Compilers often weaken or even discard software-based countermeasures commonly used to protect programs against side-channel attacks; worse, they may also introduce vulnerabilities that attackers can exploit. The solution to this problem is to develop compilers that preserve these countermeasures. Prior work establishes that (a mildly modified version of) the CompCert and Jasmin formally verified compilers preserve constant-time, an information flow policy that ensures that programs are...

Fully homomorphic encryption (FHE) has become progressively more viable in the years since its original inception in 2009. At the same time, leveraging state-of-the-art schemes in an efficient way for general computation remains prohibitively difficult for the average programmer. In this work, we introduce a new design for a fully homomorphic processor, dubbed Juliet, to enable faster operations on encrypted data using the state-of-the-art TFHE and cuFHE libraries for both CPU and GPU...

Cryptography implementations of block cipher have been written in C language due to its strong features on system-friendly features. However, the C language is prone to memory safety issues, such as buffer overflows and memory leaks. On the other hand, Rust, novel system programming language, provides strict compile-time memory safety guarantees through its ownership model. This paper presents the implementation of LEA block cipher in Rust language, demonstrating features to prevent...

In a fully non-interactive multi-signature, resp. aggregate-signature scheme (fNIM, resp. fNIA), signatures issued by many signers on the same message, resp. on different messages, can be succinctly ``combined'', resp. ``aggregated''. fNIMs are used in the Ethereum consensus protocol, to produce the certificates of validity of blocks which are to be verified by billions of clients. fNIAs are used in some PBFT-like consensus protocols, such as the production version of Diem by Aptos, to...

It is fundamental that executing cryptographic software must not leak secrets through side-channels. For software-visible side-channels, it was long believed that "constant-time" programming would be sufficient as a systematic countermeasure. However, this belief was shattered in 2018 by attacks exploiting speculative execution—so called Spectre attacks. Recent work shows that language support suffices to protect cryptographic code with minimal overhead against one class of such attacks,...

Lookup arguments allow an untrusted prover to commit to a vector $\vec f \in \mathbb{F}^n$ and show that its entries reside in a predetermined table $\vec t \in \mathbb{F}^N$. One of their key applications is to augment general-purpose SNARKs making them more efficient on subcomputations that are hard to arithmetize. In order for this "augmentation" to work out, a SNARK and a lookup argument should have some basic level of compatibility with respect to the commitment on $\vec f$. However,...

Databases play a pivotal role in the contemporary World Wide Web and the world of cloud computing. Unfortunately, numerous privacy violations have recently garnered attention in the news. To enhance database privacy, we consider Oblivious Transfer (OT), an elegant cryptographic technology. Our observation reveals that existing research in this domain primarily concentrates on theoretical cryptographic applications, overlooking various practical aspects: - OTs assume parties have direct...

Private Information Retrieval (PIR) enables a client to retrieve a database element from a semi-honest server while hiding the element being queried from the server. Maliciously-secure PIR (mPIR) [Colombo et al., USENIX Security '23] strengthens the guarantees of plain (i.e., semi-honest) PIR by ensuring that even a misbehaving server (a) cannot compromise client privacy via selective-failure attacks, and (b) must answer every query *consistently* (i.e., with respect to the same database)....

In the useful and well studied model of secret-sharing schemes, there are $n$ parties and a dealer, which holds a secret. The dealer applies some randomized algorithm to the secret, resulting in $n$ strings, called shares; it gives the $i$'th share to the $i$'th party. There are two requirements. (1) correctness: some predefined subsets of the parties can jointly reconstruct the secret from their shares, and (2) security: any other set gets no information on the secret. The collection of...

HyperPlonk is a recent SNARK proposal (Eurocrypt'23) that features a linear-time prover and supports custom gates of larger degree than Plonk. For the time being, its instantiations are only proven to be knowledge-sound (meaning that soundness is only guaranteed when the prover runs in isolation) while many applications motivate the stronger notion of simulation-extractability (SE). Unfortunately, the most efficient SE compilers are not immediately applicable to multivariate polynomial...

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...

Simulation extractability is a strong security notion of zkSNARKs that guarantees that an attacker who produces a valid proof must know the corresponding witness, even if the attacker had prior access to proofs generated by other users. Notably, simulation extractability implies that proofs are non-malleable and is of fundamental importance for applications of zkSNARKs in distributed systems. In this work, we study sufficient and necessary conditions for constructing simulation-extractable...

Fully Homomorphic Encryption (FHE) is a transformative technology that enables computations on encrypted data without requiring decryption, promising enhanced data privacy. However, its adoption has been limited due to significant performance overheads. Recent advances include the proposal of domain-specific, highly-parallel hardware accelerators designed to overcome these limitations. This paper introduces PICA, a comprehensive compiler framework designed to simplify the programming of...

