Garbled Circuits (GC) is a foundational primitive for secure two-party computation (2PC). Garbled Private Information Retrieval (GPIR) is a GC technique for looking up a public array or database (DB) on a private index unknown to either player. GPIR immediately implies GC evaluation of functions implemented as a publicly known look-up table (LUT).

A two-party fuzzy private set intersection (PSI) protocol between Alice and Bob with input sets A and B allows Alice to learn nothing more than the points of Bob that are ''δ-close'' to its points in some metric space dist . More formally, Alice learns only the set {b | dist (a,b) ≤ δ, a ∈ A, b ∈ B} for a predefined threshold δ and distance metric dist, while Bob learns nothing about Alice's set. Fuzzy PSI is a valuable privacy tool in scenarios where private set intersection needs to be computed over imprecise or measurement-based data, such as GPS coordinates or healthcare data. Previous approaches to fuzzy PSI rely on asymmetric cryptographic primitives, generic two-party computation (2PC) techniques like garbled circuits, or function secret sharing methods, all of which are computationally intensive and lead to poor concrete efficiency. This work introduces a new modular framework for fuzzy PSI, primarily built on efficient symmetric key primitives. Our framework reduces the design of efficient fuzzy PSI to a novel variant of oblivious transfer (OT), which we term distance-aware random OT (da-ROT). This variant enables the sender to obtain two random strings (r0, r1), while the receiver obtains one of these values rb, depending on whether the receiver's input keyword a and the sender's input keyword b are close in some metric space i.e., dist (a,b) ≤ δ. The da-ROT can be viewed as a natural extension of traditional OT, where the condition (choice bit) is known to the receiver. We propose efficient constructions for da-ROT based on standard OT techniques tailored for small domains, supporting distance metrics such as the Chebyshev norm, the Euclidean norm, and the Manhattan norm. By integrating these da-ROT constructions, our fuzzy PSI framework achieves up to a 14× reduction in communication cost and up to a 54× reduction in computation cost compared to previous state-of-the-art protocols, across input set sizes ranging from 28 to 216. Additionally, we extend our framework to compute fuzzy PSI cardinality and fuzzy join from traditional PSI-related functionalities. All proposed protocols are secure in the semi-honest model.

We explore Zero-Knowledge Proofs (ZKPs) of statements expressed as programs written in high-level languages, e.g., C or assembly. At the core of executing such programs in ZK is the repeated evaluation of a CPU step, achieved by branching over the CPU's instruction set. This approach is general and covers traversal-execution of a program's control flow graph (CFG): here CPU instructions are straight-line program fragments (of various sizes) associated with the CFG nodes. This highlights the usefulness of ZK CPUs with a large number of instructions of varying sizes.

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 \mathcalL _1 łor \cdots łor \mathcalL _B. Typically, ZK requires paying the price to handle all B branches. Prior works have shown how to avoid this price in communication, but not in computation.

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.

Demand for distributed computational infrastructure is growing in order to offer low latency connections to end users. The fragmenting infrastructure complicates the resource allocation process. As the number of infrastructure providers grows, points of presence are resource constrained compared to the cloud, they have diverse availability profiles, and diverse connectivity properties. Existing resource allocation approaches require providers share intimate details about their infrastructure to support the placement process, or rely on third party aggregators. Such solutions introduce strong assumptions of trust and collaboration. In this work we present Angler, the first system to allocate resources from dark pools, meaning the capacity and requests of the distributed pool of resources are unknown. Angler leverages cryptographic protocols for secure function evaluation, namely the WRK secure multiparty computation (MPC) protocol [76]. While MPC protocols can have large overheads compared to plaintext function evaluation, an end-to-end approach to the system design subverts the expensive overheads. Specifically, Angler combines a tuned implementation of a maliciously secure MPC protocol, a tailored distributed hash table, and a systematic effort to make the best allocation decision within a response time envelope. Angler is only 2x slower than resource allocation with no privacy when arbitrating among 8 providers, taking less than a second.

