International Association for Cryptologic Research

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for Cryptologic Research

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21 November 2025

Shuto Kuriyama, Russell W. F. Lai, Michał Osadnik, Lorenzo Tucci
ePrint Report ePrint Report
We present SALSAA, a more efficient and more versatile extension of the state-of-the-art lattice-based fully-succinct argument frameworks, ``RoK, paper, SISsors (RPS)'' and ``RoK and Roll (RnR)'' [Klooß, Lai, Nguyen, and Osadnik; ASIACRYPT'24, '25], integrating the sumcheck technique as a main component. This integration enables us to design an efficient norm-check protocol (controlling the norm during witness extraction) with a strictly linear-time prover while reducing proof sizes by 2-3$\times$ compared to the previous quasi-linear-time norm-check in RPS/RnR, eliminating a central performance bottleneck. The sumcheck integration also allows us to natively support a wider class of relations, including rank-1 constraint systems (R1CS), which are widely used to express real-world computations.

To demonstrate the versatility and efficiency of our framework, we showcase three impactful applications achieved by different RoKs (Reductions of Knowledge) compositions: (i) a lattice-based succinct argument of knowledge with a linear-time prover, achieving a verifier time of $41$ ms, prover runtime of $10.61$ s, and proof size of $979$ KB for a witness of $2^{28}$ $\mathbb{Z}_q$ elements; (ii) a polynomial commitment scheme with matching performance; and (iii) the first lattice-based folding scheme natively operating on $\ell_2$-norm-bounded witnesses, achieving highly efficient verification in $2.28$ ms and producing a proof of just $73$ KB for a witness of $2^{28}$ $\mathbf{Z}_q$ elements, outperforming prior works for the family of linear relations.

We provide a modular, concretely efficient Rust implementation of our framework, benchmarked over cyclotomic rings with AVX-512-accelerated NTT-based arithmetic, demonstrating the practical efficiency of our approach.
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Joseph Jaeger, Roy Stracovsky
ePrint Report ePrint Report
Anamorphic signature schemes (KPPYZ, Crypto 2023) allow users to hide encrypted messages in signatures to allow covert communication in a hypothesized scenario where encryption is outlawed by a "dictator" but authentication is permitted. We enhance the security of anamorphic signatures by proposing two parallel notions of unforgeability which close gaps in existing security definitions. The first notion considers a dictator who wishes to forge anamorphic signatures. This notion patches a divide between the definition and a stated security goal of robustness (BGHMR, Eurocrypt 2024). We port two related BGHMR constructions to the signature scheme setting and demonstrate that, as presented, both of these and a construction from KPPYZ are insecure under an active dictator. However, two of the three can easily be modified to satisfy our definition. The second notion we propose considers a recipient who wishes to forge signatures. To motivate this notion, we identify a gap in an existing security definition from KPPYZ and present attacks that allow parties to be impersonated when using schemes erroneously deemed secure. We then formalize our new unforgeability definition to close this gap. Interestingly, while the new definition is only modestly different from the old one, the change introduces subtle technical challenges that arise when proving security. We overcome these challenges in our reanalysis of existing anamorphic signature schemes by showing they achieve our new notion when built from chosen-randomness secure signatures or with encryption that satisfies a novel ideal-model simulatability property.
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Kaishuo Cheng, Joseph Jaeger
ePrint Report ePrint Report
There is a gap between the security of constrained PRFs required in some applications and the security provided by existing definitions. This gap is typically patched by only considering nonadaptive security or manually mixing the CPRF with a random oracle (implicitly constructing a new CPRF) to achieve adaptive security. We fill this gap with a new definition for constrained PRFs with strong adaptive security properties and proofs that it is achieved by practical constructions based on the cascade PRF (which generalizes the GGM construction) and AMAC. We apply the definition for analyzing searchable symmetric encryption and puncturable key wrapping.
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Joseph Jaeger, Deep Inder Mohan
ePrint Report ePrint Report
The Fuchsbauer, Kiltz, and Loss (CRYPTO 2018) claim that (some) hardness results in the algebraic group model imply the same hardness results in the generic group model was recently called into question by Katz, Zhang, and Zhou (ASIACRYPT 2022). The latter gave an interpretation of the claim under which it is incorrect. We give an alternate interpretation under which it is correct, using natural frameworks for capturing generic and algebraic models for arbitrary algebraic structures. Most algebraic analyses in the literature can be captured by our frameworks, making the claim correct for them.
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Arman Kolozyan, Bram Vandenbogaerde, Janwillem Swalens, Lode Hoste, Stefanos Chaliasos, Coen De Roover
ePrint Report ePrint Report
Zero-knowledge proofs (ZKPs) allow a prover to convince a verifier of a statement's truth without revealing any other information. In recent years, ZKPs have matured into a practical technology underpinning major applications. However, implementing ZKP programs remains challenging, as they operate over arithmetic circuits that encode the logic of both the prover and the verifier. Therefore, developers must not only express the computations for generating proofs, but also explicitly specify the constraints for verification. As recent studies have shown, this decoupling may lead to critical ZKP-specific vulnerabilities. Unfortunately, existing tools for detecting them are limited, as they: (1) are tightly coupled to specific ZKP languages, (2) are confined to the constraint level, preventing reasoning about the underlying computations, (3) target only a narrow class of bugs, and (4) suffer from scalability bottlenecks due to reliance on SMT solvers.