Generative pre-trained transformers (GPT's) are a type of large language machine learning model that are unusually adept at producing novel, and coherent, natural language. Notably, these technologies have also been extended to computer programming languages with great success. However, GPT model outputs in general are stochastic and not always correct. For programming languages, the exact specification of the computer code, syntactically and algorithmically, is strictly required in order to...

Software solutions to address computational challenges are ubiquitous in our daily lives. One specific application area where software is often used is in embedded systems, which, like other digital electronic devices, are vulnerable to side-channel analysis attacks. Although masking is the most common countermeasure and provides a solid theoretical foundation for ensuring security, recent research has revealed a crucial gap between theoretical and real-world security. This shortcoming stems...

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...

We present a succinct polynomial commitment scheme for multilinears over tiny binary fields, including that with just 2 elements. To achieve this, we develop two main ideas. Our first adapts Zeilberger, Chen and Fisch's BaseFold ('23) PCS to the binary setting; it uses FRI (ICALP '18)'s lesser-known binary variant, and reveals a new connection between that work and Lin, Chung and Han (FOCS '14)'s additive NTT. We moreover present a novel large-field-to-small-field compiler for polynomial...

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...

An Oblivious Pseudo-Random Function (OPRF) is a two-party protocol for jointly evaluating a Pseudo-Random Function (PRF), where a user has an input x and a server has an input k. At the end of the protocol, the user learns the evaluation of the PRF using key k at the value x, while the server learns nothing about the user's input or output. OPRFs are a prime tool for building secure authentication and key exchange from passwords, private set intersection, private information retrieval,...

Verifiable Random Functions (VRFs) play a pivotal role in Proof of Stake (PoS) blockchain due to their applications in secret leader election protocols. However, the original definition by Micali, Rabin and Vadhan is by itself insufficient for such applications. The primary concern is that adversaries may craft VRF key pairs with skewed output distribution, allowing them to unfairly increase their winning chances. To address this issue David, Gaži, Kiayias and Russel (2017/573) proposed a...

We present a framework for building efficient folding-based SNARKs. First we develop a new "uniformizing" compiler for NP statements that converts any poly-time computation to a sequence of identical simple steps. The resulting uniform computation is especially well-suited to be processed by a folding-based IVC scheme. Second, we develop two optimizations to folding-based IVC. The first reduces the recursive overhead of the IVC by restructuring the relation to which folding is applied. The...

A compilation of various notes written over the years on some algorithms on abelian varieties.

We present STIR (Shift To Improve Rate), an interactive oracle proof of proximity (IOPP) for Reed-Solomon codes that achieves the best known query complexity of any concretely efficient IOPP for this problem. For $\lambda$ bits of security, STIR has query complexity $O(\log d + \lambda \cdot \log \log d )$, while FRI, a popular protocol, has query complexity $O(\lambda \cdot \log d )$ (including variants of FRI based on conjectured security assumptions). STIR relies on a new technique for...

Motivated by secure database search, we present secure computation protocols for a function $f$ in the client-servers setting, where a client can obtain $f(x)$ on a private input $x$ by communicating with multiple servers each holding $f$. Specifically, we propose generic compilers from passively secure protocols, which only keep security against servers following the protocols, to actively secure protocols, which guarantee privacy and correctness even against malicious servers. Our...

Nonlocal games are a foundational tool for understanding entanglement and constructing quantum protocols in settings with multiple spatially separated quantum devices. In this work, we continue the study initiated by Kalai et al. (STOC '23) of compiled nonlocal games, played between a classical verifier and a single cryptographically limited quantum device. Our main result is that the compiler proposed by Kalai et al. is sound for any two-player XOR game. A celebrated theorem of Tsirelson...

A leakage-resilient circuit for $f:\{0,1\}^n\to\{0,1\}^m$ is a randomized Boolean circuit $C$ mapping a randomized encoding of an input $x$ to an encoding of $y=f(x)$, such that applying any leakage function $L\in \cal L$ to the wires of $C$ reveals essentially nothing about $x$. A leakage-tolerant circuit achieves the stronger guarantee that even when $x$ and $y$ are not protected by any encoding, the output of $L$ can be simulated by applying some $L'\in \cal L$ to $x$ and $y$ alone....

A Password-Authenticated Key Exchange (PAKE) protocol allows two parties to agree upon a cryptographic key, in the setting where the only secret shared in advance is a low-entropy password. The standard security notion for PAKE is in the Universal Composability (UC) framework. In recent years there have been a large number of works analyzing the UC-security of Encrypted Key Exchange (EKE), the very first PAKE protocol, and its One-encryption variant (OEKE), both of which compile an...

In the consensus problem, $n$ parties want to agree on a common value, even if some of them are corrupt and arbitrarily misbehave. If the parties have a common input $m$, then they must agree on $m$. Protocols solving consensus assume either a synchronous communication network, where messages are delivered within a known time, or an asynchronous network with arbitrary delays. Asynchronous protocols only tolerate $t_a < n/3$ corrupt parties. Synchronous ones can tolerate $t_s < n/2$...

