction order (namely, prioritizing attackers' transactions before victims' transactions) $\textit{within}$ a block. However, for the emerging directed acyclic graph (DAG)-based blockchains, these intra-block frontrunning attacks may not fully reveal the frontrunning vulnerabilities as they introduce block...

Peer-to-peer communication systems can provide many functions, including anonymized routing of network traffic, massive parallel computing environments, and distributed storage. Anonymity refers to the state of being completely nameless, with no attached identifiers. Pseudonymity involves the use of a fictitious name that can be consistently linked to a particular user, though not necessarily to the real identity. Both provide a layer of privacy, shielding the user's true identity from...

Recent oracle separations [Kretschmer, TQC'21, Kretschmer et. al., STOC'23] have raised the tantalizing possibility of building quantum cryptography from sources of hardness that persist even if the polynomial hierarchy collapses. We realize this possibility by building quantum bit commitments and secure computation from unrelativized, well-studied mathematical problems that are conjectured to be hard for $\mathsf{P}^{\#\mathsf{P}}$ -- such as approximating the permanents of complex Gaussian...

Mix networks (mixnets) enhance anonymity by routing client messages through multiple hops, intentionally delaying or reordering these messages to ensure unlinkability. However, this process increases end-to-end latency, potentially degrading the client experience. To address this issue, LARMix (NDSS, 2024) proposed a low-latency routing methodology specifically designed for stratified mixnet architectures. Our paper extends this concept to Free Routes mixnet designs, where, unlike stratified...

Proofs of partial knowledge, first considered by Cramer, Damgård and Schoenmakers (CRYPTO'94) and De Santis et al. (FOCS'94), allow for proving the validity of $k$ out of $n$ different statements without revealing which ones those are. In this work, we present a new approach for transforming certain proofs system into new ones that allows for proving partial knowledge. The communication complexity of the resulting proof system only depends logarithmically on the total number of statements...

Signature-based witness encryption (SWE) is a recently proposed notion that allows to encrypt a message with respect to a tag $T$ and a set of signature verification keys. The resulting ciphertext can only be decrypted by a party who holds at least $k$ different valid signatures w.r.t. $T$ and $k$ different verification keys out of the $n$ keys specified at encryption time. Natural applications of this primitive involve distributed settings (e.g., blockchains), where multiple parties sign...

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...

Quantum pseudorandom state generators (PRSGs) have stimulated exciting developments in recent years. A PRSG, on a fixed initial (e.g., all-zero) state, produces an output state that is computationally indistinguishable from a Haar random state. However, pseudorandomness of the output state is not guaranteed on other initial states. In fact, known PRSG constructions provably fail on some initial states. In this work, we propose and construct quantum Pseudorandom State Scramblers (PRSSs),...

Local Differential Privacy (LDP) provides a formal guarantee of privacy that enables the collection and analysis of sensitive data without revealing any individual's data. While LDP methods have been extensively studied, there is a lack of a systematic and empirical comparison of LDP methods for descriptive statistics. In this paper, we first provide a systematization of LDP methods for descriptive statistics, comparing their properties and requirements. We demonstrate that several mean...

Distributed Key Generation (DKG) is a technique that enables the generation of threshold cryptography keys among a set of mutually untrusting nodes. DKG generates keys for a range of decentralized applications such as threshold signatures, multiparty computation, and Byzantine consensus. Over the past five years, research on DKG has focused on optimizing network communication protocols to improve overall system efficiency by reducing communication complexity. However, SOTA asynchronous...

We revisit the lattice-based verifiable oblivious PRF construction from PKC'21 and remove or mitigate its central three sources of inefficiency. First, applying Rényi divergence arguments, we eliminate one superpolynomial factor from the ciphertext modulus \(q\), allowing us to reduce the overall bandwidth consumed by RLWE samples by about a factor of four. This necessitates us introducing intermediate unpredictability notions to argue PRF security of the final output in the Random Oracle...

Merkle trees play a crucial role in blockchain networks in organizing network state. They allow proving a particular value of an entry in the state to a node that maintains only the root of the Merkle trees, a hash-based signature computed over the data in a hierarchical manner. Verification of particular state entries is crucial in reaching a consensus on the execution of a block where state information is required in the processing of its transactions. For instance, a payment transaction...

Anamorphic encryptions and anamorphic signatures assume a double key pre-shared between two parties so as to enable the transmission of covert messages. How to securely and efficiently distribute a double key under the dictator's surveillance is a central problem for anamorphic cryptography, especially when the users are forced to surrender their long-term secret keys or even the randomness used in the algorithms to the dictator. In this paper, we propose Anamorphic Authentication Key...

