International Association for Cryptologic Research

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18 September 2024

Nan Wang, Dongxi Liu
ePrint Report ePrint Report
Bit-decomposition-based zero-knowledge range proofs in the discrete logarithm (DLOG) setting with a transparent setup, e.g., Bulletproof (IEEE S\&P \textquotesingle 18), Flashproof (ASIACRYPT \textquotesingle 22), and SwiftRange (IEEE S\&P \textquotesingle 24), have garnered widespread popularity across various privacy-enhancing applications. These proofs aim to prove that a committed value falls within the non-negative range $[0, 2^N-1]$ without revealing it, where $N$ represents the bit length of the range. Despite their prevalence, the current implementations still suffer from suboptimal performance. Some exhibit reduced communication costs at the expense of increased computational costs while others experience the opposite. Presently, users are compelled to utilize these proofs in scenarios demanding stringent requirements for both communication and computation efficiency.

In this paper, we introduce, FlashSwift, a stronger DLOG-based logarithmic-sized alternative. It stands out for its greater shortness and significantly enhanced computational efficiency compared with the cutting-edge logarithmic-sized ones for the most common ranges where $N \leq 64$. It is developed by integrating the techniques from Flashproof and SwiftRange without using a trusted setup. The substantial efficiency gains stem from our dedicated efforts in overcoming the inherent incompatibility barrier between the two techniques. Specifically, when $N=64$, our proof achieves the same size as Bulletproof and exhibits 1.1$\times$ communication efficiency of SwiftRange. More importantly, compared with the two, it achieves $2.3\times$ and $1.65\times$ proving efficiency, and $3.2\times$ and $1.7\times$ verification efficiency, respectively. At the time of writing, our proof also creates two new records of the smallest proof sizes, 289 bytes and 417 bytes, for 8-bit and 16-bit ranges among all the bit-decomposition-based ones without requiring trusted setups. Moreover, to the best of our knowledge, it is the first {\em configurable} range proof that is adaptable to various scenarios with different specifications, where the configurability allows to trade off communication efficiency for computational efficiency. In addition, we offer a bonus feature: FlashSwift supports the aggregation of multiple single proofs for efficiency improvement. Finally, we provide comprehensive performance benchmarks against the state-of-the-art ones to demonstrate its practicality.
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Johann Knechtel, Mohammad Eslami, Peng Zou, Min Wei, Xingyu Tong, Binggang Qiu, Zhijie Cai, Guohao Chen, Benchao Zhu, Jiawei Li, Jun Yu, Jianli Chen, Chun-Wei Chiu, Min-Feng Hsieh, Chia-Hsiu Ou, ...
ePrint Report ePrint Report
Hardware Trojans (HTs) are a longstanding threat to secure computation. Among different threat models, it is the fabrication-time insertion of additional malicious logic directly into the layout of integrated circuits (ICs) that constitutes the most versatile, yet challenging scenario, for both attackers and defenders.

Here, we present a large-scale, first-of-its-kind community effort through red-versus-blue teaming that thoroughly explores this threat. Four independently competing blue teams of 23 IC designers in total had to analyze and fix vulnerabilities of representative IC layouts, whereas a red team of 3 experts in hardware security and IC design continuously pushed the boundaries of these defense efforts through different HTs and novel insertion techniques. Importantly, we find that, despite the blue teams’ commendable efforts, even highly-optimized layouts retained at least some exploitable vulnerabilities.

Our effort follows a real-world setting for a modern 7nm technology node and industry-grade tooling for IC design, all embedded into a fully-automated and extensible benchmarking framework. To ensure the relevance of this work, strict rules that adhere to real-world requirements for IC design and manufacturing were postulated by the organizers. For example, not a single violation for timing and design-rule checks were allowed for defense techniques. Besides, in an advancement over prior art, neither red nor blue teams were allowed to use any so-called fillers and spares for trivial attack or defense approaches.

