We put forth a new paradigm for secure multi-party computation (MPC) in the preprocessing model, where a feasible one-time setup can enable a lifetime of efficient online secure computations. Our protocols match the security guarantees and low costs of the cheapest category of MPC solutions, namely 3-party protocols (3PC) secure against a single malicious party, with the qualitative advantages that one party communicates data sublinear in the circuit size, and can go offline after its initial messages. This “2+ 1“-party structure can alternatively be instantiated between 2 parties with the aid of an (untrusted) dealer. Within such existing protocols, we provide comparable online performance while improving the storage and offline dealer-to-party communication requirements by more than 3 orders of magnitude. At the technical level, we build on the Fully Linear Interactive Oracle Proof (FLIOP)-based protocol design of Boyle et al. (CRYPTO 2021). We provide an extensive assortment of algorithmic and implementation-level optimizations, design efficient distributed proofs of well-formedness of complex FLIOP correlations, and make them circuit-independent. We implement and benchmark our end-to-end system against the state of the art in the 2+1 regime, a dealer-aided variant of SPDZ for Boolean circuits. We additionally extend our techniques to the$(n+1)$party setting, where a dealer aids general dishonest-majority MPC, and provide a variant of the protocol which further achieves security with “identifiable abort.”

A Distributed Point Function (DPF) is a crypto-graphic primitive used for compressing additive secret shares of a secret unit vector across two parties. Many DPF applications require compressed shares of a sparse weight- t vector, namely a Distributed Multi-Point Function (DMPF). Despite the strong motivation and prior optimization efforts, in most use cases the best practical implementation of DMPF is still a simple brute-force combination of$t$independent DPFs. We present new constructions and optimized implementations of DMPFs in different parameter regimes, providing significant efficiency savings over existing approaches. We showcase our new constructions within applications of pseu-dorandom correlation generators (PCGs) and 2-server private set intersection (PSI). Incorporating our tools into the state-of-the-art PCG for “silent” generation of binary multiplication triples (FOLEAGE, Bombar et al, ePrint'24) yields a x2.68 improvement in throughput, with only x 1.4 blowup in the seed size. On a single core of our benchmark machine, our implementation silently generates up to 22.1 million triples per second, outperforming even the best “non-silent” protocol (Roy, CRYPTO'22), which generates 16 million triples per second.

Abstract Broadcast protocols enable a set of n parties to agree on the input of a designated sender, even facing attacks by malicious parties. In the honest-majority setting, randomization and cryptography were harnessed to achieve low-communication broadcast with sub-quadratic total communication and balanced sub-linear cost per party. However, comparatively little is known in the dishonest-majority setting. Here, the most communication-efficient constructions are based on Dolev and Strong (SICOMP ’83), and sub-quadratic broadcast has not been achieved. On the other hand, the only nontrivial $$\omega (n)$$ ω ( n ) communication lower bounds are restricted to deterministic protocols, or against strong adaptive adversaries that can perform “after the fact” removal of messages. We provide new communication lower bounds in this space, which hold against arbitrary cryptography and setup assumptions, as well as a simple sub-quadratic broadcast protocol showing near tightness of our first bound.

We study the complexity of memory checkers with computational security and prove the first general tight lower bound. Memory checkers, first introduced over 30 years ago by Blum, Evans, Gemmel, Kannan, and Naor (FOCS ’91, Algorithmica ’94), allow a user to store and maintain a large memory on a remote and unreliable server by using small trusted local storage. The user can issue instructions to the server and after every instruction, obtain either the correct value or a failure (but not an incorrect answer) with high probability. The main complexity measure of interest is the size of the local storage and the number of queries the memory checker makes upon every logical instruction. The most efficient known construction has query complexity \(O(\log n/\log \log n)\) and local space proportional to a computational security parameter, assuming one-way functions, where n is the logical memory size. Dwork, Naor, Rothblum, and Vaikuntanathan (TCC ’09) showed that for a restricted class of “deterministic and non-adaptive” memory checkers, this construction is optimal, up to constant factors. However, going beyond the small class of deterministic and non-adaptive constructions has remained a major open problem. In this work, we fully resolve the complexity of memory checkers by showing that any construction with local space p and query complexity q must satisfy \(\begin{equation*} p \ge \frac{n}{(\log n)^{O(q)}} \;. \end{equation*}\) This implies, as a special case, that \(q\ge \Omega (\log n/\log \log n)\) in any scheme, assuming that \(p\le n^{1-\varepsilon }\) for \(\varepsilon \gt 0\) . The bound applies to any scheme with computational security, completeness \(2/3\) , and inverse polynomial in n soundness (all of which make our lower bound only stronger). We further extend the lower bound to schemes where the read complexity \(q_r\) and write complexity \(q_w\) differ. For instance, we show the tight bound that if \(q_r=O(1)\) and \(p\le n^{1-\varepsilon }\) for \(\varepsilon \gt 0\) , then \(q_w\ge n^{\Omega (1)}\) . This is the first lower bound, for any non-trivial class of constructions, showing a read-write query complexity trade-off. Our proof is via a delicate compression argument showing that a “too good to be true” memory checker can be used to compress random bits of information. We draw inspiration from tools recently developed for lower bounds for relaxed locally decodable codes. However, our proof itself significantly departs from these works, necessitated by the differences between settings.