We propose waterlogs, a new direction to detect and trace synthetic text outputs from large language models based on transparency logs. Waterlogs offer major categorical advantages over watermarking: it (1) allows for the inclusion of arbitrary metadata to facilitate tracing, (2) is publicly verifiable by third parties, and (3) operates in a distributed manner while remaining robust and efficient. Waterlogs rely on a verifiable Hamming distance index, a novel data structure that we...

A broadcast encryption scheme allows a user to encrypt a message to $N$ recipients with a ciphertext whose size scales sublinearly with $N$. While broadcast encryption enables succinct encrypted broadcasts, it also introduces a strong trust assumption and a single point of failure; namely, there is a central authority who generates the decryption keys for all users in the system. Distributed broadcast encryption offers an appealing alternative where there is a one-time (trusted) setup...

Zero-Knowledge (ZK) protocols have been a subject of intensive study due to their fundamental importance and versatility in modern cryptography. However, the inherently different nature of quantum information significantly alters the landscape, necessitating a re-examination of ZK designs. A crucial aspect of ZK protocols is their round complexity, intricately linked to $\textit{simulation}$, which forms the foundation of their formal definition and security proofs. In the...

This work introduces Cryptobazaar, a novel scalable, private, and decentralized sealed-bid auction protocol. In particular, our protocol protects the privacy of losing bidders by preserving the confidentiality of their bids while ensuring public verifiability of the outcome and relying only on a single untrusted auctioneer for coordination. At its core, Cryptobazaar combines an efficient distributed protocol to compute the logical-OR for a list of unary-encoded bids with various novel...

Payment channel networks (PCNs) are a leading method to scale the transaction throughput in cryptocurrencies. Two participants can use a bidirectional payment channel for making multiple mutual payments without committing them to the blockchain. Opening a payment channel is a slow operation that involves an on-chain transaction locking a certain amount of funds. These aspects limit the number of channels that can be opened or maintained. Users may route payments through a multi-hop path and...

The field of distributed certification is concerned with certifying properties of distributed networks, where the communication topology of the network is represented as an arbitrary graph; each node of the graph is a separate processor, with its own internal state. To certify that the network satisfies a given property, a prover assigns each node of the network a certificate, and the nodes then communicate with one another and decide whether to accept or reject. We require soundness and...

In this article, we derive the weight distribution of linear codes stemming from a subclass of (vectorial) $p$-ary plateaued functions (for a prime $p$), which includes all the explicitly known examples of weakly and non-weakly regular plateaued functions. This construction of linear codes is referred in the literature as the first generic construction. First, we partition the class of $p$-ary plateaued functions into three classes $\mathscr{C}_1, \mathscr{C}_2,$ and $\mathscr{C}_3$,...

In this paper, we present an improved attack on the stream cipher Salsa20. Our improvements are based on two technical contributions. First, we make use of a distribution of a linear combination of several random variables that are derived from different differentials and explain how to exploit this in order to improve the attack complexity. Secondly, we study and exploit how to choose the actual value for so-called probabilistic neutral bits optimally. Because of the limited influence of...

One-way functions are fundamental to classical cryptography and their existence remains a longstanding problem in computational complexity theory. Recently, a provable quantum one-way function has been identified, which maintains its one-wayness even with unlimited computational resources. Here, we extend the mathematical definition of functions to construct a generalized one-way function by virtually measuring the qubit of provable quantum one-way function and randomly assigning the...

Key distribution plays a fundamental role in cryptography. Currently, the quantum scheme stands as the only known method for achieving unconditionally secure key distribution. This method has been demonstrated over distances of 508 and 1002 kilometers in the measurement-device-independent and twin-field configurations, respectively. However, quantum key distribution faces transmission distance issues and numerous side channel attacks since the basic physical picture requires the use of...

A threshold key encapsulation mechanism (TKEM) facilitates the secure distribution of session keys among multiple participants, allowing key recovery through a threshold number of shares. TKEM has gained significant attention, especially for decentralized systems, including blockchains. However, existing constructions often rely on trusted setups, which pose security risks such as a single point of failure, and are limited by fixed participant numbers and thresholds. To overcome this, we...