Recent work has produced interactive Zero Knowledge (ZK) proof systems that can express proofs as arbitrary C programs (Heath et al., 2021, henceforth referred to as ZEE); these programs can be executed by a simulated ZK processor that runs in the 10KHz range. In this work, we demonstrate that such proof systems are amenable to high degrees of parallelism. Our epoch parallelism-based approach allows the prover and verifier to divide the ZK proof into pieces such that each piece can be executed on a different machine. These proof snippets can then be glued together, and the glued parallel proofs are equivalent to the original sequential proof. We implemented and we experimentally evaluate an epoch parallel version of the ZEE proof system. By running the prover and verifier each across 31 2-core machines, we achieve a ZK processor that runs at up to 394KHz. This allowed us to run a benchmark involving the Linux program bzip2, which would have required at least 11 days with the former ZEE system, in only 8.5 hours.

Biometric authentication is getting increasingly popular because of its appealing usability and improvements in biometric sensors. At the same time, it raises serious privacy concerns since the common deployment involves storing bio-templates in remote servers. Current solutions propose to keep these templates on the client's device, outside the server's reach. This binds the client to the initial device. A more attractive solution is to have the server authenticate the client, thereby decoupling them from the device. Unfortunately, existing biometric template protection schemes either suffer from the practicality or accuracy. The state-of-the-art deep learning (DL) solutions solve the accuracy problem in face- and voice-based verification. However, existing privacy-preserving methods do not accommodate the DL methods, as they are tailored to hand-crafted feature space of specific modalities in general. In this work, we propose a novel pipeline, Justitia, that makes DL-inferences of face and voice biometrics compatible with the standard privacy-preserving primitives, like fuzzy extractors (FE). For this, we first form a bridge between Euclidean (or cosine) space of DL and Hamming space of FE, while maintaining the accuracy and privacy of underlying schemes. We also introduce efficient noise handling methods to keep the FE scheme practically applicable. We implement an end-to-end prototype to evaluate our design, then show how to improve the security for sensitive authentications and usability for non-sensitive, day-to-day, authentications. Justitia achieves the same, 0.33% false rejection at zero false acceptance, errors as the plaintext baseline does on the YouTube Faces benchmark. Moreover, combining face and voice achieves 1.32% false rejection at zero false acceptance. According to our systematical security assessments conducted through prior approaches and our novel black-box method, Justitia achieves ~25 bits and ~33 bits of security guarantees for face- and face&voice-based pipelines, respectively.

Garbled Circuit (GC) is the main practical 2PC technique, yet despite great interest in its performance, GC notoriously resists improvement. Essentially, we only know how to evaluate GC functions gate-by-gate using encrypted truth tables; given input labels, the GC evaluator decrypts the corresponding output label. Interactive protocols enjoy more sophisticated techniques. For example, we can expose to a party a (masked) private value. The party can then perform useful local computation and feed the resulting cleartext value back into the MPC. Such techniques are not known to work for GC. We show that it is, in fact, possible to improve GC efficiency, while keeping its round complexity, by exposing masked private values to the evaluator. %without introducing rounds of communication. Our improvements use garbled one-hot encodings of values. By using this encoding we improve a number of interesting functions, e.g., matrix multiplication, integer multiplication, field element multiplication, field inverses and AES S-Boxes, integer exponents, and more. We systematize our approach by providing a framework for designing such GC modules. Our constructions are concretely efficient. E.g., we improve binary matrix multiplication inside GC by more than 6x in terms of communication and by more than 4x in terms of WAN wall-clock time. Our improvement circumvents an important GC lower bound and may open GC to further improvement.