Finally, we release all methods and artifacts: the representative IC layouts and HTs, the devised attack and defense techniques, the evaluation metrics and setup, the technology setup and commercial-grade reference flow for IC design, the encompassing benchmarking framework, and all best results. This full release enables the community to continue exploring this important challenge for hardware security, in particular to focus on the urgent need for further advancements in defense strategies.
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Suparna Kundu, Quinten Norga, Angshuman Karmakar, Shreya Gangopadhyay, Jose Maria Bermudo Mera, Ingrid Verbauwhede
ePrint Report ePrint Report
Recently, the construction of cryptographic schemes based on hard lattice problems has gained immense popularity. Apart from being quantum resistant, lattice-based cryptography allows a wide range of variations in the underlying hard problem. As cryptographic schemes can work in different environments under different operational constraints such as memory footprint, silicon area, efficiency, power requirement, etc., such variations in the underlying hard problem are very useful for designers to construct different cryptographic schemes. In this work, we explore various design choices of lattice-based cryptography and their impact on performance in the real world. In particular, we propose a suite of key-encapsulation mechanisms based on the learning with rounding problem with a focus on improving different performance aspects of lattice-based cryptography. Our suite consists of three schemes. Our first scheme is Florete, which is designed for efficiency. The second scheme is Espada, which is aimed at improving parallelization, flexibility, and memory footprint. The last scheme is Sable, which can be considered an improved version in terms of key sizes and parameters of the Saber key-encapsulation mechanism, one of the finalists in the National Institute of Standards and Technology's post-quantum standardization procedure. In this work, we have described our design rationale behind each scheme. Further, to demonstrate the justification of our design decisions, we have provided software and hardware implementations. Our results show Florete is faster than most state-of-the-art KEMs on software platforms. For example, the key-generation algorithm of high-security version Florete outperforms the National Institute of Standards and Technology's standard Kyber by $47\%$, the Federal Office for Information Security's standard Frodo by $99\%$, and Saber by $57\%$ on the ARM Cortex-M4 platform. Similarly, in hardware, Florete outperforms Frodo and NTRU Prime for all KEM operations. The scheme Espada requires less memory and area than the implementation of most state-of-the-art schemes. For example, the encapsulation algorithm of high-security version Espada uses $30\%$ less stack memory than Kyber, $57\%$ less stack memory than Frodo, and $67\%$ less stack memory than Saber on the ARM Cortex-M4 platform. The implementations of Sable maintain a trade-off between Florete and Espada regarding software performance and memory requirements. Sable outperforms Saber at least by $6\%$ and Frodo by $99\%$. Through an efficient polynomial multiplier design, which exploits the small secret size, Sable outperforms most state-of-the-art KEMs, including Saber, Frodo, and NTRU Prime. The implementations of Sable that use number theoretic transform-based polynomial multiplication (SableNTT) surpass all the state-of-the-art schemes in performance, which are optimized for speed on the Cortext M4 platform. The performance benefit of SableNTT against Kyber lies in between $7-29\%$, $2-13\%$ for Saber, and around $99\%$ for Frodo.
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Weihao Wang, Shuai Han, Shengli Liu
ePrint Report ePrint Report
Anamorphic encryptions and anamorphic signatures assume a double key pre-shared between two parties so as to enable the transmission of covert messages. How to securely and efficiently distribute a double key under the dictator's surveillance is a central problem for anamorphic cryptography, especially when the users are forced to surrender their long-term secret keys or even the randomness used in the algorithms to the dictator.

In this paper, we propose Anamorphic Authentication Key Exchange (AM-AKE) to solve the problem. Similar to anamorphic encryption, AM-AKE contains a set of anamorphic algorithms besides the normal algorithms. With the help of the anamorphic algorithms in AM-AKE, the initiator and the responder are able to exchange not only a session key but also a double key. We define robustness and security notions for AM-AKE, and also prove some impossibility results on plain AM-AKE whose anamorphic key generation algorithm only outputs a key-pair. To bypass the impossibility results, we work on two sides.

-- On the one side, for plain AM-AKE, the securities have to be relaxed to resist only passive attacks from the dictator. Under this setting, we propose a generic construction of two-pass plain AM-AKE from a two-pass AKE with partially randomness-recoverable algorithms.

-- On the other side, we consider (non-plain) AM-AKE whose key generation algorithm also outputs an auxiliary trapdoor besides the key-pairs. We ask new properties from AKE: its key generation algorithm has secret extractability and other algorithms have separability. Based on such a two-pass AKE, we propose a generic construction of two-pass (non-plain) AM-AKE. The resulting AM-AKE enjoys not only robustness but also the strong security against any dictator knowing both users' secret keys and even the internal randomness of the AKE algorithms and implementing active attacks.