Rollups are special applications on distributed state machines (aka blockchains) for which the underlying state machine only logs, but does not execute transactions. Rollups have become a popular way to scale applications on Ethereum and there is now growing interest in running rollups on Bitcoin. Rollups scale throughput and reduce transaction costs by using auxiliary machines that have higher throughput and lower cost of executing transactions than the underlying blockchain. State updates...

Order fairness in the context of distributed ledgers has received recently significant attention due to a range of attacks that exploit the reordering and adaptive injection of transactions (violating what is known as “input causality”). To address such concerns an array of definitions for order fairness has been put forth together with impossibility and feasibility results highlighting the difficulty and multifaceted nature of fairness in transaction serialization. Motivated by this we...

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...

Zero-knowledge proofs allow one party to prove the truth of a statement without disclosing any extra information. Recent years have seen great improvements in zero-knowledge proofs. Among them, zero-knowledge SNARKs are notable for their compact and efficiently-verifiable proofs, but have relatively high prover costs. To accelerate proving, distributed zero-knowledge proof systems (Wu et al., Usenix Security 2018) are proposed: by distributing the proving process across multiple machines,...

We study the problem of generating public unbiased randomness in a distributed manner within the recent You Only Speak Once (YOSO) framework for stateless multiparty computation, introduced by Gentry et al. in CRYPTO 2021. Such protocols are resilient to adaptive denial-of-service attacks and are, by their stateless nature, especially attractive in permissionless environments. While most works in the YOSO setting focus on independent random corruptions, we consider YOSO protocols with...

Compared to elliptic curve cryptography, a main drawback of lattice-based schemes is the larger size of their public keys and ciphertexts. A common procedure for compressing these objects consists essentially of dropping some of their least significant bits. Albeit effective for compression, there is a limit to the number of bits to be dropped before we get a noticeable decryption failure rate (DFR), which is a security concern. To address this issue, this paper presents a family of...

This paper presents a collection of lessons learned from analyzing the real-world security of various Byzantine Fault Tolerant (BFT) consensus protocol implementations. Drawing upon our experience as a team of security experts who have both developed and audited BFT systems, including BA★, HotStuff variants, Paxos variants, and DAG-based algorithms like Narwhal and Bullshark, we identify and analyze a variety of security vulnerabilities discovered in the translation of theoretical protocols...

A crucial component of any zero-knowledge system is operations with finite fields. This, in turn, leads to the implementation of the fundamental operation: multiplying two big integers. In the realm of Bitcoin, this problem gets revisited, as Bitcoin utilizes its own stack-based and not Turing-complete scripting system called Bitcoin Script. Inspired by Elliptic Curve scalar multiplication, this paper introduces the $w$-windowed method for multiplying two numbers. We outperform...

Lattice cryptography schemes based on the learning with errors (LWE) hardness assumption have been standardized by NIST for use as post-quantum cryptosystems, and by HomomorphicEncryption.org for encrypted compute on sensitive data. Thus, understanding their concrete security is critical. Most work on LWE security focuses on theoretical estimates of attack performance, which is important but may overlook attack nuances arising in real-world implementations. The sole existing concrete...

Lattice-based cryptography is in the process of being standardized. Several proposals to deal with side-channel information using lattice reduction exist. However, it has been shown that algorithms based on Bayesian updating are often more favorable in practice. In this work, we define distribution hints; a type of hint that allows modelling probabilistic information. These hints generalize most previously defined hints and the information obtained in several attacks. We define two...

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...

Zero-knowledge Succinct Non-interactive ARguments of Knowledge (zkSNARKs) allow a prover to convince a verifier of the correct execution of a large computation in private and easily-verifiable manner. These properties make zkSNARKs a powerful tool for adding accountability, scalability, and privacy to numerous systems such as blockchains and verifiable key directories. Unfortunately, existing zkSNARKs are unable to scale to large computations due to time and space complexity requirements...

This article presents an innovative project for a Central Bank Digital Currency (CBDC) infrastructure. Focusing on security and reliability, the proposed architecture: (1) employs post-quantum cryptography (PQC) algorithms for long-term security, even against attackers with access to cryptographically-relevant quantum computers; (2) can be integrated with a Trusted Execution Environment (TEE) to safeguard the confidentiality of transaction contents as they are processed by third-parties; and...

In recent years, formal verification has emerged as a crucial method for assessing security against Side-Channel attacks of masked implementations, owing to its remarkable versatility and high degree of automation. However, formal verification still faces technical bottlenecks in balancing accuracy and efficiency, thereby limiting its scalability. Former tools like maskVerif and CocoAlma are very efficient but they face accuracy issues when verifying schemes that utilize properties of...

