We put forth Oblivious State Preparation (OSP) as a cryptographic primitive that unifies techniques developed in the context of a quantum server interacting with a classical client. OSP allows a classical polynomial-time sender to input a choice of one out of two public observables, and a quantum polynomial-time receiver to recover an eigenstate of the corresponding observable -- while keeping the sender's choice hidden from any malicious receiver. We obtain the following results: - The...

Boolean functions play an important role in designing and analyzing many cryptographic systems, such as block ciphers, stream ciphers, and hash functions, due to their unique cryptographic properties such as nonlinearity, correlation immunity, and algebraic properties. The secure evaluation of Boolean functions or Secure Boolean Evaluation (SBE) is an important area of research. SBE allows parties to jointly compute Boolean functions without exposing their private inputs. SBE finds...

Reductions are the workhorses of cryptography. They allow constructions of complex cryptographic primitives from simple building blocks. A prominent example is the non-interactive reduction from securely computing a ``complex" function $f$ to securely computing a ``simple" function $g$ via randomized encodings. Prior work equated simplicity with functions of small degree. In this work, we consider a different notion of simplicity where we require $g$ to only take inputs from a small...

We introduce a powerful attack, termed the bit-fixing correlation attack, on Goldreich's pseudorandom generators (PRGs), specifically focusing on those based on the $\mathsf{XOR}\text{-}\mathsf{THR}$ predicate. By exploiting the bit-fixing correlation property, we derive correlation equations with high bias by fixing certain bits. Utilizing two solvers to handle these high-bias correlation equations, we present inverse attacks on $\mathsf{XOR}\text{-}\mathsf{THR}$ based PRGs within the...

Oblivious Transfer (OT) is one of the fundamental building blocks in cryptography that enables various privacy-preserving applications. Constructing efficient OT schemes has been an active research area. This paper presents three efficient two-round pairing-free k-out-of-N oblivious transfer protocols with standard security. Our constructions follow the minimal communication pattern: the receiver sends k messages to the sender, who responds with n+k messages, achieving the lowest data...

We show that there exists a unitary quantum oracle relative to which quantum commitments exist but no (efficiently verifiable) one-way state generators exist. Both have been widely considered candidates for replacing one-way functions as the minimal assumption for cryptography—the weakest cryptographic assumption implied by all of computational cryptography. Recent work has shown that commitments can be constructed from one-way state generators, but the other direction has remained open. Our...

A Private Set Union (PSU) allows two parties having sets $X$ and $Y$ to securely compute the union $X \cup Y$ while revealing no additional information. Recently, there have been proposed so-called shuffle-based PSU protocols due to Garimella et. al. (PKC'21) and Jia et. al. (USENIX'22). Except a few base oblivious transfers, those proposals are fully based on symmetric key primitives and hence enjoy quite low computation costs. However, they commonly have drawbacks on large communication...

Laconic cryptography studies two-message protocols that securely compute on large amounts of data with minimal communication cost. Laconic oblivious transfer (OT) is a central primitive where the receiver's input is a large database $\mathsf{DB}$ and the sender's inputs are two messages $m_0$, $m_1$ along with an index $i$, such that the receiver learns the message determined by the choice bit $\mathsf{DB}_i$. OT becomes even more useful for secure computation when considering its laconic...

Recently, Masny and Rindal [MR19] formalized a notion called Endemic Oblivious Transfer (EOT), and they proposed a generic transformation from Non-Interactive Key Exchange (NIKE) to EOT with standalone security in the random oracle (RO) model. However, from the model level, the relationship between idealized NIKE and idealized EOT and the relationship between idealized elementary public key primitives have been rarely researched. In this work, we investigate the relationship between ideal...

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...

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

Privacy set intersection (PSI) and private information retrieval (PIR) are important areas of research in privacy protection technology. One of the key tools for both is the oblivious pseudorandom function (OPRF). Currently, existing oblivious pseudorandom functions either focus solely on efficiency without considering quantum attacks, or are too complex, resulting in low efficiency. The aim of this paper is to achieve a balance: to ensure that the oblivious pseudorandom function can...

Multi-party private set union (MPSU) protocol enables $m$ $(m > 2)$ parties, each holding a set, to collectively compute the union of their sets without revealing any additional information to other parties. There are two main categories of multi-party private set union (MPSU) protocols: The first category builds on public-key techniques, where existing works require a super-linear number of public-key operations, resulting in their poor practical efficiency. The second category builds on...

Oblivious Transfer (OT) is a fundamental cryptographic primitive, becoming a crucial component of a practical secure protocol. OT is typically implemented in software, and one way to accelerate its running time is by using hardware implementations. However, such implementations are vulnerable to side-channel attacks (SCAs). On the other hand, protecting interactive protocols against SCA is highly challenging because of their longer secrets (which include inputs and randomness), more...