Finally, we present concrete AM-AKE schemes from the popular SIG+KEM paradigm and three-KEM paradigm for constructing AKE.
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14 September 2024

Bangalore, India, 3 March - 6 March 2025
Event Calendar Event Calendar
Event date: 3 March to 6 March 2025
Submission deadline: 15 October 2024
Notification: 15 November 2024
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Wollongong, Australia, 14 July - 16 July 2025
Event Calendar Event Calendar
Event date: 14 July to 16 July 2025
Submission deadline: 6 November 2024
Notification: 22 January 2025
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West Bengal, India, 14 January - 16 January 2025
Event Calendar Event Calendar
Event date: 14 January to 16 January 2025
Submission deadline: 20 September 2024
Notification: 1 October 2024
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The chair of IT Security, Brandenburg University of Technology, Cottbus-Senftenberg
Job Posting Job Posting

Our chair performs research and teaching in the area of IT Security with a strong focus on Network Security and Online Privacy. More information about us can be found at https://www.b-tu.de/en/fg-it-sicherheit.

    Tasks:
  • Active research in the area of intrusion detection systems (IDS) for critical infrastructures, secure cyber-physical systems, and artificial intelligence / machine learning for traffic analysis
  • Implementation and evaluation of new algorithms and methods
  • Cooperation and knowledge transfer with industrial partners
  • Publication of scientific results
  • Assistance with teaching
    Requirements:
  • Master’s degree (or equivalent) and PhD degree (only for PostDocs) in Computer Science or related disciplines
  • Strong interest in IT security and/or networking and distributed systems
  • Knowledge of at least one programming language (C++, Java, etc.) and one scripting language (Perl, Python, etc.) or strong willingness to quickly learn new programming languages
  • Linux/Unix skills
  • Knowledge of data mining, machine learning, statistics and result visualization concepts is of advantage
  • Excellent working knowledge of English; German is of advantage
  • Excellent communication skills
    Applications containing the following documents:
  • A detailed Curriculum Vitae
  • Transcript of records from your Master studies
  • An electronic version of your Master thesis, if possible should be sent in a single PDF file as soon as possible, but not later than 04.10.2024 at itsec-jobs.informatik@lists.b-tu.de. Applications sent to email addresses other than that will be automatically discarded

Closing date for applications:

Contact: Prof. Dr.-Ing. Andriy Panchenko,
Email: itsec-jobs.informatik@lists.b-tu.de

More information: https://www.informatik.tu-cottbus.de/~andriy/phd-ad-btu_en.pdf

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Chalmers University of Technology, Department of Computer Science & Engineering, Gothenburg, Sweden
Job Posting Job Posting
The CryptoTeam at Chalmers University of Technology is looking for a PhD student (5 years, full position) to join the team.

This position offers an exciting opportunity to delve into the rapidly evolving field of Transparency Protocols and to make impactful contributions towards new designs, security proofs, and the uptake of this technology. You will join the CryptoTeam under the supervision of Assistant Professor Elena Pagnin and your base will be Chalmers (Gothenburg, Sweden). Chalmers is a renown University in Technical subjects, and provides a dynamic, highly international work environment within a world-leading research group with expertise in various aspects of cryptography, security, formal methods, and their applications.

For more information visit the official ad https://www.chalmers.se/en/about-chalmers/work-with-us/vacancies/?rmpage=job&rmjob=13180&rmlang=UK . Note that only applications received via the Chalmers Vacancies portal will be considered. Application deadline: October 4, 2024.

Closing date for applications:

Contact: Elena Pagnin

More information: https://www.chalmers.se/en/about-chalmers/work-with-us/vacancies/?rmpage=job&rmjob=13180&rmlang=UK

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Chinese Academy of Sciences, Academy of Mathematics and Systems Science
Job Posting Job Posting
The Academy of Mathematics and Systems Science (AMSS) of Chinese Academy of Sciences invites applications for tenured and tenure-track faculty positions at all ranks and in the areas of information theory, theoretical computer science and cryptography, coding and communication, etc. Remuneration package will be driven by market competitiveness and individual performance. Excellent fringe benefits include annual research funds, settle-down allowance and low-priced tentative apartments near office for 5 years. Successful applicants are expected to conduct full-time research in AMSS. Teaching is appreciated, but not an obligation.

