International Association
for Cryptologic Research

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 MPSU protocols: The first builds on public-key techniques. All existing works in this category involve a super-linear number of public-key operations, resulting in poor practical efficiency. The second builds on oblivious transfer and symmetric-key techniques. The only existing work in this category is proposed by Liu and Gao (ASIACRYPT 2023), which features the best concrete performance among all existing protocols, despite its super-linear computation and communication. Unfortunately, it does not achieve the standard semi-honest security, as it inherently relies on a non-collusion assumption, which is unlikely to hold in practice. Therefore, the problem of constructing a practical MPSU protocol based on oblivious transfer and symmetric-key techniques in standard semi-honest model remains open. Furthermore, there is no MPSU protocol achieving both linear computation and linear communication complexity, which leaves another unresolved problem. In this work, we resolve these two open problems.

- We propose the first MPSU protocol based on oblivious transfer and symmetric-key techniques in the standard semi-honest model. This protocol is $4.9-9.3 \times$ faster than Liu and Gao in the LAN setting. Concretely, our protocol requires only $3.6$ seconds in online phase for 3 parties with sets of $2^{20}$ items each. - We propose the first MPSU protocol achieving both linear computation and linear communication complexity, based on public-key operations. This protocol has the lowest overall communication costs and shows a factor of $3.0-36.5\times$ improvement in terms of overall communication compared to Liu and Gao.

We implement our protocols and conduct an extensive experiment to compare the performance of our protocols and the state-of-the-art. To the best of our knowledge, our implementation is the first correct and secure implementation of MPSU that reports on large-size experiments.

The one-time pad cipher is renowned for its theoretical perfect security, yet its practical deployment is primarily hindered by the key-size and distribution challenge. This paper introduces a novel approach to key distribution called q-stream, designed to make symmetric-key cryptography, and the one-time pad cipher in particular, a viable option for contemporary secure communications, and specifically, post-quantum cryptography, leveraging quantum noise and combinatorics to ensure secure and efficient key-distribution between communicating parties. We demonstrate that our key-distribution mechanism has a variable, yet quantifiable hardness of at least 504 bits, established from immutable mathematical laws, rather than conjectured-intractability, and how we overcome the one-time pad key-size issue with a localised quantum-noise seeded key-generation function, having a system hardness of at least 2304 bits, while introducing sender authentication and message integrity. Whilst the proposed solution has potential applications in fields requiring very high levels of security, such as military communications and large financial transactions, we show from our research with a prototype of q-stream, that it is sufficiently practical and scaleable for use in common browser-based web-applications, without any modification to the browser (i.e. plug-ins), running above SSL/TLS at the application level, where in tests, it achieved a key-distribution rate of around 7 million keys over a 5 minute surge-window, in a single (multi-threaded) instance of q-stream.

We show that the data storage scheme [IEEE/ACM Trans. Netw., 2023, 31(4), 1550-1565] is flawed due to the false secret sharing protocol, which requires that some random $4\times 4$ matrixes over the finite field $F_p$ (a prime $p$) are invertible. But we find its mathematical proof for invertibility is incorrect. To fix this flaw, one needs to check the invertibility of all 35 matrixes so as to generate the proper 7 secret shares.

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 complicated design, and running multiple instances. Consequently, there are no truly practical leakage-resistant OT protocols yet.

In this paper, we introduce two tailored indistinguishability-based security definitions for leakage-resilient OT, focusing on protecting the sender's state. Second, we propose a practical semi-honest secure OT protocol that achieves these security levels while minimizing the assumptions on the protocol's building blocks and the use of a secret state. Finally, we extend our protocol to support sequential composition and explore efficiency-security tradeoffs.

Matrix congruential generators is an important class of pseudorandom number generators. In this paper we show how to predict a class of Matrix congruential generators matrix congruential generators with unknown parameters. Given a few truncated digits of high-order bits output by a matrix congruential generator, we give a method based on lattice reduction to recover the parameters and the initial state of the generator.

Clustering is a crucial unsupervised learning method extensively used in the field of data analysis. For analyzing big data, outsourced computation is an effective solution but privacy concerns arise when involving sensitive information. Fully homomorphic encryption (FHE) enables computations on encrypted data, making it ideal for such scenarios. However, existing privacy-preserving clustering based on FHE are often constrained by the high computational overhead incurred from FHE, typically requiring decryption and interactions after only one iteration of the clustering algorithm. In this work, we propose a more efficient approach to evaluate the one-hot vector for the index of the minimum in an array with FHE, which fully exploits the parallelism of single-instruction-multiple-data of FHE schemes. By combining this with FHE bootstrapping, we present a practical FHE-based k-means clustering protocol whose required round of interactions between the data owner and the server is optimal, i.e., accomplishing the entire clustering process on encrypted data in a single round. We implement this protocol using the CKKS FHE scheme. Experiments show that our protocol significantly outperforms the state-of-the-art FHE-based k-means clustering protocols on various public datasets and achieves comparable accuracy to plaintext result. Additionally, We adapt our protocol to support mini-batch k-means for large-scale datasets and report its performance.

