International Association
for Cryptologic Research

Secure multi-party computation aims to allow a set of players to compute a given function on their secret inputs without revealing any other information than the result of the computation. In this work, we focus on the design of secure multi-party protocols for shared polynomial operations. We consider the classical model where the adversary is honest-but-curious, and where the coefficients (or any secret values) are either encrypted using an additively homomorphic encryption scheme or shared using a threshold linear secret-sharing scheme. Our protocols terminate after a constant number of rounds and minimize the number of secure multiplications. In their seminal article at PKC 2006, Mohassel and Franklin proposed constant-rounds protocols for the main operations on (shared) polynomials. In this work, we improve the fan-in multiplication of nonzero polynomials, the multi-point polynomial evaluation and the polynomial interpolation (on secret points) to reach a quasi-linear complexity (instead of quadratic in Mohassel and Franklin's work) in the degree of shared input/output polynomials. Computing with shared polynomials is a core component of designing multi-party protocols for privacy-preserving operations on private sets, like private disjointness test or private set intersection. Using our new protocols, we are able to improve the complexity of such protocols and to design the first variant which always returns a correct result.

We present a construction for secure computation of differentially private sparse histograms that aggregates the inputs from a large number of clients. Each client contributes a value to the aggregate at a specific index. We focus on the case where the set of possible indices is superpolynomially large. Hence, the resulting histogram will be sparse, i.e., most entries will have the value zero.

Our construction relies on two non-colluding servers and provides security against malicious adversaries that may control one of the servers and any numbers of clients. It achieves communication and computation complexities linear in the input size, and achieves the optimal error $O\big(\frac{\log(1/\delta)}{\epsilon}\big)$, independent of the size of the domain of indices. We compute the communication cost of our protocol, showing its scalability. For a billion clients, the communication cost for each server is under 26 KiB per client.

Our paper solves an open problem of the work of Bell et al. (CCS'22) which presented a solution for the semi-honest setting while incurring sublinear overhead in its efficiency. We formalize a proof approach for proving malicious security in settings where the output and possible additional information revealed during the execution need to provide differential privacy.

Rescue-XLIX is an Arithmetization-Oriented Substitution-Permutation Network over prime fields $\mathbb{F}_p$ which in one full round first applies a SPN based on $x \mapsto x^d$ followed by a SPN based on the inverse power map $x \mapsto x^\frac{1}{d}$. In a recent work, zero-dimensional Gröbner bases for SPN and Poseidon sponge functions have been constructed by utilizing weight orders. Following this approach we construct zero-dimensional Gröbner bases for Rescue-XLIX ciphers and sponge functions.

This paper gives the first lattice-based two-round threshold signature based on lattice assumptions for which the first message is independent of the message being signed without relying on fully-homomorphic encryption. Our construction supports arbitrary thresholds and is scalable to support a large number of signers, say n = 1024.

Our construction provides a careful instantiation of a generic threshold signature construction by Tessaro and Zhu (EUROCRYPT ’23) based on specific linear hash functions, which in turns can be seen as a generalization of the FROST scheme by Komlo and Goldberg (SAC ’20). Our reduction techniques are new in the context of lattice-based cryptography. Also, our scheme does not use any heavy tools, such as NIZKs or homomorphic trapdoor commitments.

Threshold Schnorr signatures are seeing increased adoption in practice, and offer practical defenses against single points of failure. However, one challenge with existing randomized threshold Schnorr signature schemes is that signers must carefully maintain secret state across signing rounds, while also ensuring that state is deleted after a signing session is completed. Failure to do so will result in a fatal key-recovery attack by re-use of nonces.

While deterministic threshold Schnorr signatures that mitigate this issue exist in the literature, all prior schemes incur high complexity and performance overhead in comparison to their randomized equivalents. In this work, we seek the best of both worlds; a deterministic and stateless threshold Schnorr signature scheme that is also simple and efficient.

Towards this goal, we present Arctic, a lightweight two-round threshold Schnorr signature that is deterministic, and therefore does not require participants to maintain state between signing rounds. As a building block, we formalize the notion of a Verifiable Pseudorandom Secret Sharing (VPSS) scheme, and define Shine, an efficient VPSS construction. Shine is secure when the total number of participants is at least 2t − 1 and the adversary is assumed to corrupt at most t − 1; i.e., in the honest majority model.