We revisit the problem of concretely efficient secure computation of sorting and selection (e.g., maximum, median, or top-k) on secret-shared data, focusing on the case of security against a single semi-honest party. Previous solutions either have a high communication overhead or many rounds of interaction, even when allowing input-independent preprocessing.

We study the complexity of memory checkers with computational security and prove the first general tight lower bound.

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 offers the following advantages compared to state-of-the-art PCG constructions: Competitive concrete efficiency backed by provable security against relevant classes of attacks; An offline-online mode that combines near-optimal cache-friendliness with simple parallelization; Concretely efficient extensions to pseudorandom correlation functions , which enable incremental generation of new correlation instances on demand, and to new kinds of correlated randomness that include circuit-dependent correlations. To further improve the concrete computational cost, we propose a method for speeding up a full-domain evaluation of a puncturable pseudorandom function (PPRF). This is independently motivated by other cryptographic applications of PPRFs.

Byzantine agreement (BA), the task of n parties to agree on one of their input bits in the face of malicious agents, is a powerful primitive that lies at the core of a vast range of distributed protocols. Interestingly, in BA protocols with the best overall communication, the demands of the parties are highly unbalanced: the amortized cost is Õ(1) bits per party, but some parties must send Ω(n) bits. In best known balanced protocols, the overall communication is sub-optimal, with each party communicating Õ(√n).

This paper presents a new protocol for solving the private heavy-hitters problem. In this problem, there are many clients and a small set of data-collection servers. Each client holds a private bitstring. The servers want to recover the set of all popular strings, without learning anything else about any client’s string. A web-browser vendor, for instance, can use our protocol to figure out which homepages are popular, without learning any user’s homepage. We also consider the simpler private subset-histogram problem, in which the servers want to count how many clients hold strings in a particular set without revealing this set to the clients.Our protocols use two data-collection servers and, in a protocol run, each client send sends only a single message to the servers. Our protocols protect client privacy against arbitrary misbehavior by one of the servers and our approach requires no public-key cryptography (except for secure channels), nor general-purpose multiparty computation. Instead, we rely on incremental distributed point functions, a new cryptographic tool that allows a client to succinctly secret-share the labels on the nodes of an exponentially large binary tree, provided that the tree has a single non-zero path. Along the way, we develop new general tools for providing malicious security in applications of distributed point functions.A limitation of our heavy-hitters protocol is that it reveals to the servers slightly more information than the set of popular strings itself. We precisely define and quantify this leakage and explain how to ameliorate its effects. In an experimental evaluation with two servers on opposite sides of the U.S., the servers can find the 200 most popular strings among a set of 400,000 client-held 256-bit strings in 54 minutes. Our protocols are highly parallelizable. We estimate that with 20 physical machines per logical server, our protocols could compute heavy hitters over ten million clients in just over one hour of computation.

Correlated secret randomness is a useful resource for many cryptographic applications. We initiate the study of pseudorandom correlation functions (PCFs) that offer the ability to securely generate virtually unbounded sources of correlated randomness using only local computation. Concretely, a PCF is a keyed function Fk such that for a suitable joint key distribution ( k0, k1), the outputs (fk0(x), fk1(x)) are indistinguishable from instances of a given target correlation. An essential security requirement is that indistinguishability hold not only for outsiders, who observe the pairs of outputs, but also for insiders who know one of the two keys. We present efficient constructions of PCFs for a broad class of useful correlations, including oblivious transfer and multiplication triple correlations, from a variable-density variant of the Learning Parity with Noise assumption (VDLPN). We also present several cryptographic applications that motivate our efficient PCF constructions. The VDLPN assumption is independently motivated by two additional applications. First, different flavors of this assumption give rise to weak pseudorandom function candidates in depth-2 AC0[⊕] that can be conjectured to have subexponential security, matching the best known learning algorithms for this class. This is contrasted with the quasipolynomial security of previous (higher-depth) AC0[⊕] candidates. We support our conjectures by proving resilience to several classes of attacks. Second, VDLPN implies simple constructions of pseudorandom generators and weak pseudorandom functions with security against XOR related-key attacks.