We build a complete and efficient ZK toolchain that handles proof statements encoded as arbitrary ANSI C programs.Zero-Knowledge (ZK) proofs are foundational in cryptography. Recent ZK research has focused intensely on non-interactive proofs of small statements, useful in blockchain scenarios. We instead target large statements that are useful, e.g., in proving properties of programs.Recent work (Heath and Kolesnikov, CCS 2020 [HK20a]) designed an efficient proof-of-concept ZK machine (ZKM). Their machine executes arbitrary programs over a minimal instruction set, authenticating in ZK the program execution. In this work, we significantly extend this research thrust, both in terms of efficiency and generality. Our contributions include:• A rich and performance-oriented architecture for representing arbitrary ZK proofs as programs.• A complete compiler toolchain providing full support for ANSI C95 programs. We ran off-the-shelf buggy versions of the Linux programs sed and gzip, proving in ZK that each program has a bug. To our knowledge, this is the first ZK system capable of executing standard Linux programs.• Improved ZK oblivious RAM (ORAM). [HK20a] introduced an efficient ZK-specific ORAM BubbleRAM that consumes O(log2n) communication per access. We extend BubbleRAM with multi-level caching, decreasing communication to O(log n) per access. This introduces the possibility of a cache miss, which we handle cheaply. Our experiments show that cache misses are rare; in isolation, i.e., ignoring other processor costs, BubbleCache improves communication over BubbleRAM by more than 8×. Using BubbleCache improves our processor’s total communication (including costs of cache misses) by ≈ 25-30%.• Numerous low-level optimizations, resulting in a CPU that is both more expressive and ≈ 5.5× faster than [HK20a]’s.• Attention to user experience. Our engineer-facing ZK instrumentation and extensions are minimal and easy to use.Put together, our system is efficient and general, and can run many standard Linux programs. The resultant machine runs at up to 11KHz on a 1Gbps LAN and supports MBs of RAM.

Zero-Knowledge (ZK) proofs (ZKP) are foundational in cryptography. Most recent ZK research focuses on non-interactive proofs (NIZK) of small statements, useful in blockchain scenarios. Another line, and our focus, instead targets proofs of large statements that are useful, e.g., in proving properties of programs in ZK. We specify a zero-knowledge processor that executes arbitrary programs written in a simple instruction set, and proves in ZK the correctness of the execution. Such an approach is well-suited for constructing ZK proofs of large statements as it efficiently supports complex programming constructs, such as loops and RAM access. Critically, we propose several novel ZK improvements that make our approach concretely efficient: (1) an efficient arithmetic representation with conversions to/from Boolean, (2) an efficient read-only memory that uses $2łog n$ OTs per access, and (3) an efficient read-write memory, øurram, which uses $\frac1 2 łog^2 n$ OTs per access. øurram beats linear scan for RAM of size $>3$ elements! Prior ZK systems used generic ORAM costing orders of magnitude more. We cast our system as a garbling scheme that can be plugged into the ZK protocol of [Jawurek et al, CCS'13]. Put together, our system is concretely efficient: for a processor instantiated with $512$KB of main memory, each processor cycle costs $24$KB of communication. We implemented our approach in \textttC++. On a 1Gbps LAN our implementation realizes a $2.1$KHz processor.

At the core of the value proposition of edge computing is the ability to put computation close enough to the data sources, on demand. However, the data sources, computational infrastructure and software services needed to come together to power emerging and future edge computing applications are fragmented across different stakeholders, each with their own incentives, policies, and constraints on resources they can afford. This fragmentation limits the ability of edge computing to guarantee to applications and data the edge which will deliver the desired benefit. In this paper, we present our vision for an Edge Exchange, a decentralized directory service for a multi-stakeholder edge, as a path forward to enabling applications to be deployed across the best available edge resources, while still providing each stakeholder with controls regarding their resource use and sharing policies.

Recent work, including ZKBoo, ZKB++, and Ligero, has developed efficient non-interactive zero-knowledge proofs of knowledge (NIZKPoKs) for Boolean circuits based on symmetric-key primitives alone, using the "MPC-in-the-head" paradigm of Ishai et al. We show how to instantiate this paradigm with MPC protocols in the preprocessing model; once optimized, this results in an NIZKPoK with shorter proofs (and comparable computation) as in prior work for circuits containing roughly 300--100,000 AND~gates. In contrast to prior work, our NIZKPoK also supports witness-independent preprocessing, which allows the prover to shift most of its work to an offline phase before the witness is known. We use our NIZKPoK to construct a signature scheme based only on symmetric-key primitives (and hence with "post-quantum" security). The resulting scheme has shorter signatures than the scheme built using ZKB++ (and comparable signing/verification time), and is even competitive with hash-based signature schemes. To further highlight the flexibility and power of our NIZKPoK, we also use it to build efficient ring and group signatures based on symmetric-key primitives alone. To our knowledge, the resulting schemes are the most efficient constructions of these primitives that offer post-quantum security.