To address these limitations, we propose a language-agnostic formal model, called the Domain Consistency Model (DCM), which captures the relationship between computations and constraints. Using this model, we provide a taxonomy of vulnerabilities based on computation-constraint mismatches, including novel subclasses overlooked by existing models. Next, we implement a lightweight automated bug detection tool, called CCC-Check, which is based on abstract interpretation. We evaluate CCC-Check on a dataset of 20 benchmark programs. Compared to the SoTA verification tool CIVER, our tool achieves a 100-1000$\times$ speedup, while maintaining a low false positive rate. Finally, using the DCM, we examine six widely adopted ZKP projects and uncover 15 previously unknown vulnerabilities. We reported these bugs to the projects' maintainers, 13 of which have since been patched. Of these 15 vulnerabilities, 12 could not be captured by existing models.
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Jianhua Wang, Tao Huang, Shuang Wu, Zilong Liu
ePrint Report ePrint Report
In this paper, we aim to explore the design of low-latency authenticated encryption schemes particularly for memory encryption, with a focus on the temporal uniqueness property. To achieve this, we present the low-latency Pseudo-Random Function (PRF) called $\mathtt{Twinkle}$ with an output up to 1152 bits. Leveraging only one block of $\texttt{Twinkle}$, we developed $\texttt{Twinkle-AE}$, a specialized authenticated encryption scheme with six variants covering different cache line sizes and security requirements. We also propose $\texttt{Twinkle-PA}$, a pointer authentication algorithm, which takes a 64-bit pointer and 64-bit context as input and outputs a tag of 1 to 32 bits. We conducted thorough security evaluations of both the PRFs and these schemes, examining their robustness against various common attacks. The results of our cryptanalysis indicate that these designs successfully achieve their targeted security objectives. Hardware implementations using the FreePDK45nm library show that $\texttt{Twinkle-AE}$ achieves an encryption and authentication latency of 3.83 $ns$ for a cache line. In comparison, $\texttt{AES}$-CTR with WC-MAC scheme and Ascon-128a achieve latencies of 9.78 $ns$ and 27.30 $ns$, respectively. For the pointer authentication scheme $\texttt{Twinkle-PA}$, the latency is 2.04 $ns$, while $\texttt{QARMA-64-}\sigma_0$ has a latency of 5.57 $ns$.
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Shunya Otomo, Kenji Yasunaga
ePrint Report ePrint Report
A recent study by Yamashita and Yasunaga (GameSec 2023) presented a constant-round deterministic broadcast protocol secure against \emph{detection-averse} adversaries --- those who prefer to attack without being detected. In this work, we revisit their protocol and observe that it remains secure even against a broader class of adversaries, not necessarily detection-averse. We formalize its detection mechanism as \emph{local detectability} and construct broadcast protocols with local detectability that address two weaknesses of the original protocol: (1) it only guarantees weak validity, and (2) it may cause false detections. Our first protocol achieves round complexity four against rational adversaries and $t+4$ against malicious adversaries, where the adversary corrupts at most $t$ parties. Our second protocol achieves the optimal round complexity of $t+1$ for malicious adversaries, while the round complexity is four against detection-averse adversaries.
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Hamidreza Khoshakhlagh
ePrint Report ePrint Report
We revisit the notion of Simulation Extractability (SE) for SNARKs in the updatable setting. We demonstrate that existing formal definitions of SE in this setting are insufficient to guarantee the required non-malleability in real-world scenarios. Towards this, we first identify and frame a malleability vulnerability: a cross-SRS reinterpretation attack, which shows that an adversary can reuse or maul proofs across different, correlated SRSs generated through the update procedure. This is made possible because existing security definitions fail to model an adversary’s ability to observe simulated proofs relative to various derived SRSs. To close this security gap, we propose a revised and stronger security notion of Updatable Simulation Extractability (USE) which was originally defined in [GKK+22]. Our definition models a dynamic environment where the SRS is adaptively updatable by the adversary, who can also query simulation oracles for proofs under the resulting family of reachable SRSs. This captures the full extent of the adversarial capabilities observed in practice. Finally, we provide positive results for popular polynomial-IOP-based SNARKs, and show that these schemes satisfy our stronger USE notion, provided the circuit-specific SRS is securely bound into the proof transcript, e.g., via a correct implementation of the Fiat-Shamir transformation.
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Election Election
This announcement is in connection with the recent IACR 2025 election conducted using the Helios electronic voting system. Regrettably, we have encountered a fatal technical problem that prevents us from concluding the election and accessing the final tally.