Reductions between problems, the mainstay of theoretical computer science, efficiently map an instance of one problem to an instance of another in such a way that solving the latter allows solving the former. The subject of this work is "lossy" reductions, where the reduction loses some information about the input instance. We show that such reductions, when they exist, have interesting and powerful consequences for lifting hardness into "useful" hardness, namely cryptography. Our first, conceptual, contribution is a definition of lossy reductions in the language of mutual information. Roughly speaking, our definition says that a reduction C is t-lossy if, for any distribution X over its inputs, the mutual information I(X;C(X)) ≤ t. Our treatment generalizes a variety of seemingly related but distinct notions such as worst-case to average-case reductions, randomized encodings (Ishai and Kushilevitz, FOCS 2000), homomorphic computations (Gentry, STOC 2009), and instance compression (Harnik and Naor, FOCS 2006). We then proceed to show several consequences of lossy reductions: 1. We say that a language L has an f-reduction to a language L' for a Boolean function f if there is a (randomized) polynomial-time algorithm C that takes an m-tuple of strings X = (x_1,…,x_m), with each x_i ∈ {0,1}^n, and outputs a string z such that with high probability, L'(z) = f(L(x_1),L(x_2),…,L(x_m)). Suppose a language L has an f-reduction C to L' that is t-lossy. Our first result is that one-way functions exist if L is worst-case hard and one of the following conditions holds: - f is the OR function, t ≤ m/100, and L' is the same as L - f is the Majority function, and t ≤ m/100 - f is the OR function, t ≤ O(m log n), and the reduction has no error This improves on the implications that follow from combining (Drucker, FOCS 2012) with (Ostrovsky and Wigderson, ISTCS 1993) that result in auxiliary-input one-way functions. 2. Our second result is about the stronger notion of t-compressing f-reductions - reductions that only output t bits. We show that if there is an average-case hard language L that has a t-compressing Majority reduction to some language for t=m/100, then there exist collision-resistant hash functions. This improves on the result of (Harnik and Naor, STOC 2006), whose starting point is a cryptographic primitive (namely, one-way functions) rather than average-case hardness, and whose assumption is a compressing OR-reduction of SAT (which is now known to be false unless the polynomial hierarchy collapses). Along the way, we define a non-standard one-sided notion of average-case hardness, which is the notion of hardness used in the second result above, that may be of independent interest.

We consider the problem of securely generating useful instances of two-party correlations, such as many independent copies of a random oblivious transfer (OT) correlation, using a small amount of communication. This problem is motivated by the goal of secure computation with silent preprocessing, where a low-communication input-independent setup, followed by local ("silent") computation, enables a lightweight "non-cryptographic" online phase once the inputs are known. Recent works of Boyle et al. (CCS 2018, Crypto 2019) achieve this goal with good concrete efficiency for useful kinds of two-party correlations, including OT correlations, under different variants of the Learning Parity with Noise (LPN) assumption, and using a small number of "base'' oblivious transfers. The protocols of Boyle et al. have several limitations. First, they require a large number of communication rounds. Second, they are only secure against semi-honest parties. Finally, their concrete efficiency estimates are not backed by an actual implementation. In this work we address these limitations, making three main contributions: Eliminating interaction. Under the same assumption, we obtain the first concretely efficient 2-round protocols for generating useful correlations, including OT correlations, in the semi-honest security model. This implies the first efficient 2-round OT extension protocol of any kind and, more generally, protocols for non-interactive secure computation (NISC) that are concretely efficient and have the silent preprocessing feature. Malicious security. We provide security against malicious parties without additional interaction and with only a modest overhead; prior to our work, no similar protocols were known with any number of rounds. Implementation. Finally, we implemented, optimized, and benchmarked our 2-round OT extension protocol, demonstrating that it offers a more attractive alternative to the OT extension protocol of Ishai et al. (Crypto 2003) in many realistic settings.