Computing the maximum from a list of secret inputs is a widely-used functionality that is employed ei- ther indirectly as a building block in secure computation frameworks, such as ABY (NDSS’15) or directly used in multiple applications that solve optimisation problems, such as secure machine learning or secure aggregation statistics. Incremental distributed point function (I-DPF) is a powerful primitive (IEEE S&P’21) that significantly reduces the client- to-server communication and are...

Resource-constrained devices such as wireless sensors and Internet of Things (IoT) devices have become ubiquitous in our digital ecosystem. These devices generate and handle a major part of our digital data. In the face of the impending threat of quantum computers on our public-key infrastructure, it is impossible to imagine the security and privacy of our digital world without integrating post-quantum cryptography (PQC) into these devices. Usually, due to the resource constraints of these...

The one-time pad cipher is renowned for its theoretical perfect security, yet its practical deployment is primarily hindered by the key-size and distribution challenge. This paper introduces a novel approach to key distribution called q-stream, designed to make symmetric-key cryptography, and the one-time pad cipher in particular, a viable option for contemporary secure communications, and specifically, post-quantum cryptography, leveraging quantum noise and combinatorics to ensure secure...

We show that the data storage scheme [IEEE/ACM Trans. Netw., 2023, 31(4), 1550-1565] is flawed due to the false secret sharing protocol, which requires that some random $4\times 4$ matrixes over the finite field $F_p$ (a prime $p$) are invertible. But we find its mathematical proof for invertibility is incorrect. To fix this flaw, one needs to check the invertibility of all 35 matrixes so as to generate the proper 7 secret shares.

EagleSign is one of the 40 “Round 1 Additional Signatures” that is accepted for consideration in the supplementary round of the Post-Quantum Cryptography standardization process, organized by NIST. Its design is based on structured lattices, and it boasts greater simplicity and performance compared to the two lattice signatures already selected for standardization: Falcon and Dilithium. In this paper, we show that those claimed advantages come at the cost of security. More precisely, we...

Verifiable Random Functions (VRFs) are cryptographic primitives that generate unpredictable randomness along with proofs that are verifiable, a critical requirement for blockchain applications in decentralized finance, online gaming, and more. Existing VRF constructions often rely on centralized entities, creating security vulnerabilities. Distributed VRFs (DVRFs) offer a decentralized alternative but face challenges like large proof sizes or dependence on computationally expensive bilinear...

Randomized distributed function computation refers to remote function computation where transmitters send data to receivers which compute function outputs that are randomized functions of the inputs. We study the applications of semantic communications in randomized distributed function computation to illustrate significant reductions in the communication load, with a particular focus on privacy. The semantic communication framework leverages generalized remote source coding methods, where...

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...

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...

We present a variant of Function Secret Sharing (FSS) schemes tailored for point, comparison, and interval functions, featuring compact key sizes at the expense of additional comparison. While existing FSS constructions are primarily geared towards $2$-party scenarios, exceptions such as the work by Boyle et al. (Eurocrypt 2015) and Riposte (S&P 2015) have introduced FSS schemes for $p$-party scenarios ($p \geq 3$). This paper aims to achieve the most compact $p$-party FSS key size to date....

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...

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...

Threshold secret sharing enables distributing a message to $n$ parties such that no subset of fewer than $t$ parties can learn the message, whereas any subset of at least $t$ parties can recover the message. Despite being a fundamental primitive, secret sharing still suffers from one significant drawback, where its message reconstruction algorithm is computationally expensive for large privacy thresholds $t$. In this paper, we aim to address this significant drawback. We study general...

Self-sovereign identity (SSI) systems empower users to (anonymously) establish and verify their identity when accessing both digital and real-world resources, emerging as a promising privacy-preserving solution for user-centric identity management. Recent work by Maram et al. proposes the privacy-preserving Sybil-resistant decentralized SSI system CanDID (IEEE S&P 2021). While this is an important step, notable shortcomings undermine its efficacy. The two most significant among them being...

Cryptocurrencies and blockchain technology provide an innovative model for reshaping digital services. Driven by the movement toward Web 3.0, recent systems started to provide distributed services, such as computation outsourcing or file storage, on top of the currency exchange medium. By allowing anyone to join and collect cryptocurrency payments for serving others, these systems create decentralized markets for trading digital resources. Yet, there is still a big gap between the promise of...

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...