Several Password Authenticated Key Exchange (PAKE) protocols have been recently proposed that leverage a Key-Encapsulation Mechanism (KEM) to create an efficient and easy-to-implement post-quantum secure PAKE. This line of work is driven by the intention of the National Institute of Standards and Technology (NIST) to soon standardize a lattice-based post-quantum KEM called $\mathsf{Kyber}$. In two recent works, Beguinet et al. (ACNS 2023) and Pan and Zeng (ASIACRYPT 2023) proposed generic...

We uncover a critical side-channel vulnerability in the Hamming Quasi-Cyclic (HQC) round 4 optimized implementation arising due to the use of the modulo operator. In some cases, compilers optimize uses of the modulo operator with compile-time known divisors into constant-time Barrett reductions. However, this optimization is not guaranteed: for example, when a modulo operation is used in a loop the compiler may emit division (div) instructions which have variable execution time depending on...

Decentralized Anonymous Credential (DAC) systems are increasingly relevant, especially when enhancing revocation mechanisms in the face of complex traceability challenges. This paper introduces IDEA-DAC, a paradigm shift from the conventional revoke-and-reissue methods, promoting direct and Integrity-Driven Editing (IDE) for Accountable DACs, which results in better integrity accountability, traceability, and system simplicity. We further incorporate an Edit-bound Conformity Check that...

As blockchains like Ethereum continue to grow, clients with limited resources can no longer store the entire chain. Light nodes that want to use the blockchain, without verifying that it is in a good state overall, can just download the block headers without the corresponding block contents. As those light nodes may eventually need some of the block contents, they would like to ensure that they are in principle available. Data availability sampling, introduced by Bassam et al., is a...

Secure multiparty computation (MPC) allows a set of $n$ parties to jointly compute a function on their private inputs. In this work, we focus on the information-theoretic MPC in the \emph{asynchronous network} setting with optimal resilience ($t<n/3$). The best-known result in this setting is achieved by Choudhury and Patra [J. Cryptol '23], which requires $O(n^4\kappa)$ bits per multiplication gate, where $\kappa$ is the size of a field element. An asynchronous complete secret...

Trusted setup is commonly used for non-interactive proof and argument systems. However, there is no guarantee that the setup parameters in these systems are generated in a trustworthy manner. Building upon previous works, we conduct a systematic study of non-interactive zero-knowledge arguments in the common reference string model where the authority running the trusted setup might be corrupted. We explore both zero-knowledge and soundness properties in this setting.  - We consider a new...

A list polynomial commitment scheme (LPC) is a polynomial commitment scheme with a relaxed binding property. Namely, in an LPC setting, a commitment to a function $f(X)$ can be opened to a list of low-degree polynomials close to $f(X)$ (w.r.t. the relative Hamming distance and over a domain $D$). The scheme also allows opening one of the polynomials of the list at an arbitrary point $x$ and convincing a verifier that one of the polynomials in the list evaluates to the purported...

We prove that the seminal KZG polynomial commitment scheme (PCS) is black-box extractable under a simple falsifiable assumption ARSDH. To create an interactive argument, we construct a compiler that combines a black-box extractable non-interactive PCS and a polynomial IOP (PIOP). The compiler incurs a minor cost per every committed polynomial. Applying the Fiat-Shamir transformation, we obtain slightly less efficient variants of well-known PIOP-based zk-SNARKs, such as Plonk, that are...

In July 2022, the US National Institute for Standards and Technology (NIST) announced the first set of Post-Quantum Cryptography standards: Kyber, Dilithium, Falcon, and SPHINCS+. Shortly after, NIST published a call for proposals for additional post-quantum signature schemes to complement their initial portfolio. In 2023, 50 submissions were received, and 40 were accepted as round-1 candidates for future standardization. In this paper, we study the suitability and performance of said...

A major unresolved question in quantum cryptography is whether it is possible to obfuscate arbitrary quantum computation. Indeed, there is much yet to understand about the feasibility of quantum obfuscation even in the classical oracle model, where one is given for free the ability to obfuscate any classical circuit. In this work, we develop a new array of techniques that we use to construct a quantum state obfuscator, a powerful notion formalized recently by Coladangelo and Gunn...

We investigate proof systems where security holds against rational parties instead of malicious ones. Our starting point is the notion of rational arguments, a variant of rational proofs (Azar and Micali, STOC 2012) where security holds against rational adversaries that are also computationally bounded. Rational arguments are an interesting primitive because they generally allow for very efficient protocols, and in particular sublinear verification (i.e. where the Verifier does not have...

Homomorphic encryption (HE) enables computation on encrypted data, which in turn facilitates the outsourcing of computation on private data. However, HE offers no guarantee that the returned result was honestly computed by the cloud. In order to have such guarantee, it is necessary to add verifiable computation (VC) into the system. The most efficient recent works in VC over HE focus on verifying operations on the ciphertext space of the HE scheme, which usually lacks the algebraic...