Secure multiparty computation enables a set of parties to securely carry out a joint computation on their private inputs without revealing anything but the output. A particularly motivated setting is that of three parties with a single corruption (hereafter denoted 3PC). This 3PC setting is particularly appealing for two main reasons: (1) it admits more efficient MPC protocols than in other standard settings; (2) it allows in principle to achieve full security (and fairness). Highly efficient protocols exist within this setting with security against a semi-honest</> adversary; however, a significant gap remains between these and protocols with stronger security against a malicious</> adversary. In this paper, we narrow this gap within concretely efficient protocols. More explicitly, we have the following contributions: Concretely Efficient Malicious 3PC. We present an optimized 3PC protocol for arithmetic circuits over rings with (amortized) communication of 1 ring element per multiplication gate per party, matching the best semi-honest protocols. The protocol applies also to Boolean circuits, significantly improving over previous protocols even for small circuits. Our protocol builds on recent techniques of Boneh et al. (Crypto 2019) for sublinear zero-knowledge proofs on distributed data, together with an efficient semi-honest protocol based on replicated secret sharing (Araki et al., CCS 2016). We present a concrete analysis of communication and computation costs, including several optimizations. For example, for 40-bit statistical security, and Boolean circuit with a million (nonlinear) gates, the overhead on top of the semi-honest protocol can involve less than 0.5KB of communication for the entire circuit,</> while the computational overhead is dominated by roughly 30 multiplications per gate in the field F247. In addition, we implemented and benchmarked the protocol for varied circuit sizes. Full Security. We augment the 3PC protocol to further provide full security</> (with guaranteed output delivery) while maintaining amortized 1 ring element communication per party per multiplication gate, and with hardly any impact on concrete efficiency. This is contrasted with the best previous 3PC protocols from the literature, which allow a corrupt party to mount a denial-of-service attack without being detected.

In this paper, we develop improved techniques for defending against adversarial examples at scale. First, we implement the state of the art version of adversarial training at unprecedented scale on ImageNet and investigate whether it remains effective in this setting - an important open scientific question (Athalye et al., 2018). Next, we introduce enhanced defenses using a technique we call logit pairing, a method that encourages logits for pairs of examples to be similar. When applied to clean examples and their adversarial counterparts, logit pairing improves accuracy on adversarial examples over vanilla adversarial training; we also find that logit pairing on clean examples only is competitive with adversarial training in terms of accuracy on two datasets. Finally, we show that adversarial logit pairing achieves the state of the art defense on ImageNet against PGD white box attacks, with an accuracy improvement from 1.5% to 27.9%. Adversarial logit pairing also successfully damages the current state of the art defense against black box attacks on ImageNet (Tramer et al., 2018), dropping its accuracy from 66.6% to 47.1%. With this new accuracy drop, adversarial logit pairing ties with Tramer et al.(2018) for the state of the art on black box attacks on ImageNet.

Oblivious linear-function evaluation (OLE) is a secure two-party protocol allowing a receiver to learn any linear combination of a pair of field elements held by a sender. OLE serves as a common building block for secure computation of arithmetic circuits, analogously to the role of oblivious transfer (OT) for boolean circuits. A useful extension of OLE is vector OLE (VOLE), allowing the receiver to learn any linear combination of two vectors held by the sender. In several applications of OLE, one can replace a large number of instances of OLE by a smaller number of instances of VOLE. This motivates the goal of amortizing the cost of generating long instances of VOLE. We suggest a new approach for fast generation of pseudo-random instances of VOLE via a deterministic local expansion of a pair of short correlated seeds and no interaction. This provides the first example of compressing a non-trivial and cryptographically useful correlation with good concrete efficiency. Our VOLE generators can be used to enhance the efficiency of a host of cryptographic applications. These include secure arithmetic computation and non-interactive zero-knowledge proofs with reusable preprocessing. Our VOLE generators are based on a novel combination of function secret sharing (FSS) for multi-point functions and linear codes in which decoding is intractable. Their security can be based on variants of the learning parity with noise (LPN) assumption over large fields that resist known attacks. We provide several constructions that offer tradeoffs between different efficiency measures and the underlying intractability assumptions.