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

Oblivious Transfer (OT) is at the heart of secure computation and is a foundation for many applications in cryptography. Over two decades of work have led to extremely efficient protocols for evaluating OT instances in the preprocessing model, through a paradigm called OT extension. A few OT instances generated in an offline phase can be used to perform many OTs in an online phase efficiently, i.e., with very low communication and computational overheads. Specifically, traditional OT...

We present a new simulation-secure quantum oblivious transfer (QOT) protocol based on one-way functions in the plain model. With a focus on practical implementation, our protocol surpasses prior works in efficiency, promising feasible experimental realization. We address potential experimental errors and their correction, offering analytical expressions to facilitate the analysis of the required quantum resources. Technically, we achieve simulation security for QOT through an equivocal and...

Oblivious Transfer (OT) is a fundamental cryptographic protocol with applications in secure Multi-Party Computation, Federated Learning, and Private Set Intersection. With the advent of quantum computing, it is crucial to develop unconditionally secure core primitives like OT to ensure their continued security in the post-quantum era. Despite over four decades since OT's introduction, the literature has predominantly relied on computational assumptions, except in cases using unconventional...

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...

We present unconditionally perfectly secure protocols in the semi-honest setting for several functionalities: (1) private elementwise equality; (2) private bitwise integer comparison; and (3) bit-decomposition. These protocols are built upon a new concept called Shared Oblivious Transfer (Shared OT). Shared OT extends the one-out-of-N String OT by replacing strings with integers modulo $M$ and allowing additive secret-sharing of all inputs and outputs. These extensions can be...

Private Set Union (PSU) protocol allows parties, each holding an input set, to jointly compute the union of the sets without revealing anything else. In the literature, scalable PSU protocols follow the “split-execute-assemble” paradigm (Kolesnikov et al., ASIACRYPT 2019); in addition, those fast protocols often use Oblivious Transfer as building blocks. Kolesnikov et al. (ASIACRYPT 2019) and Jia et al. (USENIX Security 2022), pointed out that certain security issues can be introduced in the...

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

The income of companies working on data markets steadily grows year by year. Private function evaluation (PFE) is a valuable tool in solving corresponding security problems. The task of Controlled Private Function Evaluation and its relaxed version was introduced in [Horvath et.al., 2019]. In this article, we propose and examine several different approaches for such tasks with computational and information theoretical security against static corruption adversary. The latter level of security...

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,...

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

We give a construction of a two-round batch oblivious transfer (OT) protocol in the CRS model that is UC-secure against malicious adversaries and has (near) optimal communication cost. Specifically, to perform a batch of $k$ oblivious transfers where the sender's inputs are bits, the sender and the receiver need to communicate a total of $3k + o(k) \cdot \mathsf{poly}(\lambda)$ bits. We argue that $3k$ bits are required by any protocol with a black-box and straight-line simulator. The...

Pseudorandom Correlation Functions (PCFs) allow two parties, given correlated evaluation keys, to locally generate arbitrarily many pseudorandom correlated strings, e.g. Oblivious Transfer (OT) correlations, which can then be used by the two parties to jointly run secure computation protocols. In this work, we provide a novel and simple approach for constructing PCFs for OT correlation, by relying on constrained pseudorandom functions for a class of constraints containing a weak...

We continue the study of blockcipher-based (tweakable) correlation robust hash functions, which are central building blocks of circuit garbling and oblivious-transfer extension schemes. Motivated by Roy (CRYPTO 2022), we first enhance the multi-user tweakable correlation robust notion of Guo et al. (CRYPTO 2020) with a {\it key leaking oracle} that tells the adversary whether a certain user key satisfies the adversarially-chosen predicate. We then investigate the state-of-the-art hash...

Laconic cryptography enables secure two-party computation (2PC) on unbalanced inputs with asymptotically-optimal communication in just two rounds of communication. In particular, the receiver (who sends the first-round message) holds a long input and the sender (who sends the second-round message) holds a short input, and the size of their communication to securely compute a function on their joint inputs only grows with the size of the sender's input and is independent of the receiver's...

In a seminal work, Ishai et al. (FOCS–2006) studied the viability of designing unconditionally secure protocols for key agreement and secure multi-party computation (MPC) using an anonymous bulletin board (ABB) as a building block. While their results establish the feasibility of key agreement and honest-majority MPC in the ABB model, the optimality of protocols with respect to their round and communication complexity is not studied. This paper enriches this study of unconditional security...