Electronic voting has occupied a large part of the cryptographic protocols literature. The recent reality of blockchains---in particular their need for online governance mechanisms---has put new parameters and requirements to the problem. We identify the key requirements of a blockchain governance mechanism, namely correctness (including eliminative double votes), voter anonymity, and traceability, and investigate mechanisms that can achieve them with minimal interaction and under...

In their seminal work, Ishai, Kushilevitz, Ostrovsky, and Sahai (STOC`07) presented the MPC-in-the-Head paradigm, which shows how to design Zero-Knowledge Proofs (ZKPs) from secure Multi-Party Computation (MPC) protocols. This paradigm has since then revolutionized and modularized the design of efficient ZKP systems, with far-reaching applications beyond ZKPs. However, to the best of our knowledge, all previous instantiations relied on fully-secure MPC protocols, and have not been able to...

The notion of ``efficiently testable circuits'' (ETC) was recently put forward by Baig et al.~(ITCS'23). Informally, an ETC compiler takes as input any Boolean circuit $C$ and outputs a circuit/inputs tuple $(C',\mathbb{T})$ where (completeness) $C'$ is functionally equivalent to $C$ and (security) if $C'$ is tampered in some restricted way, then this can be detected as $C'$ will err on at least one input in the small test set $\mathbb{T}$. The compiler of Baig et al. detects tampering...

We prove a tight parallel repetition theorem for $3$-message computationally-secure quantum interactive protocols between an efficient challenger and an efficient adversary. We also prove under plausible assumptions that the security of $4$-message computationally secure protocols does not generally decrease under parallel repetition. These mirror the classical results of Bellare, Impagliazzo, and Naor [BIN97]. Finally, we prove that all quantum argument systems can be generically compiled...

In this paper we revisit the problem of erasing sensitive data from memory and registers during return from a cryptographic routine. While the problem and related attacker model is fairly easy to phrase, it turns out to be surprisingly hard to guarantee security in this model when implementing cryptography in common languages such as C/C++ or Rust. We revisit the issues surrounding zeroization and then present a principled solution in the sense that it guarantees that sensitive data is...

The need for energy optimizations in modern systems forces CPU vendors to provide Dynamic Voltage Frequency Scaling (DVFS) interfaces that allow software to control the voltage and frequency of CPU cores. In recent years, the accessibility of such DVFS interfaces to adversaries has amounted to a plethora of fault attack vectors. In response, the current countermeasures involve either restricting access to DVFS interfaces or including additional compiler-based checks that let the DVFS fault...

In STOC 2019 Canetti et al. showed how to soundly instantiate the Fiat-Shamir transform assuming that prover and verifier have access to the key of a 𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑖𝑛𝑡𝑟𝑎𝑐𝑡𝑎𝑏𝑙𝑒 ℎ𝑎𝑠ℎ 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡𝑙𝑦 𝑠𝑒𝑎𝑟𝑐ℎ𝑎𝑏𝑙𝑒 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠. The transform requires the starting protocol to be a special 3-round public-coin scheme that Canetti et al. call 𝑡𝑟𝑎𝑝𝑑𝑜𝑜𝑟 𝑠𝑖𝑔𝑚𝑎-𝑝𝑟𝑜𝑡𝑜𝑐𝑜𝑙. One downside of the Canetti et al. approach is that the key of the hash function can be used only once (or a pre-determined bounded...

We propose a generic compiler that can convert any zero-knowledge proof for SIMD circuits to general circuits efficiently, and an extension that can preserve the space complexity of the proof systems. Our compiler can immediately produce new results improving upon state of the art. -By plugging in our compiler to Antman, an interactive sublinear-communication protocol, we improve the overall communication complexity for generalcircuits from $\mathcal{O}(C^{3/4})$ to...

Suppose a user wants to broadcast an encrypted message to $K$ recipients. With public-key encryption, the sender would construct $K$ different ciphertexts, one for each recipient. The size of the broadcasted message then scales linearly with $K$. A natural question is whether the sender can encrypt the message with a ciphertext whose size scales sublinearly with the number of recipients. Broadcast encryption offers one solution to this problem, but at the cost of introducing a central...

Cheater identification in secure multi-party computation (MPC) allows the honest parties to agree upon the identity of a cheating party, in case the protocol aborts. In the context of a dishonest majority, this becomes especially critical, as it serves to thwart denial-of-service attacks and mitigate known impossibility results on ensuring fairness and guaranteed output delivery. In this work, we present a new, lightweight approach to achieving identifiable abort in dishonest majority...

We propose a new compiler framework that automates code generation over multiple fully homomorphic encryption (FHE) schemes. While it was recently shown that algorithms combining multiple FHE schemes (e.g., CKKS and TFHE) achieve high execution efficiency and task utility at the same time, developing fast cross-scheme FHE algorithms for real-world applications generally require heavy hand-tuned optimizations by cryptographic experts, resulting in either high usability costs or low...