In this work, we initiate the study of bottleneck complexity as a new communication efficiency measure for secure multiparty computation (MPC). Roughly, the bottleneck complexity of an MPC protocol is defined as the maximum communication complexity required by any party within the protocol execution. We observe that even without security, bottleneck communication complexity is an interesting measure of communication complexity for (distributed) functions and propose it as a fundamental area to explore. While achieving O(n) bottleneck complexity (where n is the number of parties) is straightforward, we show that: (1) achieving sublinear bottleneck complexity is not always possible, even when no security is required. (2) On the other hand, several useful classes of functions do have o(n) bottleneck complexity, when no security is required. Our main positive result is a compiler that transforms any (possibly insecure) efficient protocol with fixed communication-pattern for computing any functionality into a secure MPC protocol while preserving the bottleneck complexity of the underlying protocol (up to security parameter overhead). Given our compiler, an efficient protocol for any function f with sublinear bottleneck complexity can be transformed into an MPC protocol for f with the same bottleneck complexity. Along the way, we build cryptographic primitives - incremental fully-homomorphic encryption, succinct non-interactive arguments of knowledge with ID-based simulation-extractability property and verifiable protocol execution - that may be of independent interest.

Homomorphic secret sharing (HSS) is the secret sharing analogue of homomorphic encryption. An HSS scheme supports a local evaluation of functions on shares of one or more secret inputs, such that the resulting shares of the output are short. Some applications require the stronger notion of additive HSS, where the shares of the output add up to the output over some finite Abelian group. While some strong positive results for HSS are known under specific cryptographic assumptions, many natural questions remain open. We initiate a systematic study of HSS, making the following contributions. - A definitional framework. We present a general framework for defining HSS schemes that unifies and extends several previous notions from the literature, and cast known results within this framework. - Limitations. We establish limitations on information-theoretic multi-input HSS with short output shares via a relation with communication complexity. We also show that additive HSS for non-trivial functions, even the AND of two input bits, implies non-interactive key exchange, and is therefore unlikely to be implied by public-key encryption or even oblivious transfer. - Applications. We present two types of applications of HSS. First, we construct 2-round protocols for secure multiparty computation from a simple constant-size instance of HSS. As a corollary, we obtain 2-round protocols with attractive asymptotic efficiency features under the Decision Diffie Hellman (DDH) assumption. Second, we use HSS to obtain nearly optimal worst-case to average-case reductions in P. This in turn has applications to fine-grained average-case hardness and verifiable computation.

We continue the study of Homomorphic Secret Sharing (HSS), recently introduced by Boyle et al. (Crypto 2016, Eurocrypt 2017). A (2-party) HSS scheme splits an input x into shares (x0,x1) such that (1) each share computationally hides x, and (2) there exists an efficient homomorphic evaluation algorithm $\Eval$ such that for any function (or "program") from a given class it holds that Eval(x0,P)+Eval(x1,P)=P(x). Boyle et al. show how to construct an HSS scheme for branching programs, with an inverse polynomial error, using discrete-log type assumptions such as DDH.

Function Secret Sharing (FSS), introduced by Boyle et al. (Eurocrypt 2015), provides a way for additively secret-sharing a function from a given function family F. More concretely, an m-party FSS scheme splits a function f : {0, 1}n -> G, for some abelian group G, into functions f1,...,fm, described by keys k1,...,km, such that f = f1 + ... + fm and every strict subset of the keys hides f. A Distributed Point Function (DPF) is a special case where F is the family of point functions, namely functions f_{a,b} that evaluate to b on the input a and to 0 on all other inputs. FSS schemes are useful for applications that involve privately reading from or writing to distributed databases while minimizing the amount of communication. These include different flavors of private information retrieval (PIR), as well as a recent application of DPF for large-scale anonymous messaging.

An Oblivious RAM (ORAM), introduced by Goldreich and Ostrovsky (JACM 1996), is a (probabilistic) RAM that hides its access pattern, i.e. for every input the observed locations accessed are similarly distributed. Great progress has been made in recent years in minimizing the overhead of ORAM constructions, with the goal of obtaining the smallest overhead possible.

We construct a multiparty computation (MPC) protocol that is secure even if a malicious adversary, in addition to corrupting 1-ε fraction of all parties for an arbitrarily small constant ε >0, can leak information about the secret state of each honest party. This leakage can be continuous for an unbounded number of executions of the MPC protocol, computing different functions on the same or different set of inputs. We assume a (necessary) "leak-free" preprocessing stage. We emphasize that we achieve leakage resilience without weakening the security guarantee of classical MPC. Namely, an adversary who is given leakage on honest parties' states, is guaranteed to learn nothing beyond the input and output values of corrupted parties. This is in contrast with previous works on leakage in the multi-party protocol setting, which weaken the security notion, and only guarantee that a protocol which leaks l bits about the parties' secret states, yields at most l bits of leakage on the parties' private inputs. For some functions, such as voting, such leakage can be detrimental.