We propose a generalization of Zhandry’s compressed oracle method to random permutations, where an algorithm can query both the permutation and its inverse. We show how to use the resulting oracle simulation to bound the success probability of an algorithm for any predicate on input-output pairs, a key feature of Zhandry’s technique that had hitherto resisted attempts at generalization to random permutations. One key technical ingredient is to use strictly monotone factorizations to represent the permutation in the oracle’s database. As an application of our framework, we show that the one-round sponge construction is unconditionally preimage resistant in the random permutation model. This proves a conjecture by Unruh.

Strike-lists are a common technique for rollback and replay prevention in protocols that require that clients remain anonymous or that their current position in a state machine remain confidential. Strike-lists are heavily used in anonymous credentials, e-cash schemes, and trusted execution environments, and are widely deployed on the web in the form of Privacy Pass (PoPETS '18) and Google Private State Tokens. In such protocols, clients submit pseudorandom tokens associated with each action (e.g., a page view in Privacy Pass) or state transition, and the token is added to a server-side list to prevent reuse.

Unfortunately, the size of a strike-list, and hence the storage required by the server, is proportional to the total number of issued tokens, $N \cdot t$, where $N$ is the number of clients and $t$ is the maximum number of tickets per client. In this work, we ask whether it is possible to realize a strike-list-like functionality, which we call the anonymous tickets functionality, with storage requirements proportional to $N \log(t)$.

For the anonymous tickets functionality we construct a secure protocol from standard assumptions that achieves server storage of $O(N)$ ciphertexts, where each ciphertext encrypts a message of length $O(\log(t))$. We also consider an extension of the strike-list functionality where the server stores an arbitrary state for each client and clients advance their state with some function $s_i\gets f(s_{i-1},\mathsf{auxinput})$, which we call the anonymous outsourced state-keeping functionality. In this setting, malicious clients are prevented from rolling back their state, while honest clients are guaranteed anonymity and confidentiality against a malicious server. We achieve analogous results in this setting for two different classes of functions.

Our results rely on a new technique to preserve client anonymity in the face of selective failure attacks by a malicious server. Specifically, our protocol guarantees that misbehavior of the server either (1) does not prevent the honest client from redeeming a ticket or (2) provides the honest client with an escape hatch that can be used to simulate a redeem in a way that is indistinguishable to the server.

A dot-product proof (DPP) is a simple probabilistic proof system in which the input statement $\mathbf{x}$ and the proof $\boldsymbol{\pi}$ are vectors over a finite field $\mathbb{F}$, and the proof is verified by making a single dot-product query $\langle \mathbf{q},(\mathbf{x} \| \boldsymbol{\pi}) \rangle$ jointly to $\mathbf{x}$ and $\boldsymbol{\pi}$. A DPP can be viewed as a 1-query fully linear PCP. We study the feasibility and efficiency of DPPs, obtaining the following results:

- Small-field DPP. For any finite field $\mathbb{F}$ and Boolean circuit $C$ of size $S$, there is a DPP for proving that there exists $\mathbf{w}$ such that $C(\mathbf{x}, \mathbf{w})=1$ with a proof $\boldsymbol{\pi}$ of length $S\cdot\mathsf{poly}(|\mathbb{F}|)$ and soundness error $\varepsilon=O(1 / \sqrt{|\mathbb{F}|})$. We show this error to be asymptotically optimal. In particular, and in contrast to the best known PCPs, there exist strictly linear-length DPPs over constant-size fields.

- Large-field DPP. If $|\mathbb{F}|\ge\mathsf{poly}(S/\varepsilon)$, there is a similar DPP with soundness error $\varepsilon$ and proof length $O(S)$ (in field elements).

The above results do not rely on the PCP theorem and their proofs are considerably simpler. We apply our DPP constructions toward two kinds of applications.

- Hardness of approximation. We obtain a simple proof for the NP-hardness of approximating MAXLIN (with dense instances) over any finite field $\mathbb{F}$ up to some constant factor $c>1$, independent of $\mathbb{F}$. Unlike previous PCP-based proofs, our proof yields exponential-time hardness under the exponential time hypothesis (ETH).

- Succinct arguments. We improve the concrete efficiency of succinct interactive arguments in the generic group model using input-independent preprocessing. In particular, the communication is comparable to sending two group elements and the verifier's computation is dominated by a single group exponentiation. We also show how to use DPPs together with linear-only encryption to construct succinct commit-and-prove arguments.