A secure multiparty computation (MPC) allows several parties to compute a function over their inputs while keeping their inputs private. In its basic setting, the protocol involves only parties that hold inputs. In distributed MPC, there are also external servers who perform a distributed protocol that executes the needed computation, without learning information on the inputs and outputs. Here we propose distributed protocols for several fundamental MPC functionalities. We begin with a...

While many modern cryptographic primitives have stood the test of time, attacker have already begun to expand their attacks beyond classical cryptanalysis by specifically targeting implementations. One of the most well-documented classes of such attacks are subversion (or substitution) attacks, where the attacker replaces the Implementation of the cryptographic primitive in an undetectable way such that the subverted implementation leaks sensitive information of the user during a protocol...

In recent years, actively secure SPDZ-like protocols for dishonest majority, like SPD$\mathbb Z_{2^k}$, Overdrive2k, and MHz2k, over base rings $\mathbb Z_{2^k}$ have become more and more efficient. In this paper, we present a new actively secure MPC protocol Multipars that outperforms these state-of-the-art protocols over $\mathbb Z_{2^k}$ by more than a factor of 2 in the two-party setup in terms of communication. Multipars is the first actively secure N-party protocol over $\mathbb...

This paper studies a multi-party private set union (mPSU), a fundamental cryptographic problem that allows multiple parties to compute the union of their respective datasets without revealing any additional information. We propose an efficient mPSU protocol which is secure in the presence of any number of colluding semi-honest participants. Our protocol avoids computationally expensive homomorphic operations or generic multi-party computation, thus providing an efficient solution for mPSU....

Recently, a novel secure quantum bit commitment (QBC) protocol has been proposed [29]. However, the protocol requires Alice and Bob to share Bell states in advance, making the protocol lacking in practicality. In this paper, we propose two new unconditionally secure quantum bit commitment protocols that do not require pre-shared Bell states based on entangled and non-entangled states, respectively. Their security stems from quantum mechanical properties such as quantum superposition, quantum...

We show the following unconditional results on quantum commitments in two related yet different models: 1. We revisit the notion of quantum auxiliary-input commitments introduced by Chailloux, Kerenidis, and Rosgen (Comput. Complex. 2016) where both the committer and receiver take the same quantum state, which is determined by the security parameter, as quantum auxiliary inputs. We show that computationally-hiding and statistically-binding quantum auxiliary-input commitments exist...

Password-Authenticated Key Exchange (PAKE) allows two parties to establish a common high-entropy secret from a possibly low-entropy pre-shared secret such as a password. In this work, we provide the first PAKE protocol with subversion resilience in the framework of universal composability (UC), where the latter roughly means that UC security still holds even if one of the two parties is malicious and the honest party's code has been subverted (in an undetectable manner). We achieve this...

Symmetric Private Information Retrieval (SPIR) is a protocol that protects privacy during data transmission. However, the existing SPIR focuses only on the privacy of the data to be requested on the server, without considering practical factors such as the payload that may be present during data transmission. This could seriously prevent SPIR from being applied to many complex data scenarios and hinder its further expansion. To solve such problems, we propose a primitive (PSKPIR) for...

We consider the problem of creating, or issuing, zero-knowledge proofs obliviously. In this setting, a prover interacts with a verifier to produce a proof, known only to the verifier. The resulting proof is transferable and can be verified non-interactively by anyone. Crucially, the actual proof cannot be linked back to the interaction that produced it. This notion generalizes common approaches to designing blind signatures, which can be seen as the special case of proving "knowledge of a...

In this work we study the problem of minimizing the round complexity for securely evaluating multiparty functionalities while making black-box use of polynomial time assumptions. In Eurocrypt 2016, Garg et al. showed that, assuming all parties have access to a broadcast channel, then at least four rounds of communication are required to securely realize non-trivial functionalities in the plain model. A sequence of works follow-up the result of Garg et al. matching this lower bound under a...

Zero-knowledge proof or argument systems for generic NP statements (such as circuit satisfiability) have typically been instantiated with cryptographic commitment schemes; this implies that the security of the proof system (e.g., computational or statistical) depends on that of the chosen commitment scheme. The MPC-in-the-Head paradigm (Ishai et al., JoC 2009) uses the same approach to construct zero-knowledge systems from the simulated execution of secure multiparty computation...

A recent series of works (Hecht, IACR ePrint, 2020–2021) propose to build post-quantum public-key encapsulation, digital signatures, group key agreement and oblivious transfer from "R-propped" variants of the Symmetrical Decomposition and Discrete Logarithm problems for matrix groups over $\mathbb{F}_{2^8}$. We break all four proposals by presenting a linearisation attack on the Symmetrical Decomposition platform, a forgery attack on the signature scheme, and a demonstration of the...