We prove that Arctic is secure under the discrete logarithm assumption in the random oracle model, similarly assuming at minimum 2t − 1 number of signers and a corruption threshold of at most t − 1. For moderately sized groups (i.e., when n ≤ 20), Arctic is more than an order of magnitude more efficient than prior deterministic threshold Schnorr signatures in the literature. For small groups where n ≤ 10, Arctic is three orders of magnitude more efficient.

VOLE-in-the-head paradigm recently introduced by Baum et al. (Crypto 2023) allows 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 vector oblivious linear evaluation (VOLE) and leads to resulting ZK protocols that have linear proof size and are simpler, smaller, and faster than related approaches based on MPC-in-the-head. We propose a new candidate post-quantum signature scheme from the Multivariate Quadratic(MQ) problem based on a new protocol for the VOLE-in-the-head paradigm, which significantly reduces the signature size compared to previous works. We achieve a signature size of 2.5KB for a 128-bit security level. Compared to the state-of-the-art MQ-based signature schemes, our signature scheme achieves a factor from 3 to 4 improvement in terms of the signature size while keeping the computational efficiency competitive

Direct Anonymous Attestation (DAA) is a cryptographic protocol that enables users with a Trusted Platform Module (TPM) to authenticate without revealing their identity. Thus, DAA emerged as a good privacy-enhancing solution. Current standards have security based on factorization and discrete logarithm problem making them vulnerable to quantum computer attacks. Recently, a number of lattice-based DAA has been propose in the literature to start transition to quantum-resistant cryptography. In addition to these, DAA has been adapted to Vehicle Ad-hoc NETwork system (VANETs) to offer secure vehicule-to-vehicule/infrastructure communication (V2V and V2I). In this paper, we provide an implementation of the most advanced post-quantum DAA for VANETs. We explore the cryptographic foundations, construction methodologies, and the performance of this scheme, offering insights into their suitability for various real-world use cases.

Fully Homomorphic Encryption (FHE) is a cryptographic primitive that allows performing arbitrary operations on encrypted data. Since the conception of the idea in [RAD78], it was considered a holy grail of cryptography. After the first construction in 2009 [Gen09], it has evolved to become a practical primitive with strong security guarantees. Most modern constructions are based on well-known lattice problems such as Learning with Errors (LWE). Besides its academic appeal, in recent years FHE has also attracted significant attention from industry, thanks to its applicability to a considerable number of real-world use-cases. An upcoming standardization effort by ISO/IEC aims to support the wider adoption of these techniques. However, one of the main challenges that standards bodies, developers, and end users usually encounter is establishing parameters. This is particularly hard in the case of FHE because the parameters are not only related to the security level of the system, but also to the type of operations that the system is able to handle. In this paper, we provide examples of parameter sets for LWE targeting particular security levels that can be used in the context of FHE constructions. We also give examples of complete FHE parameter sets, including the parameters relevant for correctness and performance, alongside those relevant for security. As an additional contribution, we survey the parameter selection support offered in open-source FHE libraries.

We construct perfect zero-knowledge probabilistically checkable proofs (PZK-PCPs) for every language in #P. This is the first construction of a PZK-PCP for any language outside BPP. Furthermore, unlike previous constructions of (statistical) zero-knowledge PCPs, our construction simultaneously achieves non-adaptivity and zero knowledge against arbitrary (adaptive) polynomial-time malicious verifiers.

Our construction consists of a novel masked sumcheck PCP, which uses the combinatorial nullstellensatz to obtain antisymmetric structure within the hypercube and randomness outside of it. To prove zero knowledge, we introduce the notion of locally simulatable encodings: randomised encodings in which every local view of the encoding can be efficiently sampled given a local view of the message. We show that the code arising from the sumcheck protocol (the Reed--Muller code augmented with subcube sums) admits a locally simulatable encoding. This reduces the algebraic problem of simulating our masked sumcheck to a combinatorial property of antisymmetric functions.

Banks publish daily a list of available securities/assets (axe list) to selected clients to help them effectively locate Long (buy) or Short (sell) trades at reduced financing rates. This reduces costs for the bank, as the list aggregates the bank's internal firm inventory per asset for all clients of long as well as short trades. However, this is somewhat problematic: (1) the bank's inventory is revealed; (2) trades of clients who contribute to the aggregated list, particularly those deemed large, are revealed to other clients. Clients conducting sizable trades with the bank and possessing a portion of the aggregated asset exceeding $50\%$ are considered to be concentrated clients. This could potentially reveal a trading concentrated client's activity to their competitors, thus providing an unfair advantage over the market.

