International Association for Cryptologic Research

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02 June 2025

Hans Heum
ePrint Report ePrint Report
Contrary to expectation, we show that simulation-based selective-opening security (SSO) does not imply indistinguishability-based selective opening security (ISO) in the CCA setting, making them incomparable in the presence of either encryption randomness leakage (sender opening) or secret key leakage (receiver opening). This contrasts the CPA case, where SSO-CPA is known to be strictly stronger than ISO-CPA in the presence of sender and/or receiver opening. Our separation result holds relative to all message distributions with sufficiently high min-entropy. On the other hand, restricting to message distributions with low enough min-entropy gives rise to an implication. Our separation result does not rely on the presence of selective openings. At a glance, this may seem to contradict known equivalence results between indistinguishability, semantic security, and selective opening security under trivial openings. We reconcile the apparent contradiction by showing that the selective-opening CCA landscape splits into a “high-entropy” and a “low-entropy” world which must be considered separately.
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Hong-Sen Yang, Qun-Xiong Zheng, Jing Yang
ePrint Report ePrint Report
The LowMC-based post-quantum signature scheme Picnic was selected as a third-round candidate for NIST PQC, attracting wide attention to the design of efficient and secure post-quantum signature schemes using Symmetric Techniques for Advanced Protocols (STAP). Symmetric primitives designed for advanced protocols such as secure multi-party computation (MPC), fully homomorphic encryption (FHE), and zero-knowledge (ZK) proof systems, with the goal of reducing the number of multiplication operations, are referred to as arithmetic-oriented (AO) primitives. These cryptographic primitives are typically constructed over large finite fields, which makes classical statistical analysis methods like differential and linear cryptanalysis inefficient. Due to their inherent algebraic properties, the mainstream security evaluation approaches are based on algebraic attacks. In this paper, we analyze the security of the MPC-friendly primitives \textsc{Rain} (CCS 2022) and AIM (CCS 2023) used in the post-quantum signature schemes Rainier and AIMer. Existing algebraic attacks on \textsc{Rain} and AIM were conducted over $\mathbb{F}_2$. We propose a novel algebraic attack over $\mathbb{F}_{2^n}$ that uses the polynomial decomposition to reduce degrees of equations. By further combining with the guess-and-determine technique, meet-in-the-middle modeling, and resultant, we are able to attack \textsc{Rain} and the full AIM. Specifically, we successfully attacked 2-round \textsc{Rain} with $2^{73.7}/2^{107.0}/2^{138.9}$ primitive calls, 3-round \textsc{Rain} with $2^{160.6}/2^{236.0}/2^{311.1}$ primitive calls, for the $128/192/256$-bit key. For the full AIM, we successfully attacked it with $2^{114.0}/2^{163.2}/2^{228.3}$ primitive calls for the $128/192/256$-bit key. The attack complexities mainly lie in solving univariate polynomial equations and computing resultants, and hence the complexity evaluations are accurate.
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Karthikeyan Bhargavan, Lasse Letager Hansen, Franziskus Kiefer, Jonas Schneider-Bensch, Bas Spitters
ePrint Report ePrint Report
We present an effective methodology for the formal verification of practical cryptographic protocol implementations written in Rust. Within a single proof framework, we show how to develop machine-checked proofs of diverse properties like runtime safety, parsing correctness, and cryptographic protocol security. All analysis tasks are driven by the software developer who writes annotations in the Rust source code and chooses a backend prover for each task, ranging from a generic proof assistant like F$\star$ to dedicated crypto-oriented provers like ProVerif and SSProve Our main contribution is a demonstration of this methodology on Bert13, a portable, post-quantum implementation of TLS 1.3 written in Rust and verified both for security and functional correctness. To our knowledge, this is the first security verification result for a protocol implementation written in Rust, and the first verified post-quantum TLS 1.3 library.
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Zhengrong Lu, Hongbo Yu, Xiaoen Lin, Sitong Yuan
ePrint Report ePrint Report