Closing date for applications:

Contact: Dr. Zhifang Zhang, email: zfz@amss.ac.cn; Dr. Yanbin Pan, email: panyanbin@amss.ac.cn; Dr. Xiutao Feng, email: fengxt@amss.ac.cn

More information: https://www.mathjobs.org/jobs/list/23139

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Hebrew University of Jerusalem
Job Posting Job Posting
Fully funded Ph.D. and postdoc positions at the Hebrew University of Jerusalem are available at the Cryptography Group at the School of Computer Science and Engineering. Email applications should include a CV and references (if available).

Closing date for applications:

Contact: Ilan Komargodski (ilank at cs dot huji dot ac dot il)

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University of Amsterdam, Netherlands
Job Posting Job Posting
Do you like solving challenges in cyber security? Do you want to become part of a growing team of cybersecurity researchers at the University of Amsterdam whose research contributes to securing our digital world? The Theory of Computer Science (TCS) and Complex Cyber Infrastructure (CCI) research groups of the Informatics Institute are looking for a new assistant professor in cyber security. You will be able to hire a PhD student as part of the startup-package.

You will conduct research in the “Challenges in Cyber Security” project, one of the few projects receiving funding in the prestigious NWO Gravitation program. In cooperation with researchers from TU Eindhoven, Radboud University Nijmegen, VU Amsterdam, and CWI, you will work on the grand challenges of cybersecurity in areas such as cryptography, software security, or physical security. Besides cutting-edge research, you will also contribute to education – for example, in the top-rated Security and Network Engineering MSc program – and other activities, including acquisition and management of funded research projects, supervision of PhD students, and supervision of BSc/MSc graduation projects.

Closing date for applications:

Contact: Christian Schaffner

More information: https://vacatures.uva.nl/UvA/job/Assistant-Professor-in-Cyber-Security/802718502/

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Suvadeep Hajra, Debdeep Mukhopadhyay
ePrint Report ePrint Report
Side-channel analysis (SCA) compromises the security of cryptographic devices by exploiting various side-channel leakages such as power consumption, electromagnetic (EM) emanations, or timing variations, posing a practical threat to the security and privacy of modern digital systems. In power or EM SCA, statistical or machine learning methods are employed to extract secret information from power/EM traces. In many practical scenarios, raw power/EM traces can span hundreds of thousands of features, with relevant leakages occurring over only a few small segments. Consequently, existing SCAs often select a small number of features before launching the attack, making their success highly dependent on the feasibility of feature selection. However, feature selection may not always be possible, such as in the presence of countermeasures like masking or jitters.

Several recent works have employed deep learning (DL) methods to conduct SCA on long raw traces, thereby reducing dependence on feature selection steps. However, these methods often perform poorly against various jitter-based countermeasures. While some of these methods have shown high robustness to jitter-based countermeasures on relatively shorter traces, we demonstrate in this work that their performance deteriorates as trace lengths increase. Based on these observations, we develop a hierarchical DL model for SCA on long traces that is robust against various countermeasures. The proposed model, HierNet, extracts information from long traces using a two-level information assimilation process. At the base level, a DL model with shift-invariance is employed to extract information from smaller trace segments. Subsequently, a top-level DL model integrates the outputs of the base model to generate the final output. The proposed model has been experimentally evaluated against various combinations of masking, random delay, and clock jitter countermeasures using traces with lengths exceeding $200K$ features. The results have been compared with three existing SCA benchmark models. They demonstrate HierNet's superiority in several scenarios, such as on long traces, against clock jitter countermeasures, and low training data scenarios. In particular, while other models fail to reach the guessing entropy $1$ using as many as $5K$ traces, HierNet achieves the same with fewer than or close to $10$ traces.
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Chengru Zhang, Xiao Yang, David Oswald, Mark Ryan, Philipp Jovanovic
ePrint Report ePrint Report
With the increasing spread of fake videos for misinformation, proving the provenance of an edited video (without revealing the original one) becomes critical. To this end, we introduce Eva, the first cryptographic protocol for authenticating lossy-encoded videos. Compared to previous cryptographic methods for image authentication, Eva supports significantly larger amounts of data that undergo complex transformations during encoding. We achieve this by decomposing repetitive and manageable components from video codecs, which can then be handled using Incrementally Verifiable Computation (IVC). By providing a formal definition and security model for proofs of video authenticity, we demonstrate the security of Eva under well-established cryptographic assumptions.