For this election and in accordance with the bylaws of the IACR, the three members of the IACR 2025 Election Committee acted as independent trustees, each holding a portion of the cryptographic key material required to jointly decrypt the results. This aspect of Helios’ design ensures that no two trustees could collude to determine the outcome of an election or the contents of individual votes on their own: all trustees must provide their decryption shares.

Unfortunately, one of the three trustees has irretrievably lost their private key, an honest but unfortunate human mistake, and therefore cannot compute their decryption share. As a result, Helios is unable to complete the decryption process, and it is technically impossible for us to obtain or verify the final outcome of this election.

This situation is visible on the public election page in Helios, where the trustees are listed: you can see that two trustees have successfully uploaded their decryption share material, whereas one has not. We point this out so that one can independently confirm that the issue arises from the strict cryptographic requirements of the system itself. You can consult this information at: https://vote.heliosvoting.org/helios/elections/e1130d04-aac6-11f0-95c8-3a40ecaef3ba/trustees/view

After careful consideration, we have decided that the only responsible course of action is to void this election and start a new election from scratch.

The new election will run from November 21 to December 20, using the same IACR membership electoral roll and the same list of candidates, which you can consult here: https://www.iacr.org/elections/2025/candidates.php

For all eligible voters, you will receive a separate Helios message inviting you to participate in the new run of the IACR 2025 election. Please note that if you opted out from Helios emails, we could not add you to the list of voters for the new election. In this case, you may opt back in at https://vote.heliosvoting.org/optin/ and send an email to elections@iacr.org to let us know, so that we can add you to the list of voters.

We are deeply sorry for this failure and for the disruption it has caused; this situation should not have happened, and we take it very seriously. We respectfully ask for your understanding and patience while we remedy the problem and ensure that the renewed process is as smooth, secure, and transparent as possible.

We are already drawing lessons from this incident and putting safeguards in place, so that it cannot reoccur. In particular, we will adopt a 2-out-of-3 threshold mechanism for the management of private keys, and we will circulate a clear written procedure for all trustees to follow before and during the election. Following the resignation of Moti Yung from his position as trustee for this election, he will be replaced by Michel Abdalla.

With our sincere apologies and best regards,

The IACR 2025 Election committee, with the approval of the IACR Board of Directors

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20 November 2025

Award Award
We are proud to announce the winners of the 2025 IACR Test-of-Time Award for Asiacrypt.

The IACR Test-of-Time Award honors papers published at the 3 IACR flagship conferences 15 years ago which have had a lasting impact on the field.

The Test-of-Time award for Asiacrypt 2010 is awarded to the following paper:

Constant-Size Commitments to Polynomials and Their Applications
by Aniket Kate, Gregory M. Zaverucha, and Ian Goldberg

For introducing the first constant-size polynomial commitment scheme, a cornerstone of modern succinct zero-knowledge proofs.


Congratulations to the winners!
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19 November 2025

Marten van Dijk, Dandan Yuan
ePrint Report ePrint Report
In this work, we initiate the formal study of oblivious batch updates over outsourced encrypted Bloom filters, focusing on scenarios where a storage-limited sender must insert or delete batches of elements in a Bloom filter maintained on an untrusted server. Our survey identifies only two prior approaches (CCS 2008 and CCS 2012) that can be adapted to this problem. However, they either fail to provide adequate security in dynamic scenarios or incur prohibitive update costs that scale with the filter’s maximum capacity rather than the actual batch size.