RIPEMD-128 is an ISO/IEC standard hash function based on a double-branch Merkle-Damgård structure. Its compression function includes two branches with distinct Boolean functions and message expansion permutations. To perform a collision attack, differential characteristics must be constructed simultaneously for both branches under the same message word difference, and the message modification order must align with conditions in both branches. These factors make collision attacks on (reduced) RIPEMD-128 highly challenging. In 2014, an attack on 40 steps of RIPEMD-128 was achieved by Wang with no state differences in round 3. In this work, we analyze message permutation properties and propose two new structures for creating message differences. These structures enable high-probability local collisions in both branches of round 3, extending the attack to more steps. Notably, the second structure can eliminate all state differences in round 3, allowing the attack to cover more than three whole rounds. To ensure practical attacks, we limit the number of conditions based on our message modification strategy and use multi-step message modification techniques to control more conditions. As a result, we successfully generate colliding message pairs for 46-step and 54-step reduced RIPEMD-128, with time complexities of approximately $2^{42}$ and $2^{54}$, respectively.
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Toomas Krips, Pille Pullonen-Raudvere
ePrint Report ePrint Report
Distributed point functions (DPFs), introduced in 2014, are a widely used primitive in secure computation for a wide variety of applications. However, until now, constructions for DPFs with polylogarithmic-size keys have been known only for the two-party setting. We propose a scheme for a polylogarithmic-size DPF for an arbitrary number of parties. We use a technique where a secret-shared vector is mapped to collinear vectors by public matrices serves as an invariant for off-path leaves. We show, using a technique by Shamir, that when we work over Z_pq , these vectors are hard to compute if factoring is hard. We also show that our scheme is a secure DPF, provided that two new assumptions hold, one of which is related to Generic Group Model and the other to MinRank. The output of our scheme is in the exponent in some group where Diffie-Hellman type problems are hard. Although this limits the usability of our scheme, we believe that our scheme is the first distributed point function for more than two parties with a key size that is polylogarithmic in the size of the domain and that does not use fully homomorphic encryption.
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Xiaolin Duan, Fan Huang, Yaqi Wang, Honggang Hu
ePrint Report ePrint Report
At Crypto 2009, Heninger and Shacham presented a branch-and-prune algorithm for reconstructing RSA private keys given a random fraction of its private components. This method is widely adopted in side-channel attacks, and its complexity is closely related to the specific leakage pattern encountered. In this work, we identified a novel leakage model in the Miller-Rabin primality test implemented in OpenSSL. Under certain side-channel attacks against fixed-window modular exponentiation (e.g., recovering the least significant $b$ bits from each window), the proposed model enables staggered recovery of bits in $p$ and $q$, reducing uncertainty in key reconstruction. In particular, this model includes previously undocumented scenarios where full key recovery is achievable without branching. To understand how the proposed leakage model could contribute to attacks on modular exponentiation, we investigated the global and local behavior of key reconstruction. Our evaluation demonstrates that the proposed scenarios enable more efficient key reconstruction and retain this advantage when additional erasure bits are introduced. Moreover, in specific cases, successful reconstruction remains achievable within practical time even if the bits obtained are less than 50%. Finally, we conducted a series of experiments to confirm the practicality of our assumption, successfully recovering the lower 4 bits from each 6-bit window.
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Roberto Avanzi, Bishwajit Chakraborty, Eik List
ePrint Report ePrint Report
We introduce the large block cipher Vistrutah, featuring 256- and 512-bit block sizes. Vistrutah is an iterated cipher where each "step" applies two AES rounds to each 128-bit block of the state, followed by a cell permutation across the entire state. Building upon established design principles from Simpira, Haraka, Pholkos, and ASURA, Vistrutah achieves high performance by leveraging AES instructions.