Password-authenticated key exchange (PAKE) is a class of protocols enabling two parties to convert a shared (possibly low-entropy) password into a high-entropy joint session key. Strong asymmetric PAKE (saPAKE), an extension that models the client-server setting where servers may store a client's password for repeated authentication, was the subject of standardization efforts by the IETF in 2019-20. In this work, we present the most computationally efficient saPAKE protocol so far: a...

Data formats used for cryptographic inputs have historically been the source of many attacks on cryptographic protocols, but their security guarantees remain poorly studied. One reason is that, due to their low-level nature, formats often fall outside of the security model. Another reason is that studying all of the uses of all of the formats within one protocol is too difficult to do by hand, and requires a comprehensive, automated framework. We propose a new framework, “Comparse”, that...

Registration-Based Encryption (RBE) [Garg et al. TCC'18] is a public-key encryption mechanism in which users generate their own public and secret keys, and register their public keys with a central authority called the key curator. Similarly to Identity-Based Encryption (IBE), in RBE users can encrypt by only knowing the public parameters and the public identity of the recipient. Unlike IBE, though, RBE does not suffer the key escrow problem — one of the main obstacles of IBE's adoption in...

We investigate the conditions under which straight-line extractable NIZKs in the random oracle model (i.e. without a CRS) permit multiparty realizations that are black-box in the same random oracle. We show that even in the semi-honest setting, any MPC protocol to compute such a NIZK cannot make black-box use of the random oracle or a hash function instantiating it if security against all-but-one corruptions is desired, unless the number of queries made by the verifier to the oracle grows...

In the context of circuits leaking the internal state, there are various models to analyze what the adversary can see, like the $p$-random probing model in which the adversary can see the value of each wire with probability $p$. In this model, for a fixed $p$, it's possible to reach an arbitrary security by 'expanding' a stateless circuit via iterated compilation, reaching a security of $2^{-\kappa}$ with a polynomial size in $\kappa$. The existing proofs of the expansion work by first...

Fault injection attacks represent an effective threat to embedded systems. Recently, Laurent et al. have reported that fault injection attacks can leverage faults inside the microarchitecture. However, state-of-the-art counter-measures, hardware-only or with hardware support, do not consider the integrity of microarchitecture control signals that are the target of these faults. We present MAFIA, a microarchitecture protection against fault injection attacks. MAFIA ensures integrity of...

Vector Oblivious Linear Evaluation (VOLE) supports fast and scalable interactive Zero-Knowledge (ZK) proofs. Despite recent improvements to VOLE-based ZK, compiling proof statements to a control-flow oblivious form (e.g., a circuit) continues to lead to expensive proofs. One useful setting where this inefficiency stands out is when the statement is a disjunction of clauses L1 ∨ · · · ∨ LB. Typically, ZK requires paying the price to handle all B branches. Prior works have shown how to avoid...

Modern SNARK designs usually feature a frontend-backend paradigm: The frontend compiles a user's program into some equivalent circuit representation, while the backend calls for a SNARK specifically made for proving circuit satisfiability. While the circuit may be defined over small fields, the backend prover often needs to lift the computation to much larger fields for achieving soundness. This gap results in concrete overheads, for example, when proving SHA2 programs with pairing-based...

Side-channel attacks are a fundamental threat to the security of cryptographic implementations. One of the most prominent countermeasures against side-channel attacks is masking, where each intermediate value of the computation is secret shared, thereby concealing the computation's sensitive information. An important security model to study the security of masking schemes is the random probing model, in which the adversary obtains each intermediate value of the computation with some...

Real-world cryptographic implementations nowadays are not only attacked via classical cryptanalysis but also via implementation attacks, including passive attacks (observing side-channel information about the inner computation) and active attacks (inserting faults into the computation). While countermeasures exist for each type of attack, countermeasures against combined attacks have only been considered recently. Masking is a standard technique for protecting against passive side-channel...

In the dishonest-majority setting, generic secure multiparty computation (MPC) protocols are fundamentally vulnerable to attacks in which malicious participants learn their outputs and then force the protocol to abort before outputs are delivered to the honest participants. In other words, generic MPC protocols typically guarantee security with abort. This flavor of security permits denial-of-service attacks in many applications, unless the cheating participants who cause aborts are...

Homomorphic encryption (HE) allows computing encrypted data in the ciphertext domain without knowing the encryption key. It is possible, however, to break fully homomorphic encryption (FHE) algorithms by using side channels. This article demonstrates side-channel leakages of the Microsoft SEAL HE library. The proposed attack can steal encryption keys during the key generation phase by abusing the leakage of ternary value assignments that occurs during the number theoretic transform (NTT)...