Correlated secret randomness is a useful resource for secure computation protocols, often enabling dramatic speedups compared to protocols in the plain model. This has motivated a line of work on identifying and securely generating useful correlations. Different kinds of correlations can vary greatly in terms of usefulness and ease of generation. While there has been major progress on efficiently generating oblivious transfer (OT) correlations, other useful kinds of correlations are...

Oblivious Pseudo-Random Functions (OPRFs) are a central tool for building modern protocols for authentication and distributed computation. For example, OPRFs enable simple login protocols that do not reveal the password to the provider, which helps to mitigate known shortcomings of password-based authentication such as password reuse or mix-up. Reliable treatment of passwords becomes more and more important as we login to a multitude of services with different passwords in our daily...

We give the first construction of a fully black-box round-optimal secure multiparty computation (MPC) protocol in the plain model. Our protocol makes black-box use of a sub-exponentially secure two-message statistical sender private oblivious transfer (SSP-OT), which in turn can be based on (sub-exponential variants of) almost all of the standard cryptographic assumptions known to imply public-key cryptography.

We present a new framework for building round-optimal (two-round) $adaptively$ secure MPC. We show that a relatively weak notion of OT that we call $indistinguishability \ OT \ with \ receiver \ oblivious \ sampleability$ (r-iOT) is enough to build two-round, adaptively secure MPC against $malicious$ adversaries in the CRS model. We then show how to construct r-iOT from CDH, LPN, or isogeny-based assumptions that can be viewed as group actions (such as CSIDH and CSI-FiSh). This yields the...

In oblivious finite automata evaluation, one party holds a private automaton, and the other party holds a private string of characters. The objective is to let the parties know whether the string is accepted by the automaton or not, while keeping their inputs secret. The applications include DNA searching, pattern matching, and more. Most of the previous works are based on asymmetric cryptographic primitives, such as homomorphic encryption and oblivious transfer. These primitives are...

As a fundamental operation in fixed-point arithmetic, truncation can bring the product of two fixed-point integers back to the fixed-point representation. In large-scale applications like privacy-preserving machine learning, it is essential to have faithful truncation that accurately eliminates both big and small errors. In this work, we improve and extend the results of the oblivious transfer based faithful truncation protocols initialized by Cryptflow2 (Rathee et al., CCS 2020)....

We instantiate the hash-then-evaluate paradigm for pseudorandom functions (PRFs), $\mathsf{PRF}(k, x) := \mathsf{wPRF}(k, \mathsf{RO}(x))$, which builds a PRF $\mathsf{PRF}$ from a weak PRF $\mathsf{wPRF}$ via a public preprocessing random oracle $\mathsf{RO}$. In applications to secure multiparty computation (MPC), only the low-complexity wPRF performs secret-depending operations. Our construction replaces RO by $f(k_H , \mathsf{elf}(x))$, where $f$ is a non-adaptive PRF and the key $k_H$...

In the dishonest-majority setting, secure multiparty computation (MPC) with identifiable abort (IA) guarantees that honest parties can identify and agree upon at least one cheating party if the protocol does not produce an output. Known MPC constructions with IA rely on generic zero-knowledge proofs, adaptively secure oblivious transfer (OT) protocols, or homomorphic primitives, and thus incur a substantial penalty with respect to protocols that abort without identifiability. We introduce...

Statistical sender privacy (SSP) is the strongest achievable security notion for two-message oblivious transfer (OT) in the standard model, providing statistical security against malicious receivers and computational security against semi-honest senders. In this work we provide a novel construction of SSP OT from the Decisional Diffie-Hellman (DDH) and the Learning Parity with Noise (LPN) assumptions achieving (asymptotically) optimal amortized communication complexity, i.e. it achieves rate...

Consider the standard setting of two-party computation where the sender has a secret function $f$ and the receiver has a secret input $x$ and the output $f(x)$ is delivered to the receiver at the end of the protocol. Let us consider the unidirectional message model where only one party speaks in each round. In this setting, Katz and Ostrovsky (Crypto 2004) showed that at least four rounds of interaction between the parties are needed in the plain model (i.e., no trusted setup) if the...

The relationship between oblivious transfer (OT) and public-key encryption (PKE) has been studied by Gertner et al. (FOCS 2000). They showed that OT can be constructed from special types of PKE, i.e., PKE with oblivious sampleability of public keys or ciphertexts. In this work, we give new black-box constructions of OT from PKE without any oblivious sampleability. Instead, we require that the PKE scheme is rerandomizable, meaning that one can use the public key to rerandomize a ciphertext...

