Faster Unbalanced Private Set Intersection

Protocols for Private Set Intersection (PSI) are important cryptographic primitives that perform joint operations on datasets in a privacy-preserving way. They allow two parties to compute the intersection of their private sets without revealing any additional information beyond the intersection itself. Unfortunately, PSI implementations in the literature do not usually employ the best possible cryptographic implementation techniques. This results in protocols presenting computational and communication complexities that are prohibitive, particularly in the case when one of the participants is a low-powered device and there are bandwidth restrictions. This paper builds on modern cryptographic engineering techniques and proposes optimizations for a promising one-way PSI protocol based on public-key cryptography. For the case when one of the parties holds a set much smaller than the other (a realistic assumption in many scenarios) we show that our improvements and optimizations yield a protocol that outperforms the communication complexity and the run time of previous proposals by around one thousand times

PEPSI: Practically Efficient Private Set Intersection in the Unbalanced Setting

Two parties with private data sets can find shared elements using a Private Set Intersection (PSI) protocol without revealing any information beyond the intersection. Circuit PSI protocols privately compute an arbitrary function of the intersection - such as its cardinality, and are often employed in an unbalanced setting where one party has more data than the other. Existing protocols are either computationally inefficient or require extensive server-client communication on the order of the larger set. We introduce Practically Efficient PSI or PEPSI, a non-interactive solution where only the client sends its encrypted data. PEPSI can process an intersection of 1024 client items with a million server items in under a second, using less than 5 MB of communication. Our work is over 4 orders of magnitude faster than an existing non-interactive circuit PSI protocol and requires only 10% of the communication. It is also up to 20 times faster than the work of Ion et al., which computes a limited set of functions and has communication costs proportional to the larger set. Our work is the first to demonstrate that non-interactive circuit PSI can be practically applied in an unbalanced setting

Unbalanced Circuit-PSI from Oblivious Key-Value Retrieval

Circuit-based Private Set Intersection (circuit-PSI) enables two parties, a client and a server, with their input sets $X$ and $Y$ respectively, to securely compute a function $f$ on the intersection $X \cap Y$, while keeping $X \cap Y$ secret from both parties. Although several computationally efficient circuit-PSI protocols have been proposed recently, they most focus on the balanced scenario where $|X|$ is similar to $|Y|$. However, in many realistic scenarios, a circuit-PSI protocol may be performed in the unbalanced case where $|X|$ is remarkably smaller than $|Y|$ (e.g., the client is a constrained device holding a small set, while the server is a service provider holding a large set). Directly applying existing protocols to this scenario will lead to significant efficiency issues because the communication complexity of the protocols scales at least linearly with the size of the larger set, i.e., $\max(|X|, |Y|)$. In this work, we put forth efficient constructions for unbalanced circuit-PSI with sublinear communication complexity in the size of the larger set. The main insight is that we formalize unbalanced circuit-PSI as obliviously retrieving values corresponding to keys from a set of key-value pairs. To this end, we present a new functionality called Oblivious Key-Value Retrieval (OKVR) and design the OKVR protocol from a new notion called sparse Oblivious Key-Value Stores (sparse OKVS). We conduct extensive experiments and the results show that our constructions remarkably outperform the state-of-the-art circuit-PSI schemes (EUROCRYPT\u2719, PETs\u2722, CCS\u2722), i.e., $1.84 \sim 48.86 \times$ communication improvement and $1.50 \sim39.81 \times$ faster computation. Very recently, Son and Jeong (AsiaCCS\u2723) also present unbalanced circuit-PSI protocols, and our constructions outperform them by $1.18 \sim 15.99 \times$ and $1.22 \sim 10.44 \times$ in communication and computation overhead, respectively, depending on set sizes and network environments