YOSO-style MPC protocols (Gentry et al., Crypto'21), are a promising framework where the overall computation is partitioned into small, short-lived pieces, delegated to subsets of one-time stateless parties. Such protocols enable gaining from the security benefits provided by using a large community of participants where "mass corruption" of a large fraction of participants is considered unlikely, while keeping the computational and communication costs manageable. However, fully realizing...

Most succinct arguments (SNARKs) are initially only proven knowledge sound (KS). We show that the commonly employed compilation strategy from polynomial interactive oracle proofs (PIOP) via polynomial commitments to knowledge sound SNARKS actually also achieves other desirable properties: weak unique response (WUR) and trapdoorless zero-knowledge (TLZK); and that together they imply simulation extractability (SIM-EXT). The factoring of SIM-EXT into KS + WUR + TLZK is becoming a...

We introduce a new candidate post-quantum digital signature scheme from the regular syndrome decoding (RSD) assumption, an established variant of the syndrome decoding assumption which asserts that it is hard to find $w$-regular solutions to systems of linear equations over $\mathbb{F}_2$ (a vector is regular if it is a concatenation of $w$ unit vectors). Our signature is obtained by introducing and compiling a new 5-round zero-knowledge proof system constructed using the MPC-in-the-head...

Succinct Non-interactive Arguments of Knowledge (SNARKs) enable a party to cryptographically prove a statement regarding a computation to another party that has constrained resources. Practical use of SNARKs often involves a Zero-Knowledge Virtual Machine (zkVM) that receives an input program and input data, then generates a SNARK proof of the correct execution of the input program. Most zkVMs emulate the von Neumann architecture and must prove relations between a program's execution and its...

This work defines a notion of secure multiparty computation: MPC with fall-back security. Fall-back security for an $n$-party protocol is defined with respect to an adversary structure $\mathcal{Z}$ wherein security is guaranteed in the presence of both a computationally unbounded adversary with adversary structure $\mathcal{Z}$, and a computationally bounded adversary corrupting an arbitrarily large subset of the parties. This notion was considered in the work of Chaum (Crypto 89) via the...

This paper introduces arithmetic sketching, an abstraction of a primitive that several previous works use to achieve lightweight, low-communication zero-knowledge verification of secret-shared vectors. An arithmetic sketching scheme for a language $\mathcal{L} \in \mathbb{F}^n$ consists of (1) a randomized linear function compressing a long input x to a short “sketch,” and (2) a small arithmetic circuit that accepts the sketch if and only if $x \in \mathcal{L}$, up to some small error. If...

In MPC, we usually represent programs as circuits. This is a poor fit for programs that use complex control flow, as it is costly to compile control flow to circuits. This motivated prior work to emulate CPUs inside MPC. Emulated CPUs can run complex programs, but they introduce high overhead due to the need to evaluate not just the program, but also the machinery of the CPU, including fetching, decoding, and executing instructions, accessing RAM, etc. Thus, both circuits and CPU...

Constructing advanced cryptographic primitives such as obfuscation or broadcast encryption from standard hardness assumptions in the post quantum regime is an important area of research, which has met with limited success despite significant effort. It is therefore extremely important to find new, simple to state assumptions in this regime which can be used to fill this gap. An important step was taken recently by Wee (Eurocrypt '22) who identified two new assumptions from lattices, namely...

The widely used Signal protocol provides protection against state exposure attacks through forward security (protecting past messages) and post-compromise security (for restoring security). It supports immediate decryption, allowing messages to be re-ordered or dropped at the protocol level without affecting correctness. In this work, we consider strong active attack detection for secure messaging with immediate decryption, where parties are able to immediately detect active attacks under...

Addition of $n$ inputs is often the easiest nontrivial function to compute securely. Motivated by several open questions, we ask what can be computed securely given only an oracle that computes the sum. Namely, what functions can be computed in a model where parties can only encode their input locally, then sum up the encodings over some Abelian group $\G$, and decode the result to get the function output. An *additive randomized encoding* (ARE) of a function $f(x_1,\ldots,x_n)$ maps...

Polynomial commitments schemes are a powerful tool that enables one party to commit to a polynomial $p$ of degree $d$, and prove that the committed function evaluates to a certain value $z$ at a specified point $u$, i.e. $p(u) = z$, without revealing any additional information about the polynomial. Recently, polynomial commitments have been extensively used as a cryptographic building block to transform polynomial interactive oracle proofs (PIOPs) into efficient succinct arguments. In...

Zero Knowledge Proofs (ZKPs) are cryptographic protocols by which a prover convinces a verifier of the truth of a statement with- out revealing any other information. Typically, statements are expressed in a high-level language and then compiled to a low-level representation on which the ZKP operates. Thus, a bug in a ZKP compiler can com- promise the statement that the ZK proof is supposed to establish. This paper takes a step towards ZKP compiler correctness by partially veri- fying...