We present a new method for transforming zero-knowledge protocols in the designated verifier setting into public-coin protocols, which can be made non-interactive and publicly verifiable. Our transformation applies to a large class of ZK protocols based on oblivious transfer. In particular, we show that it can be applied to recent, fast protocols based on vector oblivious linear evaluation (VOLE), with a technique we call VOLE-in-the-head, upgrading these protocols to support public...

Considering password-based authentication technique, password memorability is a real challenge on users. Hence, password reuse across different web applications is a common trend among users which makes websites vulnerable to credential stuffing attack. A solution as password manager helps the users to create random passwords for different websites on the user machine. However, it has practical challenges. Password database breach detection is another related and challenging task....

Given $\ell$ parties with sets $X_1, \dots, X_\ell$ of size $n$, we would like to securely compute the intersection $\cap_{i=1}^\ell X_i$, if it is larger than $n-t$ for some threshold $t$, without revealing any other additional information. It has previously been shown (Ghosh and Simkin, Crypto 2019) that this function can be securely computed with a communication complexity that only depends on $t$ and in particular does not depend on $n$. For small values of $t$, this results in protocols...

The recent development of pseudorandom correlation generators (PCG) holds tremendous promise for highly efficient MPC protocols. Among other correlations, PCGs allow for the efficient generation of oblivious transfer (OT) and vector oblivious linear evaluations (VOLE) with sublinear communication and concretely good computational overhead. This type of PCG makes use of a so-called LPN-friendly error-correcting code. That is, for large dimensions the code should have very efficient encoding...

In the framework of Impagliazzo's five worlds, a distinction is often made between two worlds, one where public-key encryption exists (Cryptomania), and one in which only one-way functions exist (MiniCrypt). However, the boundaries between these worlds can change when quantum information is taken into account. Recent work has shown that quantum variants of oblivious transfer and multi-party computation, both primitives that are classically in Cryptomania, can be constructed from one-way...

Lossy trapdoor functions (LTFs) constitute a useful and versatile cryptographic building block. LTFs have found applications in various types of encryption schemes, are closely connected to statistically secure oblivious transfer protocols, and have led to the first constructions of group-based trapdoor functions. However, with one recent exception, all known group-based LTFs are comparatively inefficient, and in particular suffer from large images. In this work, we attempt to explain this...

Topology-Hiding Computation (THC) enables parties to securely compute a function on an incomplete network without revealing the network topology. It is known that secure computation on a complete network can be based on oblivious transfer (OT), even if a majority of the participating parties are corrupt. In contrast, THC in the dishonest majority setting is only known from assumptions that imply (additively) homomorphic encryption, such as Quadratic Residuosity, Decisional Diffie-Hellman,...

Secure computation often benefits from the use of correlated randomness to achieve fast, non-cryptographic online protocols. A recent paradigm put forth by Boyle $\textit{et al.}$ (CCS 2018, Crypto 2019) showed how pseudorandom correlation generators (PCG) can be used to generate large amounts of useful forms of correlated (pseudo)randomness, using minimal interactions followed solely by local computations, yielding silent secure two-party computation protocols (protocols where the...

The computational overhead of a cryptographic task is the asymptotic ratio between the computational cost of securely realizing the task and that of realizing the task with no security at all. Ishai, Kushilevitz, Ostrovsky, and Sahai (STOC 2008) showed that secure two-party computation of Boolean circuits can be realized with constant computational overhead, independent of the desired level of security, assuming the existence of an oblivious transfer (OT) protocol and a local...

We present a three-round protocol for threshold ECDSA signing with malicious security against a dishonest majority, which information-theoretically UC-realizes a standard threshold signing functionality, assuming only ideal commitment and two-party multiplication primitives. Our protocol combines an intermediate representation of ECDSA signatures that was recently introduced by Abram et al. (Eurocrypt'22) with an efficient statistical consistency check reminiscent of the ones used by the...

Motivated by the privacy requirements in network intrusion detection and DNS policy checking, we have developed a suite of protocols and algorithms for regular expression matching with enhanced privacy: - A new regular expression matching algorithm that is oblivious to the input strings, of which the complexity is only $O(mn)$ where $m$ and $n$ are the length of strings and the regular expression respectively. It is achieved by exploiting the structure of the Thompson nondeterministic...

Oblivious Pseudorandom Functions (OPRFs) are an elementary building block in cryptographic and privacy-preserving applications. However, while there are numerous pre-quantum secure OPRF constructions, few options exist in a post-quantum secure setting, and of those even fewer are practical for modern-day applications. In this work, we focus on isogeny group actions, as the associated low bandwidth leads to efficient constructions. Our results focus on the Naor-Reingold OPRF. We introduce...