To make Eva efficient, we construct an IVC based on folding schemes that incorporate lookup arguments, resulting in a linear-time prover whose proofs can be compressed to a constant size. We further improve the performance of Eva through various optimizations, including tailored circuit design and GPU acceleration. The evaluation of our implementation shows that Eva is practical: for a $1$-minute HD ($1280 \times 720$) video encoded in H.264 at $30$ frames per second, Eva generates a proof in about $2.5$ hours on consumer-grade hardware at a speed of $5.5$ μs per pixel, surpassing previous cryptographic image authentication schemes that support arbitrary editing operations by more than an order of magnitude.
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Pascal Reisert, Marc Rivinius, Toomas Krips, Sebastian Hasler, Ralf Küsters
ePrint Report ePrint Report
Many of the currently best actively secure Multi-Party Computation (MPC) protocols like SPDZ (Damgård et al., CRYPTO 2012) and improvements thereof use correlated randomness to speed up the time-critical online phase. Although many of these protocols still rely on classical Beaver triples, recent results show that more complex correlations like matrix or convolution triples lead to more efficient evaluations of the corresponding operations, i.e. matrix multiplications or tensor convolutions. In this paper, we address the evaluation of multivariate polynomials with a new form of randomness: polytuples. We use the polytuples to construct a new family of randomized encodings which then allow us to evaluate the given multivariate polynomial. Our approach can be fine-tuned in various ways to the constraints of applications at hand, in terms of round complexity, bandwidth, and tuple size. We show that for many real-world setups, a polytuples-based online phase outperforms state-of-the-art protocols based on Beaver triples.
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Alessandro Chiesa, Marcel Dall'Agnol, Ziyi Guan, Nicholas Spooner, Eylon Yogev
ePrint Report ePrint Report
Sigma protocols are elegant cryptographic proofs that have become a cornerstone of modern cryptography. A notable example is Schnorr's protocol, a zero-knowledge proof-of-knowledge of a discrete logarithm. Despite extensive research, the security of Schnorr's protocol in the standard model is not fully understood.

In this paper we study Kilian's protocol, an influential public-coin interactive protocol that, while not a sigma protocol, shares striking similarities with sigma protocols. The first example of a succinct argument, Kilian's protocol is proved secure via rewinding, the same idea used to prove sigma protocols secure. In this paper we show how, similar to Schnorr's protocol, a precise understanding of the security of Kilian's protocol remains elusive. We contribute new insights via upper bounds and lower bounds. - Upper bounds. We establish the tightest known bounds on the security of Kilian's protocol in the standard model, via strict-time reductions and via expected-time reductions. Prior analyses are strict-time reductions that incur large overheads or assume restrictive properties of the PCP underlying Kilian's protocol. - Lower bounds. We prove that significantly improving on the bounds that we establish for Kilian's protocol would imply improving the security analysis of Schnorr's protocol beyond the current state-of-the-art (an open problem). This partly explains the difficulties in obtaining tight bounds for Kilian's protocol.
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Peizhao Zhou, Xiaojie Guo, Pinzhi Chen, Tong Li, Siyi Lv, Zheli Liu
ePrint Report ePrint Report
Secure Multi-party Computation (MPC) provides a promising solution for privacy-preserving multi-source data analytics. However, existing MPC-based collaborative analytics systems (MCASs) have unsatisfying performance for scenarios with dynamic databases. Naively running an MCAS on a dynamic database would lead to significant redundant costs and raise performance concerns, due to the substantial duplicate contents between the pre-updating and post-updating databases.

In this paper, we propose $Shortcut$, a framework that can work with MCASs to enable efficient queries on dynamic databases that support data insertion, deletion, and update. The core idea of $Shortcut$ is to materialize previous query results and directly update them via our query result update (QRU) protocol to obtain current query results. We customize several efficient QRU protocols for common SQL operators, including Order-by-Limit, Group-by-Aggregate, Distinct, Join, Select, and Global Aggregate. These protocols are composable to implement a wide range of query functions. In particular, we propose two constant-round protocols to support data insertion and deletion. These protocols can serve as important building blocks of other protocols and are of independent interest. They address the problem of securely inserting/deleting a row into/from an ordered table while keeping the order. Our experiments show that $Shortcut$ outperforms naive MCASs for minor updates arriving in time, which captures the need of many realistic applications (e.g., insurance services, account data management). For example, for a single query after an insertion, $Shortcut$ achieves up to $186.8 \times$ improvement over those naive MCASs without our QRU protocols on a dynamic database with $2^{16} \sim 2^{20}$ rows, which is common in real-life applications.
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Masayuki Fukumitsu, Shingo Hasegawa
ePrint Report ePrint Report
We consider the multi-user security under the adaptive corruptions and key leakages ($\rm{MU^{c\&l}}$ security) for lattice-based signatures. Although there exists an $\rm{MU^{c\&l}}$ secure signature based on a number-theoretic assumption, or a leakage-resilient lattice-based signature in the single-user setting, $\rm{MU^{c\&l}}$ secure lattice-based signature is not known.