Chameleon hash (CH) is a trapdoor hash function. Generally it is hard to find collisions, but with the help of a trapdoor, finding collisions becomes easy. CH plays an important role in converting a conventional blockchain to a redactable one. However, most of existing CH schemes are too weak to support redactable blockchains. The currently known CH schemes serving for redactable blockchains have the best security of so-called ``full collision resistance (f-CR)'', but they are built either...

Ring-LWE based homomorphic encryption computations in large depth use a combination of two techniques: 1) decomposition of big numbers into small limbs/digits, and 2) efficient cyclotomic multiplications modulo $X^N+1$. It was long believed that the two mechanisms had to be strongly related, like in the full-RNS setting that uses a CRT decomposition of big numbers over an NTT-friendly family of prime numbers, and NTT over the same primes for multiplications. However, in this setting, NTT...

This note provides an update on the Open Specification Language (OSL) circuit compiler. OSL is a language based on predicate logic which is amenable to compilation to arithmetic constraint systems for use in constructing (zk-)SNARKs. This system provides an alternative to universal zk-VMs and low level ad hoc constructions of arithmetic constraint systems, which is potentially more efficient than universal zk-VMs but more cost effective as a development approach than low level ad hoc constructions.

A zero-knowledge proof (ZKP) is a powerful cryptographic primitive used in many decentralized or privacy-focused applications. However, the high overhead of ZKPs can restrict their practical applicability. We design a programming language, Ou, aimed at easing the programmer's burden when writing efficient ZKPs, and a compiler framework, Lian, that automates the analysis and distribution of statements to a computing cluster. Lian uses programming language semantics, formal methods, and...

Secure distributed generation of RSA moduli (e.g., generating $N=pq$ where none of the parties learns anything about $p$ or $q$) is an important cryptographic task, that is needed both in threshold implementations of RSA-based cryptosystems and in other, advanced cryptographic protocols that assume that all the parties have access to a trusted RSA modulo. In this paper, we provide a novel protocol for secure distributed RSA key generation based on the Miller-Rabin test. Compared with the...

Accumulation is a simple yet powerful primitive that enables incrementally verifiable computation (IVC) without the need for recursive SNARKs. We provide a generic, efficient accumulation (or folding) scheme for any $(2k-1)$-move special-sound protocol with a verifier that checks $\ell$ degree-$d$ equations. The accumulation verifier only performs $k+2$ elliptic curve multiplications and $k+d+O(1)$ field/hash operations. Using the compiler from BCLMS21 (Crypto 21), this enables building...

Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties in such a way that certain authorized subsets can reconstruct the secret, while unauthorized subsets obtain no information about it. Previous works on QSS for general access structures focused solely on the existence of perfectly secure schemes, and the share size of the known schemes is necessarily exponential even in cases where the access structure is computed by polynomial size...

We study sufficient conditions for compiling simulation-extractable zkSNARKs from information-theoretic interactive oracle proofs (IOP) using a simulation-extractable commit-and-prove system for its oracles. Specifically, we define simulation extractability for opening and evaluation proofs of polynomial commitment schemes, which we then employ to prove the security of zkSNARKS obtained from polynomial IOP prove systems, such as Plonk and Marlin. To instantiate our methodology we...

Secure Multi-Party Computation (MPC) is continuously becoming more and more practical. Many optimizations have been introduced, making MPC protocols more suitable for solving real-world problems. However, the MPC protocols and optimizations are usually implemented as a standalone proof of concept or in an MPC framework and are tightly coupled with special-purpose circuit formats, such as Bristol Format. This makes it very hard and time-consuming to re-use algorithmic advances and implemented...

We develop a simple compiler that generically adds publicly-verifiable deletion to a variety of cryptosystems. Our compiler only makes use of one-way functions (or one-way state generators, if we allow the public verification key to be quantum). Previously, similar compilers either relied on the use of indistinguishability obfuscation (Bartusek et. al., ePrint:2023/265) or almost-regular one-way functions (Bartusek, Khurana and Poremba, arXiv:2303.08676).

As the technical feasibility of a quantum computer becomes more and more likely, post-quantum cryptography algorithms are receiving particular attention in recent years. Among them, code-based cryptosystems were first considered unsuited for hardware and embedded software implementations because of their very large key sizes. However, recent work has shown that such implementations are practical, which also makes them susceptible to physical attacks. In this article, we propose a horizontal...

We present a general compiler to add the publicly verifiable deletion property for various cryptographic primitives including public key encryption, attribute-based encryption, and quantum fully homomorphic encryption. Our compiler only uses one-way functions, or more generally hard quantum planted problems for NP, which are implied by one-way functions. It relies on minimal assumptions and enables us to add the publicly verifiable deletion property with no additional assumption for the...

Garbled circuits are a fundamental cryptographic primitive that allows two or more parties to securely evaluate an arbitrary Boolean circuit without revealing any information beyond the output using a constant number of communication rounds. Garbled circuits have been introduced by Yao (FOCS’86) and generalized to the multi-party setting by Beaver, Micali and Rogaway (STOC’90). Since then, several works have improved their efficiency by providing different garbling schemes and several...