To address these limitations, we introduce a new cryptographic primitive, $\textit{Oblivious Bloom Filter Insertion}$ ($\textsf{OBFI}$), and propose novel constructions. At the core of our design is a novel building block, $\textit{Oblivious Bucket Distribution}$ ($\textsf{OBD}$), which enables a storage-limited sender to distribute a large array of elements, uniformly sampled from a finite domain, into small, fixed-size buckets in a data-oblivious manner determined by element order. The design of $\textsf{OBD}$ is further supported by identifying and proving a new structural property of such arrays, which establishes tight and explicit probabilistic bounds on the number of elements falling within predefined subranges of the domain.

Our $\textsf{OBFI}$ constructions achieve adaptive data-obliviousness and ensure that batch update costs scale primarily with the batch size. Depending on the variant, the sender’s storage requirement ranges from $O(\lambda)$, where $\lambda$ is the security parameter, down to $O(1)$. Finally, we demonstrate the practicality of $\textsf{OBFI}$ by integrating it into representative Bloom-filter-based cryptographic protocols for Searchable Symmetric Encryption, Public-key Encryption with Keyword Search, and Outsourced Private Set Intersection, thereby obtaining batch-updatable counterparts with state-of-the-art security and performance.
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Amit Agarwal, Kushal Babel, Sourav Das, Babak Poorebrahim Gilkalaye, Arup Mondal, Benny Pinkas, Peter Rindal, Aayush Yadav
ePrint Report ePrint Report
A Batched Threshold Encryption (BTE) scheme enables a committee of servers to perform a lightweight (in terms of communication and computation) threshold decryption of an arbitrary batch of ciphertexts from a larger pool, while ensuring the privacy of ciphertexts that are outside the batch. Such a primitive has a direct application in designing encrypted mempools for MEV protection in modern blockchains. Bormet et al. (USENIX 2025) recently proposed a BTE scheme called “BEAT-MEV” which is concretely efficient for small to moderate batch sizes.

In this work, we improve and extend the BEAT-MEV scheme in multiple ways. First, we improve the computational cost from quadratic to quasilinear in the batch size, thus making it practical for large batch sizes. This improvement is achieved by substituting the key-homomorphic punctured PRF used in BEAT-MEV with an FFT-friendly alternative. Second, we extend the ideas in their scheme to the weighted setting, where each server in the committee has an associated 'weight' value (e.g., stake weight of validators in PoS blockchains), while crucially ensuring that the communication cost remains independent of the weights. In contrast, BEAT-MEV with naive virtualization would incur communication cost linear in the total weight. Third, for handling the small failure rate inherent in BEAT-MEV scheme due to index collisions across different clients at the time of encryption, we propose a generalization of their suggested approach which offers an option to trade off between ciphertext size and server communication for a given failure rate.

We implement and evaluate our scheme and compare it with BEAT-MEV to demonstrate our concrete improvement. In the unweighted setting, we improve the computational cost (without increasing the communication cost) by ≈ 6× for a batch size of 512 ciphertexts. In the weighted setting, we improve the communication cost (without compromising computation time), over BEAT-MEV with naive virtualization, by ≈ 50× for 100 validators with total stake weight 5000 distributed as per the latest Solana stake distribution.
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Hanlin Ren, Yichuan Wang, Yan Zhong
ePrint Report ePrint Report
Given a circuit $G: \{0, 1\}^n \to \{0, 1\}^m$ with $m > n$, the *range avoidance* problem ($\text{Avoid}$) asks to output a string $y\in \{0, 1\}^m$ that is not in the range of $G$. Besides its profound connection to circuit complexity and explicit construction problems, this problem is also related to the existence of *proof complexity generators* --- circuits $G: \{0, 1\}^n \to \{0, 1\}^m$ where $m > n$ but for every $y\in \{0, 1\}^m$, it is infeasible to prove the statement "$y\not\in\mathrm{Range}(G)$" in a given propositional proof system.