In this paper, we propose the first linear two-party secure-computation private set intersection (PSI) protocol, in the semi-honest adversary model, computing the following functionality. One of the parties ($P_X$) inputs a set of items $X = \{x_j \mid 1 \le j \le n_X\}$, whereas the other party ($P_Y$) inputs a set of items $Y = \{y_i \mid 1\le i \le n_Y \}$ and a set of corresponding data pairs $D_Y = \{ (d_i^0,d_i^1) \mid 1 \le i \le n_Y\}$ having the same cardinality with $Y$. While...

Can a sender non-interactively transmit one of two strings to a receiver without knowing which string was received? Does there exist minimally-interactive secure multiparty computation that only makes (black-box) use of symmetric-key primitives? We provide affirmative answers to these questions in a model where parties have access to shared EPR pairs, thus demonstrating the cryptographic power of this resource. First, we construct a one-shot (i.e., single message) string oblivious...

Gradient Boosting Decision Tree (GBDT) and its variants are widely used in industry, due to their strong interpretability. Secure multi-party computation allows multiple data owners to compute a function jointly while keeping their input private. In this work, we present Squirrel, a two-party GBDT training framework on a vertically split dataset, where two data owners each hold different features of the same data samples. Squirrel is private against semi-honest adversaries, and no sensitive...

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...

Secure computation enables mutually distrusting parties to jointly compute a function on their secret inputs, while revealing nothing beyond the function output. A long-running challenge is understanding the required communication complexity of such protocols---in particular, when communication can be sublinear in the circuit representation size of the desired function. For certain functions, such as Private Information Retrieval (PIR), this question extends to even sublinearity in the input...

Laconic cryptography is an emerging paradigm that enables cryptographic primitives with sublinear communication complexity in just two messages. In particular, a two-message protocol between Alice and Bob is called laconic if its communication and computation complexity are essentially independent of the size of Alice's input. This can be thought of as a dual notion of fully-homomorphic encryption, as it enables "Bob-optimized" protocols. This paradigm has led to tremendous progress in...

Long-term security, a variant of Universally Composable (UC) security introduced by Müller-Quade and Unruh (JoC ’10), allows to analyze the security of protocols in a setting where all hardness assumptions no longer hold after the protocol execution has finished. Such a strict notion is highly desirable when properties such as input privacy need to be guaranteed for a long time, e.g. zero-knowledge proofs for secure electronic voting. Strong impossibility results rule out so-called...

It is an important question to find constructions of quantum cryptographic protocols which rely on weaker computational assumptions than classical protocols. Recently, it has been shown that oblivious transfer and multi-party computation can be constructed from one-way functions, whereas this is impossible in the classical setting in a black-box way. In this work, we study the question of building quantum public-key encryption schemes from one-way functions and even weaker assumptions....

We provide a generic construction to turn any classical Zero-Knowledge (ZK) protocol into a composable (quantum) oblivious transfer (OT) protocol, mostly lifting the round-complexity properties and security guarantees (plain-model/statistical security/unstructured functions…) of the ZK protocol to the resulting OT protocol. Such a construction is unlikely to exist classically as Cryptomania is believed to be different from Minicrypt. In particular, by instantiating our construction using...

Actively secure two-party computation (2PC) is one of the canonical building blocks in modern cryptography. One main goal for designing actively secure 2PC protocols is to reduce the communication overhead, compared to semi-honest 2PC protocols. In this paper, we make significant progress in closing this gap by proposing two new actively secure constant-round 2PC protocols, one with one-way communication of $2\kappa+5$ bits per AND gate (for $\kappa$-bit computational security and any...

We study the complexity of two-party secure arithmetic computation where the goal is to evaluate an arithmetic circuit over a finite field $F$ in the presence of an active (aka malicious) adversary. In the passive setting, Applebaum et al. (Crypto 2017) constructed a protocol that only makes a *constant* (amortized) number of field operations per gate. This protocol uses the underlying field $F$ as a black box, makes black-box use of (standard) oblivious transfer, and its security is based...

In this work we apply the Type-Safe (TS) generic group model, recently introduced by Zhandry (2022), to the more general setting of group actions and extend it to the universal composability (UC) framework of Canetti (2000). We then relax this resulting model, that we call UC-TS, to define an algebraic action framework (UC-AA), where the adversaries can behave algebraically, similarly to the algebraic group model (AGM), but for group actions. Finally, we instantiate UC-AA with isogeny-based...