Atlas-X Axe Obfuscation, powered by new differential private methods, enables a bank to obfuscate its published axe list on a daily basis while under continual observation, thus maintaining an acceptable inventory Profit and Loss (P\&L) cost pertaining to the noisy obfuscated axe list while reducing the clients' trading activity leakage. Our main differential private innovation is a differential private aggregator for streams (time series data) of both positive and negative integers under continual observation.

For the last two years, Atlas-X system has been live in production across three major regions—USA, Europe, and Asia—at J.P. Morgan, a major financial institution, facilitating significant profitability. To our knowledge, it is the first differential privacy solution to be deployed in the financial sector. We also report benchmarks of our algorithm based on (anonymous) real and synthetic data to showcase the quality of our obfuscation and its success in production.

Classifying images has become a straightforward and accessible task, thanks to the advent of Deep Neural Networks. Nevertheless, not much attention is given to the privacy concerns associated with sensitive data contained in images. In this study, we propose a solution to this issue by exploring an intersection between Machine Learning and cryptography. In particular, Fully Homomorphic Encryption (FHE) emerges as a promising solution, as it enables computations to be performed on encrypted data. We, therefore, propose a Residual Network implementation based on FHE which allows the classification of encrypted images, ensuring that only the user can see the result. We suggest a circuit which reduces the memory requirements by more than 85% compared to the most recent works, while maintaining a high level of accuracy and a short computational time. We implement the circuit using the well-known CKKS scheme, which enables approximate encrypted computations. We evaluate the results from three perspectives: memory requirements, computational time and calculations precision. We demonstrate that it is possible to evaluate an encrypted ResNet20 in less than five minutes on a laptop using approximately 15GB of memory, achieving an accuracy of 91.67% on the CIFAR-10 dataset, which is almost equivalent to the accuracy of the plain model (92.60%).

Given two elliptic curves and the degree of an isogeny between them, finding the isogeny is believed to be a difficult problem---upon which rests the security of nearly any isogeny-based scheme. If, however, to the data above we add information about the behavior of the isogeny on a large enough subgroup, the problem can become easy, as recent cryptanalyses on SIDH have shown. Between the restriction of the isogeny to a full $N$-torsion subgroup and no ''torsion information'' at all lies a spectrum of interesting intermediate problems, raising the question of how easy or hard each of them is. Here we explore modular isogeny problems where the torsion information is masked by the action of a group of $2\times 2$ matrices. We give reductions between these problems, classify them by their difficulty, and link them to security assumptions found in the literature.

In this paper, we describe new quantum generic attacks on 6 rounds balanced Feistel networks with internal functions or internal permutations. In order to obtain our new quantum attacks, we revisit a result of Childs and Eisenberg that extends Ambainis' collision finding algorithm to the subset finding problem. In more details, we continue their work by carefully analyzing the time complexity of their algorithm. We also use four points structures attacks instead of two points structures attacks that leads to a complexity of $\mathcal{O}(2^{8n/5})$ instead of $\mathcal{O}(2^{2n})$. Moreover, we have also found a classical (i.e. non quantum) improved attack on $6$ rounds with internal permutations. The complexity here will be in $\mathcal{O}(2^{2n})$ instead of $\mathcal{O}(2^{3n})$ previously known.

Lattice-based cryptography has emerged as a promising new candidate to build cryptographic primitives. It offers resilience against quantum attacks, enables fully homomorphic encryption, and relies on robust theoretical foundations. Zero-knowledge proofs (ZKPs) are an essential primitive for various privacy-preserving applications. For example, anonymous credentials, group signatures, and verifiable oblivious pseudorandom functions all require ZKPs. Currently, the majority of ZKP systems are based on elliptic curves, which are susceptible to attacks from quantum computers. This project presents the first implementation of Lantern, a state-of-the-art lattice-based ZKP system that can create compact proofs, which are a few dozen kilobytes large, for basic statements. We thoroughly explain the theory behind the scheme and give a full implementation in a Jupyter Notebook using SageMath to make Lantern more accessible to researchers. Our interactive implementation allows users to fully understand the scheme and its building blocks, providing a valuable resource to understand both ZKPs and lattice cryptography. Albeit not optimized for performance, this implementation allows us to construct a Module-LWE secret proof in 35s on a consumer laptop. Through our contributions, we aim to advance the understanding and practical utilization of lattice-based ZKP systems, particularly emphasizing accessibility for the broader research community.