We present a new paradigm for multi-party private set intersection (PSI) that allows $n$ parties to compute the intersection of their datasets without revealing any additional information. We explore a variety of instantiations of this paradigm. Our protocols avoid computationally expensive public-key operations and are secure in the presence of any number of semi-honest participants (i.e., without an honest majority).

Cut-and-choose (CC) is the standard approach to making Yao's garbled circuit two-party computation (2PC) protocol secure against malicious adversaries. Traditional cut-and-choose operates at the level of entire circuits, whereas the LEGO paradigm (Nielsen & Orlandi, TCC 2009) achieves asymptotic improvements by performing cut-and-choose at the level of individual gates. In this work we propose a unified approach called DUPLO that spans the entire continuum between these two extremes. The cut-and-choose step in our protocol operates on the level of arbitrary circuit "components," which can range in size from a single gate to the entire circuit itself.

Attribute-based methods provide authorization to parties based on whether their set of attributes (e.g., age, organization, etc.) fulfills a policy. In attribute-based encryption (ABE), authorized parties can decrypt, and in attribute-based credentials (ABCs), authorized parties can authenticate themselves. In this paper, we combine elements of ABE and ABCs together with garbled circuits to construct attribute-based key exchange (ABKE). Our focus is on an interactive solution involving a client that holds a certificate (issued by an authority) vouching for that client's attributes and a server that holds a policy computable on such a set of attributes. The goal is for the server to establish a shared key with the client but only if the client's certified attributes satisfy the policy. Our solution enjoys strong privacy guarantees for both the client and the server, including attribute privacy and unlinkability of client sessions.

We describe a lightweight protocol for oblivious evaluation of a pseudorandom function (OPRF) in the presence of semihonest adversaries. In an OPRF protocol a receiver has an input r; the sender gets output s and the receiver gets output F(s; r), where F is a pseudorandom function and s is a random seed. Our protocol uses a novel adaptation of 1-out-of-2 OT-extension protocols, and is particularly efficient when used to generate a large batch of OPRF instances. The cost to realize m OPRF instances is roughly the cost to realize 3:5m instances of standard 1-out-of-2 OTs (using state-of-the-art OT extension). We explore in detail our protocol's application to semihonest secure private set intersection (PSI). The fastest state-of- the-art PSI protocol (Pinkas et al., Usenix 2015) is based on efficient OT extension. We observe that our OPRF can be used to remove their PSI protocol's dependence on the bit-length of the parties' items. We implemented both PSI protocol variants and found ours to be 3.1{3.6 faster than Pinkas et al. for PSI of 128-bit strings and sufficiently large sets. Concretely, ours requires only 3.8 seconds to securely compute the intersection of 220-size sets, regardless of the bitlength of the items. For very large sets, our protocol is only 4:3 slower than the insecure naive hashing approach for PSI.

We present Shallow MAC (ShMAC), a fixed-input-length message authentication code that performs most of the computation prior to the availability of the message. Specifically, ShMAC’s message-dependent computation is much faster and smaller in hardware than the evaluation of a pseudorandom permutation (PRP) and can be implemented by a small shallow circuit, while its precomputation consists of one PRP evaluation. A main building block for ShMAC is the notion of strong differential uniformity (SDU), which we introduce and which may be of independent interest. We show an efficient SDU construction built from previously considered differentially uniform functions. Our main motivating application is a system architecture where a hardware-secured processor uses memory controlled by an adversary. We also present in technical detail a novel, efficient approach to encrypting and authenticating memory and discuss the associated tradeoffs, while paying special attention to minimizing hardware costs and the reduction of Dynamic Random Access Memory latency.