In p-noisy coin-tossing, Alice and Bob obtain fair coins which are of opposite values with probability p. Its Oblivious-Transfer (OT) complexity refers to the least number of OTs required by a semi-honest perfectly secure 2-party protocol for this task. We show a tight bound of Θ(log 1/p) for the OT complexity of p-noisy coin-tossing. This is the first instance of a lower bound for OT complexity that is independent of the input/output length of the function. We obtain our result by...

In the setting of subversion, an adversary tampers with the machines of the honest parties thus leaking the honest parties' secrets through the protocol transcript. The work of Mironov and Stephens-Davidowitz (EUROCRYPT’15) introduced the idea of reverse firewalls (RF) to protect against tampering of honest parties' machines. All known constructions in the RF framework rely on the malleability of the underlying operations in order for the RF to rerandomize/sanitize the transcript. RFs are...

The notion of Endemic Oblivious Transfer (EOT) was introduced by Masny and Rindal (CCS'19). EOT offers a weaker security guarantee than the conventional random OT; namely, the malicious parties can fix their outputs arbitrarily. The authors presented a 1-round UC-secure EOT protocol under a tailor-made and non-standard assumption, Choose-and-Open DDH, in the RO model. In this work, we systematically study EOT in the UC/GUC framework. We present a new 1-round UC-secure EOT construction...

Alon et al. (CRYPTO 2021) introduced a multiparty quantum computation protocol that is secure with identifiable abort (MPQC-SWIA). However, their protocol allows only inside MPQC parties to know the identity of malicious players. This becomes problematic when two groups of people disagree and need a third party, like a jury, to verify who the malicious party is. This issue takes on heightened significance in the quantum setting, given that quantum states may exist in only a single copy....

We present the first round-optimal and plausibly quantum-safe oblivious transfer (OT) and multi-party computation (MPC) protocols from the computational CSIDH assumption - the weakest and most widely studied assumption in the CSIDH family of isogeny-based assumptions. We obtain the following results: - The first round-optimal maliciously secure OT and MPC protocols in the plain model that achieve (black-box) simulation-based security while relying on the computational CSIDH...

GGM tree is widely used in the design of correlated oblivious transfer (COT), subfield vector oblivious linear evaluation (sVOLE), distributed point function (DPF), and distributed comparison function (DCF). Often, the cost associated with GGM tree dominates the computation and communication of these protocols. In this paper, we propose a suite of optimizations that can reduce this cost by half. • Halving the cost of COT and sVOLE. Our COT protocol introduces extra correlation to each...

We study the security of the random oblivious transfer extension protocol of Keller, Orsini, and Scholl (CRYPTO '15), whose security proof was recently invalidated by Roy (CRYPTO '22). We show that KOS is asymptotically secure. Our proof involves a subtle analysis of the protocol's "correlation check", and introduces several new techniques. We also study the protocol's concrete security. We establish concrete security for security parameter values on the order of 5,000. We present evidence...

The Non-Interactive Anonymous Router (NIAR) model was introduced by Shi and Wu [SW21] as an alternative to conventional solutions to the anonymous routing problem, in which a set of senders wish to send messages to a set of receivers. In contrast to most known approaches to support anonymous routing (e.g. mix-nets, DC-nets, etc.) which rely on a network of routers communicating with users via interactive protocols, the NIAR model assumes a $single$ router and is inherently...

The existence of one-way functions is one of the most fundamental assumptions in classical cryptography. In the quantum world, on the other hand, there are evidences that some cryptographic primitives can exist even if one-way functions do not exist [Morimae and Yamakawa, CRYPTO 2022; Ananth, Qian, and Yuen, CRYPTO 2022]. We therefore have the following important open problem in quantum cryptography: What is the most fundamental element in quantum cryptography? In this direction, Brakerski,...

We give round-optimal {\em black-box} constructions of two-party and multiparty protocols in the common random/reference string (CRS) model, with security against malicious adversaries, based on any two-round oblivious transfer (OT) protocol in the same model. Specifically, we obtain two types of results. \begin{enumerate} \item {\bf Two-party protocol.} We give a (two-round) {\it two-sided NISC} protocol that makes black-box use of two-round (malicious-secure) OT in the CRS model....

In recent years, functional encryption (FE) has established itself as one of the fundamental primitives in cryptography. The choice of model of computation to represent the functions associated with the functional keys plays a critical role in the complexity of the algorithms of an FE scheme. Historically, the functions are represented as circuits. However, this results in the decryption time of the FE scheme growing proportional to not only the worst case running time of the function but...

In the classical notion of multiparty computation (MPC), an honest party learning private inputs of others, either as a part of protocol specification or due to a malicious party's unspecified messages, is not considered a potential breach. Several works in the literature exploit this seemingly minor loophole to achieve the strongest security of guaranteed output delivery via a trusted third party, which nullifies the purpose of MPC. Alon et al. (CRYPTO 2020) presented the notion of Friends...