For each component of Vistrutah, we conducted a systematic evaluation of functions that can be efficiently implemented across different vector instruction set architectures. Our evaluation methodology combines latency estimation with security analysis, aiming to maximize the ratio of "bits of security per unit of time." This approach ensures we achieve the highest security or, equivalently, the best performance for this class of designs. Implementation results confirm the accuracy of our latency model.

We support our security claims with a comprehensive cryptanalysis.

A core design principle is the use of an inline key schedule: all round keys are computed during each encryption or decryption operation without requiring memory storage. Key schedules like the AES's must precompute and store round keys in memory for acceptable performance. This creates security vulnerabilities: such implementations become more susceptible to memory read oracles and, as demonstrated by Kamal and Youssef, more vulnerable to cold boot attacks. We consider these designs unsuitable for modern software security requirements. Vistrutah's approach minimizes leakage to at most one value during context switches. Furthermore, expensive key schedules reduce key agility, limiting the design of modes of operation.

Vistrutah is particularly well-suited for Birthday-Bound modes of operation, including Synthetic IV modes and Accordion modes for 256-bit block ciphers. It also serves effectively as a building block for compression functions (such as Matyas-Meyer-Oseas) in wide Merkle–Damg\aa rd hash functions. Additionally, it can implement "ZIP" wide pseudo-random functions as recently proposed by Flórez-Gutiérrez et al. in 2024.

Our cryptanalysis includes consideration of related-key security for two key reasons. First, strong related-key security demonstrates the robustness of both the key schedule and the cipher as a whole. Second, in counter-mode-based modes, Vistrutah's ability to change key with no overhead may allow the designer of a mode of operation to place counters (or values obtained from other update functions) in the key input rather than the plaintext input. This approach makes it easier to achieve Beyond the Birthday Bound security.

As a by-product of this research, we identified design flaws in Ghidle that affect both its security and performance. Our security analysis accounts for these weaknesses. We also developed Vistrutah-B, a variant of Vistrutah that addresses Ghidle's issues while maintaining comparable performance in most aspects. Nevertheless, Vistrutah retains superior diffusion properties.
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Eylon Yogev, Shany Ben-David
ePrint Report ePrint Report
Recently, the concept of incompressible encryption has emerged as a powerful enhancement to key-leakage resilience. In an incompressible encryption scheme, an adversary who intercepts ciphertexts is forced to dedicate a significant amount of memory to store them in full if they wish to extract any information about the plaintext later when the secret key becomes available. Given two messages, the security game involves two adversaries: the first adversary receives an encryption of one of the messages and produces a compressed state. Then, the second adversary, given both the secret key and the compressed state, attempts to determine which message was encrypted.

Several positive results exist in incompressible cryptography. On the one hand, there are constructions based on minimal assumptions but with a poor rate (i.e., rate tends to 0). On the other hand, there are rate-1 constructions that achieve optimal efficiency but rely on strong cryptographic assumptions, such as obfuscation.

A stronger security notion, known as everlasting security, has been proposed for incompressible encryption. In this formulation, the second adversary, who receives the compressed state and the secret key, is allowed to be computationally unbounded. While this notion is conceptually appealing, no constructions of everlasting incompressible encryption are currently known, regardless of the underlying assumption or even in idealized models.

In this work, we give the first construction of everlasting incompressible encryption. In fact, we show that everlasting incompressible encryption is inherent in any sufficiently secure public-key encryption scheme. Specifically, we prove that any public-key encryption scheme with subexponential security (when instantiated with an appropriate security parameter) already satisfies the definition of everlasting incompressible encryption with subexponential security. Furthermore, our scheme achieves rate-1, improving upon existing results even for the weaker notion of standard incompressible encryption.
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Joshua G. Stern
ePrint Report ePrint Report
To prevent privacy-preserving digital assets from becoming instruments of despotism via unitary-executivist compliance regimes, we propose OptAttest, a hybrid zero-knowledge architecture. This system empowers users to optionally generate verifiable attestation history for the current (Hop 0) and immediately preceding (Hop 1) transactions involving their private commitments. For crucial 0-hop multi-list attestations, users employ Zero-Knowledge Proofs (ZKPs) of claims from selected Verifiable Credentials (VCs). Users achieve per-transaction efficiency with diverse VC types by pre-computing and caching proofs of their VC validity. This approach avoids mandated adherence to singular, fallible external standards. Opted-in lightweight updates create cryptographic accumulator summaries, verified by network infrastructure (e.g., Layer 2 scaling solutions using Zero-Knowledge Virtual Machines), and are paired with user-managed Intermediate Attestation Data Packets (IADPs) containing detailed evidence. For comprehensive verification, users can then generate full recursive proofs from these IADPs for their attestation-enabled funds, leveraging native zkVM recursion. The protocol facilitates optional attestation generation, not enforcement, allowing downstream policy application. Aiming to cultivate a permissionless ethos, we propose a user-centric balance between privacy and verifiable accountability, distinct from models compelling broader data access. Folding schemes are noted as potential future enhancements for recursive proof efficiency.
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30 May 2025

Balthazar Bauer, Georg Fuchsbauer, Fabian Regen
ePrint Report ePrint Report
Equivalence class signatures (EQS), introduced by Hanser and Slamanig (AC’14, J.Crypto’19), sign vectors of elements from a bi- linear group. Their main feature is “adaptivity”: given a signature on a vector, anyone can transform it to a (uniformly random) signature on any multiple of the vector. A signature thus authenticates equivalence classes and unforgeability is defined accordingly. EQS have been used to improve the efficiency of many cryptographic applications, notably (delegatable) anonymous credentials, (round-optimal) blind signatures, group signa- tures and anonymous tokens. EQS security implies strong anonymity (or blindness) guarantees for these schemes which hold against malicious signers without trust assumptions.