We explore Zero-Knowledge proofs (ZKP) 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.

We formalize and design an efficient tight ZK CPU, where the cost (both computation and communication, for each party) of each step depends only on the instruction taken. This qualitatively improves over state-of-the-art, where cost scales with the size of the largest CPU instruction (largest CFG node).

Our technique is formalized in the standard commit-and-prove paradigm, so our results are compatible with a variety of (interactive and non-interactive) general-purpose ZK.

We implemented an interactive tight arithmetic (over $\mathbb{F}_{2^{61}-1}$) ZK CPU based on Vector Oblivious Linear Evaluation (VOLE) and compared it to the state-of-the-art non-tight VOLE-based ZK CPU Batchman (Yang et al. CCS’23). In our experiments, under the same hardware configuration, we achieve comparable performance when instructions are of the same size and a $5$-$18×$ improvement when instructions are of varied size. Our VOLE-based ZK CPU can execute $100$K (resp. $450$K) multiplication gates per second in a WAN-like (resp. LAN-like) setting. It requires ≤ $102$ Bytes per multiplication gate. Our basic building block, ZK Unbalanced Read-Only Memory (ZK UROM), may be of an independent interest.

Event date: 19 December to 20 December 2024
Submission deadline: 9 July 2024
Notification: 13 August 2024

Event date: 25 September to 27 September 2024
Submission deadline: 22 April 2024
Notification: 9 July 2024

Event date: 24 September to 27 September 2024
Submission deadline: 14 April 2024
Notification: 17 June 2024

We have several open PhD internship positions in Bell Labs (Belgium) for PhD students or Postdocs.

At Bell Labs, the research arm of Nokia, we are currently designing and building systems that offer (1) computational integrity, (2) confidentiality, and (3) low-latency operations.

Internship Details:

As an intern in our lab, you'll have the opportunity to contribute to applied research in one of these areas, including:

Zero-Knowledge Proofs: Dive into topics like SNARKs, STARKs, and MPC-in-the-Head to enhance computational integrity. Computing on Encrypted Data: Explore homomorphic encryption (FHE) and secure multiparty computation (MPC) to address confidentiality challenges.
Acceleration: Investigate optimized implementations, software architecture, novel ZKP/FHE/MPC circuits, systems and friendly primitives.

Any other relevant subjects in this area are also welcome, such as zkML, FHE+ML, verifiable FHE, applications of MPC, and beyond.


Candidate Profile:

• You are currently doing a PhD or PostDoc
• Some familiarity with one of the areas: FHE, MPC or ZKP
• Both applied and theoretical researchers are welcome

What we offer:

• Fully funded internship with benefits (based on Belgian income standards)
• Internship any time from now until the end of 2024
• Possibility to visit local university crypto groups (e.g. COSIC KU Leuven)
• A wonderful desk with a view of the Zoo of Antwerp (elephants and bisons visible)
• Having access to the best beers and chocolates in the world

Closing date for applications:

Contact: Emad Heydari Beni (emad.heydari_beni@nokia-bell-labs.com)

At the Department of Software Systems and Cybersecurity (SSC) at Monash, we have several openings for PhD positions. The topics of interest are post-quantum cryptography (based on lattices and/or hash), their applications, and their secure and efficient software and hardware implementations.

• Amongst the benefits:
  • We provide highly competitive scholarships opportunities to collaborate with leading academic and industry experts in the above-mentioned areas.
  • There will be opportunities to participate in (inter)nationally funded projects.
  • We have a highly collaborative and friendly research environment.
  • You will have an opportunity to live/study in one of the most liveable and safest cities in the world.

The positions will be filled as soon as suitable candidates are found.

• Entry requirements include:
  • Some mathematical and cryptography backgrounds.
  • Some knowledge/experience in coding (for example, Python, C/C++, and/or SageMath) is a plus.
  • Must have completed (or be about to complete within the next 6 months) a significant research component either as part of their undergraduate (honours) degree or masters degree.
  • Should have excellent verbal and written communication skills in English.

How to apply. Please fill out the following form (also clickable from the advertisement title): https://docs.google.com/forms/d/e/1FAIpQLSetFZLvDNug5SzzE-iH97P9TGzFGkZB-ly_EBGOrAYe3zUYBw/viewform?usp=sf_link

Closing date for applications:

Contact: Amin Sakzad (amin.sakzad@monash.edu)

More information: https://www.monash.edu/it/ssc/cybersecurity/people