We introduce a new notion of public key encryption, knowledge encryption, for which its ciphertexts can be reduced to the public-key, i.e., any algorithm that can break the ciphertext indistinguishability can be used to extract the (partial) secret key. We show that knowledge encryption can be built solely on any two-round oblivious transfer with game-based security, which are known based on various standard (polynomial-hardness) assumptions, such as the DDH, the Quadratic($N^{th}$)...

We present a new template for building oblivious transfer from quantum information that we call the ``fixed basis'' framework. Our framework departs from prior work (eg., Crepeau and Kilian, FOCS '88) by fixing the correct choice of measurement basis used by each player, except for some hidden trap qubits that are intentionally measured in a conjugate basis. We instantiate this template in the quantum random oracle model (QROM) to obtain simple protocols that implement, with security...

We present a new framework for building round-optimal one-sided statistically secure two party computation (2PC) protocols in the plain model. We demonstrate that a relatively weak notion of oblivious transfer (OT), namely a three round elementary oblivious transfer $\textsf{eOT}$ with statistical receiver privacy, along with a non-interactive commitment scheme suffices to build a one-sided statistically secure two party computation protocol with black-box simulation. Our framework enables...

In the classical model of computation, it is well established that one-way functions (OWF) are minimal for computational cryptography: They are essential for almost any cryptographic application that cannot be realized with respect to computationally unbounded adversaries. In the quantum setting, however, OWFs appear not to be essential (Kretschmer 2021; Ananth et al., Morimae and Yamakawa 2022), and the question of whether such a minimal primitive exists remains open. We consider EFI...

Secure multiparty computation can often utilize a trusted source of correlated randomness to achieve better efficiency. A recent line of work, initiated by Boyle et al. (CCS 2018, Crypto 2019), showed how useful forms of correlated randomness can be generated using a cheap, one-time interaction, followed by only "silent" local computation. This is achieved via a pseudorandom correlation generator (PCG), a deterministic function that stretches short correlated seeds into long instances of a...

A pseudorandom correlation generator (PCG) is a recent tool for securely generating useful sources of correlated randomness, such as random oblivious transfers (OT) and vector oblivious linear evaluations (VOLE), with low communication cost. We introduce a simple new design for PCGs based on so-called expand-accumulate codes, which first apply a sparse random expander graph to replicate each message entry, and then accumulate the entries by computing the sum of each prefix. Our design...

We give black-box, round-optimal protocol compilers from semi-honest security to malicious security in the Random Oracle Model (ROM) and in the 1-out-of-2 oblivious transfer (OT) correlations model. We use our compilers to obtain the following black-box constructions of general-purpose protocols for secure computation tolerating static, malicious corruptions of all-but-one participants: \begin{itemize} \item A two-round, two-party protocol in the random oracle model, making...

We revisit the problem of constant-round malicious secure two-party computation by considering the use of simple correlations, namely sources of correlated randomness that can be securely generated with sublinear communication complexity and good concrete efficiency. The current state-of-the-art protocol of Katz et al. (Crypto 2018) achieves malicious security by realizing a variant of the authenticated garbling functionality of Wang et al. (CCS 2017). Given oblivious transfer...

Machine learning algorithms crucially depend on non-linear mathematical functions such as division (for normalization), exponentiation (for softmax and sigmoid), tanh (as an activation function), logarithm (for cross-entropy loss), and square root (for back-propagation of normalization layers). However, when machine learning is performed over secure computation, these protocols incur a large communication overhead and high round complexity. In this work, we propose new multi-party...

In this work we present a novel actively secure multiparty computation protocol in the dishonest majority setting, where the computation domain is a ring of the type $\mathbb{Z}_{2^k}$. Instead of considering an "extension ring" of the form $\mathbb{Z}_{2^{k+\kappa}}$ as in SPD$\mathbb{Z}_{2^k}$ (Cramer et al, CRYPTO 2018) and its derivatives, we make use of an actual ring extension, or more precisely, a Galois ring extension $\mathbb{Z}_{p^k}[\mathtt{X}]/(h(\mathtt{X}))$ of large enough...

Multiparty randomized encodings (Applebaum, Brakerski, and Tsabary, SICOMP 2021) reduce the task of securely computing a complicated multiparty functionality $f$ to the task of securely computing a simpler functionality $g$. The reduction is non-interactive and preserves information-theoretic security against a passive (semi-honest) adversary, also referred to as privacy. The special case of a degree-2 encoding $g$ (2MPRE) has recently found several applications to secure multiparty...