We examine the existing lattice-based signature schemes from the viewpoint of $\rm{MU^{c\&l}}$ security, and find that the security of the Lyubashevsky's signature, which is proven to have the ordinary single-user security only, can be extended to the multi-user security even if we take the adaptive corruptions and the key leakages into account.

Our security proof in the multi-user setting makes use of the feature of the SIS problem so that a SIS instance is set to the public parameter and a reduction algorithm can set a public key with a secret key in order to answer a corruption query. We also show that the entropy of the secret key is kept under the bounded leakage with a high probability and then the leakage resilience of signature holds.
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Fuchun Lin, Chaoping Xing, Yizhou Yao
ePrint Report ePrint Report
Studies of vector oblivious linear evaluation (VOLE)-based zero-knowledge (ZK) protocols flourish in recent years. Such ZK protocols feature optimal prover computation and a flexibility for handling arithmetic circuits over arbitrary fields. However, most of them have linear communication, which constitutes a bottleneck for handling large statements in a slow network. The pioneer work AntMan (CCS'22), achieved sublinear communication for the first time within VOLE-based ZK, but lost the advantage of fast proving. In this work, we propose two new VOLE-based ZK constructions that achieve sublinear communication and linear computation, simultaneously. Let $\mathcal{C}$ be a circuit with size $S$, input size $n$, and depth $d$. In particular, our first ZK, specialized for layered circuits, has communication $O(n+d\log{S})$, while our second ZK can be used to prove general circuits and has communication $O(n+d\log{S}+d^2)$.

Our results are obtained by introducing the powerful sum-check techniques from the mature line of works on interactive proofs into the context of VOLE-based ZK for the first time. Reminiscent of the non-interactive line-point zero-knowledge proof system (ITC'21), we introduce an interactive line-point zero-knowledge (ILPZK) proof system, which closely connects with VOLE-based ZK protocols. In addition, our works also enrich the studies of ZK based on interactive proofs, with new interesting features (e.g., having information-theoretic UC-security, naturally supporting any field) achieved.
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Aner Ben-Efraim, Lior Breitman, Jonathan Bronshtein, Olga Nissenbaum, Eran Omri
ePrint Report ePrint Report
Garbled circuits are a powerful and important cryptographic primitive, introduced by Yao [FOCS 1986] for secure two-party computation. Beaver, Micali and Rogaway (BMR) [STOCS 1990] extended the garbled circuit technique to construct the first constant-round secure multiparty computation (MPC) protocol. In the BMR protocol, the garbled circuit size grows linearly and the online computation time grows quadratically with the number of parties. Previous solutions to avoid this relied on key-homomorphic PRFs, incurring a large garbled circuit size and slow online computation time. We present MYao, a new multiparty protocol for achieving a ``Yao'' garbled circuit, i.e., the garbled circuit size and online computation time are independent of the number of parties. The key innovation is that the parties collaboratively compute the PRF in MPC, which was previously believed to be inefficient. In this paper, we challenge this long-standing assumption by basing the garbled circuit construction on ``MPC-friendly'' PRFs. One of the highlights of our new technique is that we are able to achieve, for the first time, full row-reduction in multiparty garbled circuits. To achieve this optimization without increasing the number of rounds, we utilize free-XOR and half gates, presenting a new technique for choosing the keys, based on a naturally occurring relation between the 2 keys of the 2 half-gates. MYao reduces the garbled circuit size by more than 90%, the total communication by more than 75%, and the online computation time by more than 10%, compared to all known solutions based on key-homomorphic PRFs, thus substantially improving the overall efficiency in both the offline and the online phases. Furthermore, MYao significantly improves over semi-honest BMR in online phase efficiency when the number of parties exceeds 80.
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