The Blind Seer system (Oakland 2014) is an efficient and scalable DBMS that affords both client query privacy and server data protection. It also provides the ability to enforce authorization policies on the system, restricting client's queries while maintaining the privacy of both query and policy. Blind Seer supports a rich query set, including arbitrary boolean formulas, and is provably secure with respect to a controlled amount of search pattern leakage. No other system to date achieves this tradeoff of performance, generality, and provable privacy. A major shortcoming of Blind Seer is its reliance on semi-honest security, particularly for access control and data protection. A malicious client could easily cheat the query authorization policy and obtain any database records satisfying any query of its choice, thus violating basic security features of any standard DBMS. In sum, Blind Seer offers additional privacy to a client, but sacrifices a basic security tenet of DBMS. In the present work, we completely resolve the issue of a malicious client. We show how to achieve robust access control and data protection in Blind Seer with virtually no added cost to performance or privacy. Our approach also involves a novel technique for a semi-private function secure function evaluation (SPF-SFE) that may have independent applications. We fully implement our solution and report on its performance.

Query privacy in secure DBMS is an important feature, although rarely formally considered outside the theoretical community. Because of the high overheads of guaranteeing privacy in complex queries, almost all previous works addressing practical applications consider limited queries (e.g., just keyword search), or provide a weak guarantee of privacy. In this work, we address a major open problem in private DB: efficient sub linear search for arbitrary Boolean queries. We consider scalable DBMS with provable security for all parties, including protection of the data from both server (who stores encrypted data) and client (who searches it), as well as protection of the query, and access control for the query. We design, build, and evaluate the performance of a rich DBMS system, suitable for real-world deployment on today medium-to large-scale DBs. On a modern server, we are able to query a formula over 10TB, 100M-record DB, with 70 searchable index terms per DB row, in time comparable to (insecure) MySQL (many practical queries can be privately executed with work 1.2-3 times slower than MySQL, although some queries are costlier). We support a rich query set, including searching on arbitrary boolean formulas on keywords and ranges, support for stemming, and free keyword searches over text fields. We identify and permit a reasonable and controlled amount of leakage, proving that no further leakage is possible. In particular, we allow leakage of some search pattern information, but protect the query and data, provide a high level of privacy for individual terms in the executed search formula, and hide the difference between a query that returned no results and a query that returned a very small result set. We also support private and complex access policies, integrated in the search process so that a query with empty result set and a query that fails the policy are hard to tell apart.

General two-party Secure Function Evaluation (SFE) allows mutually distrusting parties to correctly compute any function on their private input data, without revealing the inputs. Two-party SFE can benefit almost any client-server interaction where privacy is required, such as privacy-preserving credit checking, medical classification, or face recognition. Today, SFE is a subject of immense amount of research in a variety of directions and is not easy to navigate. In this article, we systematize the most practically important works of the vast research knowledge on general SFE. We argue that in many cases the most efficient SFE protocols are obtained by combining several basic techniques, e.g., garbled circuits and (additively) homomorphic encryption. As a valuable methodological contribution, we present a framework in which today's most efficient techniques for general SFE can be viewed as building blocks with well-defined interfaces that can be easily combined into a complete efficient solution. Further, our approach naturally allows automated protocol generation (compilation) and has been implemented partially in the TASTY framework. In summary, we provide a comprehensive guide in state-of-the-art SFE, with the additional goal of extracting, systematizing and unifying the most relevant and promising general SFE techniques. Our target audience are graduate students wishing to enter the SFE field and advanced engineers seeking to develop SFE solutions. We hope our guide paints a high-level picture of the field, including most common approaches and their trade-offs and gives precise and numerous pointers to formal treatment of its specific aspects.

Traditional approaches to generic secure computation begin by representing the function f being computed as a circuit. If f depends on each of its input bits, this implies a protocol with complexity at least linear in the input size. In fact, linear running time is inherent for non-trivial functions since each party must "touch" every bit of their input lest information about the other party's input be leaked. This seems to rule out many applications of secure computation (e.g., database search) in scenarios where inputs are huge.

We present information-theoretically secure schemes for sharing and modifying secrets among a dynamic swarm of computing devices. The schemes support an unlimited number of changes to the swarm including players joining and leaving the swarm, while swarms may be merged, cloned or split. The schemes securely and distributively maintain a global state for the swarm, and support an unlimited number of changes to the state according to received input. Our schemes are based on a novel construction of a strongly oblivious universal Turing Machine and on a distributed evaluation of this TM that reveals nothing to an adversary beyond a bound on the space complexity of the TM.