Unforgeability of the original EQS construction is proven directly in the generic group model. While there are constructions from standard assumptions, these either achieve prohibitively weak security notions (PKC’18) or they require a common reference string (AC’19, PKC’22), which reintroduces trust assumptions avoided by EQS.

In this work we ask whether EQS schemes that satisfy the original secu- rity model can be proved secure under standard (or even non-interactive) assumptions with standard techniques. Our answer is negative: assum- ing a reduction that, after running once an adversary breaking unforge- ability, breaks a non-interactive computational assumption, we construct efficient meta-reductions that either break the assumption or break class- hiding, another security requirement for EQS.
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Jeju, South Korea, 20 August - 22 August 2025
Event Calendar Event Calendar
Event date: 20 August to 22 August 2025
Submission deadline: 13 June 2025
Notification: 18 July 2025
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Graz, Österreich, 1 September - 5 September 2025
School School
Event date: 1 September to 5 September 2025
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Industrial Systems Institute/Research Center ATHENA
Job Posting Job Posting
Company Description

The Industrial Systems Institute (ISI) is a public research institute under the supervision of the General Secretariat for Research and Technology of the Greek Ministry of Education and Religious Affairs, Culture and Sports. Founded in Patras in June 1998, ISI is part of the Research and Innovation Centre in Information, Communication, and Knowledge Technologies “Athena” since 2003. The institute focuses on contributing to high-technology sectors related to integrated industrial systems, aiming to increase the competitiveness of the Greek industry through the application of state-of-the-art technologies. ISI is currently hosted in Patras Science Park premises.

Role Description

This is a full-time hybrid role for Early-Career or Postdoctoral Researchers in Side-Channel Attacks & Countermeasures for Post-Quantum Cryptography (PQC). The positions are based in Greece, with some work from home being acceptable. Day-to-day tasks include conducting research in side-channel attacks and countermeasures for PQC and developing countermeasures in software and/or FPGA hardware.

Qualifications
  • Solid programming background in C/C++ programming language
  • Basic signal processing knowledge
  • Research and Data Analysis skills
  • Experience with AI model libraries (e.g., Pytorch, Tensorflow)
  • Strong written and verbal communication skills
  • Ability to work independently and as part of a team
  • Experience in post-quantum cryptography is a plus
  • Experience in Hardware Programming Languages or High Level Synthesis tools is a plus
  • Basic Laboratory Skills on oscilloscopes and electronics (for the side channel attack position) is a plus
  • PhD or Master’s degree in a relevant field

Closing date for applications:

Contact: Dr. Apostolos Fournaris

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28 May 2025

Bence Mali
ePrint Report ePrint Report
Some of the most valuable applications of homomorphic encryption, such as encrypted machine learning inference, require efficient large-scale plaintext-ciphertext and ciphertext-ciphertext matrix multiplications. Current state-of-the-art techniques for matrix multiplications all build on the ability to pack many ciphertexts into a ciphertext and compute on them in a Single Instruction, Multiple Data (SIMD) manner. However, to fit the operation of matrix multiplication into this computational model, a large number of additional costly operations need to be performed, such as the rotation of elements between the plaintext slots.