Private set intersection: A systematic literature review

Secure Multi-party Computation (SMPC) is a family of protocols which allow some parties to compute a function on their private inputs, obtaining the output at the end and nothing more. In this work, we focus on a particular SMPC problem named Private Set Intersection (PSI). The challenge in PSI is how two or more parties can compute the intersection of their private input sets, while the elements that are not in the intersection remain private. This problem has attracted the attention of many researchers because of its wide variety of applications, contributing to the proliferation of many different approaches. Despite that, current PSI protocols still require heavy cryptographic assumptions that may be unrealistic in some scenarios. In this paper, we perform a Systematic Literature Review of PSI solutions, with the objective of analyzing the main scenarios where PSI has been studied and giving the reader a general taxonomy of the problem together with a general understanding of the most common tools used to solve it. We also analyze the performance using different metrics, trying to determine if PSI is mature enough to be used in realistic scenarios, identifying the pros and cons of each protocol and the remaining open problems.This work has been partially supported by the projects: BIGPrivDATA (UMA20-FEDERJA-082) from the FEDER Andalucía 2014– 2020 Program and SecTwin 5.0 funded by the Ministry of Science and Innovation, Spain, and the European Union (Next Generation EU) (TED2021-129830B-I00). The first author has been funded by the Spanish Ministry of Education under the National F.P.U. Program (FPU19/01118). Funding for open access charge: Universidad de Málaga/CBU

Improved Secure Efficient Delegated Private Set Intersection

Private Set Intersection (PSI) is a vital cryptographic technique used for securely computing common data of different sets. In PSI protocols, often two parties hope to find their common set elements without needing to disclose their uncommon ones. In recent years, the cloud has been playing an influential role in PSI protocols which often need huge computational tasks. In 2017, Abadi et al. introduced a scheme named EO-PSI which uses a cloud to pass on the main computations to it and does not include any public-key operations. In EO-PSI, parties need to set up secure channels beforehand; otherwise, an attacker can easily eavesdrop on communications between honest parties and find private information. This paper presents an improved EO-PSI scheme which has the edge on the previous scheme in terms of privacy and complexity. By providing possible attacks on the prior scheme, we show the necessity of using secure channels between parties. Also, our proposed protocol is secure against passive attacks without having to have any secure channels. We measure the protocol's overhead and show that computational complexity is considerably reduced and also is fairer compared to the previous scheme.Comment: 6 pages, presented in proceedings of the 28th Iranian Conference on Electrical Engineering (ICEE 2020). Final version of the paper has been adde

Private Set Operations from Multi-Query Reverse Private Membership Test

Private set operations allow two parties to perform secure computation on their private sets, including intersection, union and functions of intersection/union. In this paper, we put forth a framework to perform private set operations. The technical core of our framework is the multi-query reverse private membership test (mqRPMT) protocol (Zhang et al., USENIX Security 2023), in which a client with a vector $X = (x_1, \dots, x_n)$ interacts with a server holding a set $Y$, and eventually the server learns only a bit vector $(e_1, \dots, e_n)$ indicating whether $x_i \in Y$ without learning the value of $x_i$, while the client learns nothing. We present two constructions of mqRPMT from newly introduced cryptographic notions, one is based on commutative weak pseudorandom function (cwPRF), and the other is based on permuted oblivious pseudorandom function (pOPRF). Both cwPRF and pOPRF can be realized from the decisional Diffie-Hellman (DDH)-like assumptions in the random oracle model. We also introduce a slightly weaker version of mqRPMT dubbed mqRPMT$^*$, in which the client also learns the cardinality of $X \cap Y$. We show that mqRPMT$^*$ can be built from a category of multi-query private membership test (mqPMT) called Sigma-mqPMT, which in turn can be realized from DDH-like assumptions or oblivious polynomial evaluation. This makes the first step towards establishing the relation between mqPMT and mqRPMT. We demonstrate the practicality of our framework with implementations. By plugging our cwPRF-based mqRPMT into the framework, we obtain various PSO protocols that are superior or competitive to the state-of-the-art protocols. For intersection functionality, our protocol is faster than the most efficient one for small sets. For cardinality functionality, our protocol achieves a $2.4-10.5\times$ speedup and a $10.9-14.8\times$ shrink in communication cost. For cardinality-with-sum functionality, our protocol achieves a $28.5-76.3\times$ speedup and $7.4\times$ shrink in communication cost. For union functionality, our protocol is the first one that attains strict linear complexity, and requires the lowest concrete computation and communication costs in all settings, achieving a $2.7-17\times$ speedup and about $2\times$ shrink in communication cost. Specifically, for input sets of size $2^{20}$, our PSU protocol requires roughly 100 MB of communication and 16 seconds using 4 threads on a laptop in the LAN setting. Our improvement on PSU also translates to related functionality, yielding the most efficient private-ID protocol to date. Moreover, by plugging our FHE-based mqRPMT$^*$ to the general framework, we obtain a PSU$^*$ protocol (the sender additionally learns the intersection size) suitable for unbalanced setting, whose communication complexity is linear in the size of the smaller set and logarithmic in the larger set