This paper connects these two problems with the existence of *demi-bits generators*, a fundamental cryptographic primitive against nondeterministic adversaries introduced by Rudich (RANDOM '97). $\bullet$ We show that the existence of demi-bits generators implies $\text{Avoid}$ is hard for nondeterministic algorithms. This resolves an open problem raised by Chen and Li (STOC '24). Furthermore, assuming the demi-hardness of certain LPN-style generators or Goldreich's PRG, we prove the hardness of $\text{Avoid}$ even when the instances are constant-degree polynomials over $\mathbb{F}_2$. $\bullet$ We show that the dual weak pigeonhole principle is unprovable in Cook's theory $\mathsf{PV}_1$ under the existence of demi-bits generators secure against $\mathbf{AM}/_{O(1)}$, thereby separating Jeřábek's theory $\mathsf{APC}_1$ from $\mathsf{PV}_1$. Previously, Ilango, Li, and Williams (STOC '23) obtained the same separation under different (and arguably stronger) cryptographic assumptions. $\bullet$ We transform demi-bits generators to proof complexity generators that are *pseudo-surjective* in certain parameter regime. Pseudo-surjectivity is the strongest form of hardness considered in the literature for proof complexity generators.

Our constructions are inspired by the recent breakthroughs on the hardness of $\text{Avoid}$ by Ilango, Li, and Williams (STOC '23) and Chen and Li (STOC '24). We use *randomness extractors* to significantly simplify the construction and the proof.
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Kasra Abbaszadeh, Hossein Hafezi, Jonathan Katz, Sarah Meiklejohn
ePrint Report ePrint Report
Succinct zero-knowledge arguments (zk-SNARKs) enable a prover to convince a verifier of the truth of a statement via a succinct and efficiently verifiable proof without revealing any additional information about the secret witness. A barrier to practical deployment of zk-SNARKs is their high proving cost. With this motivation, we study server-aided zk-SNARKs, where a client/prover outsources most of its work to a single, untrusted server while the server learns nothing about the witness or even the proof. We formalize this notion and show how to realize server-aided proving for widely deployed zk-SNARKs, including Nova, Groth16, and Plonk.

The key building block underlying our designs is a new primitive, encrypted multi-scalar multiplication (EMSM), that enables private delegation of multi-scalar multiplications (MSMs). We construct an EMSM from variants of the learning parity with noise assumption in which the client does $O(1)$ group operations, while the server’s work matches that of the plaintext MSM.

We implement and evaluate our constructions. Compared to local proving, our techniques lower the client's computation by up to $20\times$ and reduce the proving latency by up to $9\times$.
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Bergerat Loris, Bonte Charlotte, Benjamin R. Curtis, Jean-Baptiste Orfila, Pascal Paillier, Samuel Tap
ePrint Report ePrint Report
Fully Homomorphic Encryption (FHE) schemes typically experience significant data expansion during encryption, leading to increased computational costs and memory demands during homomorphic evaluations compared to their plaintext counterparts. This work builds upon prior methods aimed at reducing ciphertext expansion by leveraging matrix secrets under the Matrix-LWE assumption. In particular, we consider a ciphertext format referred to in this work as common mask (CM) ciphertexts, which comprises a shared mask and multiple message bodies. Each body encrypts a distinct message while reusing the common random mask. We demonstrate that all known FHEW/TFHE style ciphertext variants and operations can be naturally extended to this CM format. Our benchmarks highlight the potential for amortizing operations using the CM structure, significantly reducing overhead. For instance, in the boolean setting, we have up to a 51% improvement when packing 8 messages. Beyond ciphertext compression and amortized evaluations, the CM format also enables the generalization of several core-TFHE operations. Specifically, we support applying distinct lookup tables on different encrypted messages within a single CM ciphertext and private linear operations on messages encrypted within the same CM ciphertext.
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Tamir Tassa, Arthur Zamarin
ePrint Report ePrint Report
Secure multiparty computation (MPC) enables mutually distrustful parties to jointly compute functions over private data without revealing their inputs. A central paradigm in MPC is the secret-sharing-based model, where secret sharing underpins the efficient realization of arithmetic, comparison, numerical, and Boolean operations on shares of private inputs. In this paper, we systematize protocols for these operations, with particular attention to two foundational contributions \cite{ChidaGHIKLN18,NO07} that devised secure multiplication and comparison. Our survey provides a unified, self-contained exposition that highlights the composability, performance trade-offs, and implementation choices of these protocols. We further demonstrate how they support practical privacy-preserving systems, including recommender systems, distributed optimization platforms, and e-voting infrastructures. By clarifying the protocol landscape and connecting it to deployed and emerging applications, we identify concrete avenues for improving efficiency, scalability, and integration into real-world MPC frameworks. Our goal is to bridge theory and practice, equipping both researchers and practitioners with a deeper understanding of secret-sharing-based MPC as a foundation for privacy technologies.
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Ulrich Haböck
ePrint Report ePrint Report
We outline how to generalize the Guruswami-Sudan list decoder anal- ysis from Ben–Sasson, Carmon, Ishai, Kopparty and Saraf [BCI+20] in order to obtain a “global” proximity gap, called mutual correlated agree- ment in Arnon, Chiesa, Fenzi and Yogev [WHIR 2024], or strong correlated agreement in Zeilberger [Khatam 24].
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18 November 2025