In this work we propose an orthogonal approach to performing encrypted matrix operations with BGV-like encryption schemes, where the plaintext and ciphertext spaces are generalized to a matrix ring of arbitrary dimension. To deal with the inherent problem of noncommutativity in the case of matrix rings, we present a new superoperator technique to better represent linear and quadratic expressions in the secret key, which allows for the relinearization of ciphertexts after multiplication. The security of the modified encryption schemes is based on Module-LWE with module rank equal to the dimension of the matrices. With this construction, we demonstrate that Ring-LWE, Module-LWE, and LWE are potentially equally efficient for homomorphic encryption, both in terms of useful information density and noise growth, only for different sizes of matrices.
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Christoph Coijanovic, Laura Hetz, Kenneth G. Paterson, Thorsten Strufe
ePrint Report ePrint Report
Anonymous communication is vital for enabling individuals to participate in social discourse without fear of marginalization or persecution. An important but often overlooked part of anonymous communication is the bootstrapping of new communication channels, generally assumed to occur out-of-band. However, if the bootstrapping discloses metadata, communication partners are revealed even if the channel itself is fully anonymized. We propose Sabot, the first anonymous bootstrapping protocol that achieves both strong cryptographic privacy guarantees and bandwidth-efficient communication. In Sabot, clients cooperatively generate a private relationship matrix, which encodes who wants to contact whom. Clients communicate with k ≥ 2 servers to obtain “their” part of the matrix and augment the received information using Private Information Retrieval (PIR) to learn about their prospective communication partners. Compared to previous solutions, Sabot achieves stronger privacy guarantees and reduces the bandwidth overhead by an order of magnitude.
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Giulio Malavolta, Tamer Mour
ePrint Report ePrint Report
A proof of quantumness (PoQ) allows a classical verifier to efficiently test if a quantum machine is performing a computation that is infeasible for any classical machine. In this work, we propose a new approach for constructing PoQ protocols where soundness holds unconditionally assuming a bound on the memory of the prover, but otherwise no restrictions on its runtime. In this model, we propose two protocols: 1. A simple protocol with a quadratic gap between the memory required by the honest parties and the memory bound of the adversary. The soundness of this protocol relies on Raz's (classical) memory lower bound for matrix inversion (Raz, FOCS 2016). 2. A protocol that achieves an exponential gap, building on techniques from the literature on the bounded storage model (Dodis et al., Eurocrypt 2023).

Both protocols are also efficiently verifiable. Despite having worse asymptotics, our first protocol is conceptually simple and relies only on arithmetic modulo 2, which can be implemented with one-qubit Hadamard and CNOT gates, plus a single one-qubit non-Clifford gate.
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Elaine Shi, Rose Silver, Changrui Mu
ePrint Report ePrint Report
We initiate the study of a new abstraction called incremental decentralized data archival (${\sf iDDA}$). Specifically, imagine that there is an ever-growing, massive database such as a blockchain, a comprehensive human knowledge base like Wikipedia, or the Internet archive. We want to build a decentralized archival of such datasets to ensure long-term robustness and sustainability.

We identify several important properties that an ${\sf iDDA}$ scheme should satisfy. First, to promote heterogeneity and decentralization, we want to encourage even weak nodes with limited space (e.g., users' home computers) to contribute. The minimum space requirement to contribute should be approximately independent of the data size. Second, if a collection of nodes together receive rewards commensurate with contributing a total of $m$ blocks of space, then we want the following reassurances: 1) if $m$ is at least the database size, we should be able to reconstruct the entire dataset; and 2) these nodes should actually be commiting roughly $m$ space in aggregate --- even when $m$ is much larger than the data size, the nodes should be storing redundant copies of the database rather than storing just one copy, and yet impersonating arbitrarily many pseudonyms to get unbounded rewards.

We propose new definitions that mathematically formalize the aforementioned requirements of an ${\sf iDDA}$ scheme. We also devise an efficient construction in the random oracle model which satisfies the desired security requirements. Our scheme incurs only $\widetilde{O}(1)$ audit cost, as well as $\widetilde{O}(1)$ update cost for both the publisher and each node, where $\widetilde{O}(\cdot)$ hides polylogarithmic factors. Further, the minimum space provisioning required to contribute is as small as polylogarithmic.

Our construction exposes several interesting technical challenges. Specifically, we show that a straightforward application of the standard hierarchical data structure fails, since both our security definition and the underlying cryptographic primitives we employ lack the desired compositional guarantees. We devise novel techniques to overcome these compositional issues, resulting in a construction with provable security while still retaining efficiency. Finally, our new definitions also make a conceptual contribution, and lay the theoretical groundwork for the study of ${\sf iDDA}$. We raise several interesting open problems along this direction.
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Yilei Chen, Liheng Ji, Wenjie Li
ePrint Report ePrint Report
In TCC 2018, Boneh, Ishai, Passelègue, Sahai, and Wu propose candidates of weak and strong PRFs by evaluating linear functions over coprime moduli alternatively. Such PRFs can be evaluated by low-depth circuits and are MPC-friendly. However, they have not been able to base the security of their PRFs on well-formed assumptions other than assuming that the PRF constructions themselves are secure.