We revisit the problem of {\em reusable} non-interactive secure computation (NISC). A standard NISC protocol for a sender-receiver functionality $f$ enables the receiver to encrypt its input $x$ such that any sender, on input $y$, can send back a message revealing only $f(x,y)$. Security should hold even when either party can be malicious. A {\em reusable} NISC protocol has the additional feature that the receiver's message can be safely reused for computing multiple outputs $f(x,y_i)$. Here...

As zero-knowledge proofs gain increasing adoption, the cryptography community has designed domain-specific languages (DSLs) that facilitate the construction of zero-knowledge proofs (ZKPs). Many of these DSLs, such as Circom, facilitate the construction of arithmetic circuits, which are essentially polynomial equations over a finite field. In particular, given a program in a zero-knowledge proof DSL, the compiler automatically produces the corresponding arithmetic circuit. However, a...

We construct quantum public-key encryption from one-way functions. In our construction, public keys are quantum, but ciphertexts are classical. Quantum public-key encryption from one-way functions (or weaker primitives such as pseudorandom function-like states) are also proposed in some recent works [Morimae-Yamakawa, eprint:2022/1336; Coladangelo, eprint:2023/282; Barooti-Grilo-Malavolta-Sattath-Vu-Walter, eprint:2023/877]. However, they have a huge drawback: they are secure only when...

This work is motivated by the following question: can an untrusted quantum server convince a classical verifier of the answer to an efficient quantum computation using only polylogarithmic communication? We show how to achieve this in the quantum random oracle model (QROM), after a non-succinct instance-independent setup phase. We introduce and formalize the notion of post-quantum interactive oracle arguments for languages in QMA, a generalization of interactive oracle proofs...

In STOC 1989, Rabin and Ben-Or (RB) established an important milestone in the fields of cryptography and distributed computing by showing that every functionality can be computed with statistical (information-theoretic) security in the presence of an active (aka Byzantine) rushing adversary that controls up to half of the parties. We study the round complexity of general secure multiparty computation and several related tasks in the RB model. Our main result shows that every...

We introduce Lurk, a new LISP-based programming language for zk-SNARKs. Traditional approaches to programming over zero-knowledge proofs require compiling the desired computation into a flat circuit, imposing serious constraints on the size and complexity of computations that can be achieved in practice. Lurk programs are instead provided as data to the universal Lurk interpreter circuit, allowing the resulting language to be Turing-complete without compromising the size of the resulting...

The advent of quantum computers has sparked significant interest in post-quantum cryptographic schemes, as a replacement for currently used cryptographic primitives. In this context, lattice-based cryptography has emerged as the leading paradigm to build post-quantum cryptography. However, all existing viable replacements of the classical Diffie-Hellman key exchange require additional rounds of interactions, thus failing to achieve all the benefits of this protocol. Although earlier work has...

Is it possible to prove the deletion of a computer program after having executed it? While this task is clearly impossible using classical information alone, the laws of quantum mechanics may admit a solution to this problem. In this work, we propose a new approach to answer this question, using quantum information. In the interactive settings, we present the first fully-secure solution for blind delegation with certified deletion, assuming post-quantum hardness of the learning with errors...

(Asymmetric) Password-based Authenticated Key Exchange ((a)PAKE) protocols allow two parties establish a session key with a pre-shared low-entropy password. In this paper, we show how Encrypted Key Exchange (EKE) compiler [Bellovin and Merritt, S&P 1992] meets tight security in the Universally Composable (UC) framework. We propose a strong 2DH variant of EKE, denoted by 2DH-EKE, and prove its tight security in the UC framework based on the CDH assumption. The efficiency of 2DH-EKE is...

The pair encodings framework is an important result in the simplified design of complex attribute-based encryption schemes. In particular, it reduces the effort of proving security of a scheme to proving security of the associated pair encoding, which can then be transformed into a provably secure pairing-based encryption scheme with a compiler. Especially the symbolic property, as introduced by Agrawal and Chase (EUROCRYPT '17), has proven to be a valuable security notion that is both...

Non-interactive zero-knowledge proofs (NIZKs) and in particular succinct NIZK arguments of knowledge (zk-SNARKs) increasingly see real-world adoption in large and complex systems. Many zk-SNARKs require a trusted setup, i.e., a common reference string (CRS), and for practical use it is desirable to reduce the trust in the CRS generation. The latter can be achieved via the notions of subversion or updatable CRS. Another important property when deployed in large systems is the ability to...

We study satisfiability modulo the theory of finite fields and give a decision procedure for this theory. We implement our procedure for prime fields inside the cvc5 SMT solver. Using this theory, we con- struct SMT queries that encode translation validation for various zero knowledge proof compilers applied to Boolean computations. We evalu- ate our procedure on these benchmarks. Our experiments show that our implementation is superior to previous approaches (which encode...