Silence Laboratories (remote)
Job Posting Job Posting
Silence Laboratories is looking for cryptography research interns for the summer of 2026. Candidates must be students enrolled in a PhD program, or otherwise be able to demonstrate a comparable level of proficiency in cryptography. The internship will be centered on a privacy preserving computation product being built at Silence, and will involve investigating the underlying theory (likely a subfield of MPC) and ideally result in a prototype implementation.

At Silence, you can expect unique and impactful opportunities to put theory to practice, freedom in how you approach your work, competitive pay, and a chance to work with some of the top research and engineering talent.

The internship will be fully remote and for a duration of 3 months, although exact dates can be flexible. Please send your CV and a link to your homepage (if available) to internships@silencelaboratories.com with the title “Summer 2026 Application [Your Name]” by Dec 20th 2025 for full consideration.

Closing date for applications:

Contact: internships@silencelaboratories.com

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Chongrong Li, Pengfei Zhu, Yun Li, Zhanpeng Guo, Jingyu Li, Yuncong Hu, Zhicong Huang, Cheng Hong
ePrint Report ePrint Report
Secure lookup table (LUT) protocols allow retrieving values from a table at secret indices, and have become a promising approach for the secure evaluation of non-linear functions. Most existing LUT protocols target the two-party setting, where the best protocols achieve a communication cost of $O(N)$ for a table of size $N$. MAESTRO (Morita et al., USENIX Security 2025) represents the state-of-the-art LUT protocol for AES in the three-party honest-majority setting, with a communication cost of $O(N^{1/2})$; malicious security is achieved with distributed zero-knowledge proofs. However, it only supports single-input tables over characteristic-2 fields $\mathbb{F}_{2^k}$ and lacks support for multi-input tables over rings $\mathbb{Z}_{2^k}$, which are more widely used in modern computation. Moreover, the $O(N^{1/2})$ cost remains expensive for large-scale applications; their efficient distributed zero-knowledge proofs are specialized for AES and cannot be easily applied to $\mathbb{Z}_{2^k}$.

In this work, we present MARLUT, a new generalized and optimized LUT construction supporting multi-input tables over both rings $\mathbb{Z}_{2^k}$ and fields $\mathbb{F}_{2^k}$ with malicious security. We achieve this by (1) extending the semi-honest LUT protocol from MAESTRO, utilizing high-dimensional tensors to reduce its communication cost to $O(N^{1/3})$, and (2) designing a new distributed zero-knowledge proof for inner-product relations over $\mathbb{Z}_{2^k}$. Our distributed zero-knowledge proof is more efficient than the state-of-the-art work (Li et al., CCS 2024) and may be of independent interest. Experiments show that on a table of size $2^{16}$, our semi-honest LUT protocol reduces the offline computational and communication cost by a factor of $5.95$ and $3.23$, respectively. Our distributed zero-knowledge proofs show up to $7.07\times$ and $4.97\times$ speedups over the state-of-the-art protocol on ring $\mathbb{Z}_{2^8}$ and $\mathbb{Z}_{2^{16}}$, respectively.
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Palash Sarkar
ePrint Report ePrint Report
The first contribution of the paper is to put forward an abstract definition of the Grain family of stream ciphers which formalises the different components that are required to specify a particular member of the family. Our second contribution is to provide new and strengthened definitions of the components. These include definining new classes of nonlinear Boolean functions, improved definition of the state update function during initialisation, choice of the tap positions, and the possibility of the linear feedback shift register being smaller than the nonlinear feedback shift register. The third contribution of the paper is to put forward seven concrete proposals of stream ciphers by suitably instantiating the abstract family, one at the 80-bit security level, and two each at the 128-bit, 192-bit, and the 256-bit security levels. At the 80-bit security level, compared to the well known Grain~v1, the new proposal uses Boolean functions with improved cryptographic properties \textit{and} an overall lower gate count. At the 128-bit level, compared to ISO/IEC standard Grain-128a, the new proposals use Boolean functions with improved cryptographic properties; one of the proposals require a few extra gates, while the other has an overall lower gate count. At the 192-bit, and the 256-bit security levels, there are no proposals in the literature with smaller gate counts.
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