Collaborative graph learning represents a learning paradigm where multiple parties jointly train a graph neural network (GNN) using their own proprietary graph data. To honor the data privacy of all parties, existing solutions for collaborative graph learning are either based on federated learning (FL) or secure machine learning (SML). Although promising in terms of efficiency and scalability due to their distributed training scheme, FL-based approaches fall short in providing provable...

This Systematization of Knowledge conducts a survey of contemporary distributed blockchain protocols, with the aim of identifying cryptographic and design techniques which practically enable both expressive programmability and user data confidentiality. To facilitate a framing which supports the comparison of concretely very different protocols, we define an epoch-based computational model in the form of a flexible UC-style ideal functionality which divides the operation of...

This paper presents a new architecture for metadata-private messaging that counters scalability challenges by offloading most computations to the clients. At the core of our design is a distributed private information retrieval (PIR) protocol, where the responder delegates its work to alleviate PIR's computational bottleneck and catches misbehaving delegates by efficiently verifying their results. We introduce DPIR, a messaging system that uses distributed PIR to let a server storing...

Distributed randomness beacons (DRBs) are fundamental for various decentralised applications, such as consensus protocols, decentralised gaming and lotteries, and collective governance protocols. These applications are heavily used on modern blockchain platforms. This paper presents the so far most efficient direct construction and implementation of a non-interactive distributed verifiable random function (NI-DVRF) that is fully compatible with Ethereum. Our NI-DVRF scheme adopts...

We propose a new framework based on random submersions — that is projection over a random subspace blinded by a small Gaussian noise — for constructing verifiable short secret sharing and showcase it to construct efficient threshold lattice-based signatures in the hash-and-sign paradigm, when based on noise flooding. This is, to our knowledge, the first hash-and-sign lattice-based threshold signature. Our threshold signature enjoys the very desirable property of robustness, including at key...

In this note, we study the interplay between the communication from a verifier in a general private-coin interactive protocol and the number of random bits it uses in the protocol. Under worst-case derandomization assumptions, we show that it is possible to transform any $I$-round interactive protocol that uses $\rho$ random bits into another one for the same problem with the additional property that the verifier's communication is bounded by $O(I\cdot \rho)$. Importantly, this is done with...

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...

In past years, entire research communities have arisen to address concerns of privacy and fairness in data analysis. At present, however, the public must trust that institutions will re-implement algorithms voluntarily to account for these social concerns. Due to additional cost, widespread adoption is unlikely without effective legal enforcement. A technical challenge for enforcement is that the methods proposed are often probabilistic mechanisms, whose output must be drawn according to...

Distributed Point Function (DPF) provides a way for a dealer to split a point function $f_{\alpha, \beta}$ into multiple succinctly described function-shares, where the function $f_{\alpha, \beta}$ for a special input $\alpha$, returns a special output value $\beta$, and returns a fixed value $0$ otherwise. As the security requirement, any strict subset of the function-shares reveals nothing about the function $f_{\alpha,\beta}$. However, each function-share can be individually evaluated on...

This paper introduces and develops the concept of ``ticketing'', through which atomic broadcasts are orchestrated by nodes in a distributed system. The paper studies different ticketing regimes that allow parallelism, yet prevent slow nodes from hampering overall progress. It introduces a hybrid scheme which combines managed and unmanaged ticketing regimes, striking a balance between adaptivity and resilience. The performance evaluation demonstrates how managed and unmanaged ticketing...

For more than forty years, two principal questions have been asked when designing verifiable election systems: how will the integrity of the results be demonstrated and how will the privacy of votes be preserved? Many approaches have been taken towards answering the first question such as use of MixNets and homomorphic tallying. But in the academic literature, the second question has always been answered in the same way: decryption capabilities are divided amongst multiple independent...

Motivated by the problem of detecting AI-generated text, we consider the problem of watermarking the output of language models with provable guarantees. We aim for watermarks which satisfy: (a) undetectability, a cryptographic notion introduced by Christ, Gunn & Zamir (2024) which stipulates that it is computationally hard to distinguish watermarked language model outputs from the model's actual output distribution; and (b) robustness to channels which introduce a constant fraction of...

Recent years have exhibited an increase in applications that distribute trust across $n$ servers to protect user data from a central point of attack. However, these deployments remain limited due to a core obstacle: establishing $n$ distinct trust domains. An application provider, a single trust domain, cannot directly deploy multiple trust domains. As a result, application providers forge business relationships to enlist third-parties as trust domains, which is a manual, lengthy, and...