In this paper, we formalize a new assumption called Learning with Alternating Moduli (LAM). We show that over certain large moduli, the LAM assumption is as hard as the Learning with Errors (LWE) assumption. For LAM over constant moduli, we do not know how to base its hardness on the LWE assumption. Instead, we provide (i) polynomial-time attacks on LAM with constant prime-power moduli and certain constant non-prime-power moduli, and (ii) evidence of the sub-exponential hardness of LAM with other moduli by analyzing the effect of typical attacks.

More specifically, we put forward two new attacks. The first attack is a recursive algorithm that solves LWE with certain constant composite moduli and error distributions. The algorithm extends the Arora-Ge algorithm for LWE from prime moduli to composite moduli, and it also solves LAM for certain parameters. The second attack is a polynomial-time attack that rules out the existence of weak PRFs in $\mathsf{NC}^0[p]$ for any prime $p$.

Based on our studies, we propose candidate weak PRFs in $\mathsf{NC}^0[p_1,p_2]$ for some distinct primes $p_1,p_2$ based on LAM over constant moduli, or the Learning with Rounding (LWR) assumption over constant moduli. Compared to the weak PRF candidates by Boneh et al., our weak PRF candidates live in the same complexity class while having the advantage of being based on well-formed assumptions.
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Tapas Pal, Robert Schädlich, Erkan Tairi
ePrint Report ePrint Report
Registered functional encryption (RFE) is a generalization of public-key encryption that enables computation on encrypted data (like classical FE), but without needing a central trusted authority. Concretely, the users choose their own public keys and register their keys together with a function with an (untrusted) key curator. The key curator aggregates all of the individual public keys into a short master public key, which serves as the public key of the FE scheme.

Currently, we only know RFE constructions for restricted functionalities using standard assumptions, or for all circuits using powerful tools such as indistinguishability obfuscation, and only in the non-uniform model. In this work, we make progress on this front by providing the first lattice-based constructions of RFE for pseudorandom functionalities, where the model of computation is either non-uniform (unbounded depth circuits) or uniform (Turing machines). Intuitively, we call a functionality pseudorandom if the output of the circuit is indistinguishable from uniform for every input seen by the adversary. Security relies on LWE and a recently introduced primitive called pseudorandom FE (prFE), which currently can be instantiated from evasive LWE.

We illustrate the versatility of these new functionalities for RFE by leveraging them to achieve key-policy and ciphertext-policy registered attribute-based encryption and registered predicate encryption schemes (KP-RABE, CP-RABE and RPE) for both unbounded depth circuits and Turing machines. Existing RABE constructions support only bounded depth circuits, and prior to our work there neither existed RABE for uniform models of computation nor RPE. As an appealing feature, all our constructions enjoy asymptotic optimality in the sense that their parameters depend neither on the length of public attributes nor the size of policies.

Along the way, we can also improve on the state-of-the-art for classical attribute-based encryption (ABE) and predicate encryption (PE). Specifically, we obtain new constructions for KP-ABE, CP-ABE and PE for Turing machines with optimal asymptotic parameters. For KP-ABE, this is an in improvement in terms of efficiency, whereas for CP-ABE and PE we are not aware of any prior purely lattice-based construction supporting Turing machines.
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Geoffroy Couteau, Naman Kumar, Xiaxi Ye
ePrint Report ePrint Report
We give the first constructions of multiparty pseudorandom correlation generators, distributed point functions, and (negligible-error) homomorphic secret sharing for constant-degree polynomials for any number of parties without using LWE or iO. Our constructions are proven secure under the combination of LPN with dimension $n$, $2n$ samples, and noise rate $n^{\varepsilon-1}$ for a small constant $\varepsilon$, and MQ with $n$ variables and $n^{1+\delta}$ equations.

As applications of our results, we obtain from the same assumptions secure multiparty computation protocols with sublinear communication and silent preprocessing, as well as private information retrieval for $M$ servers and size-$\lambda^d$ databases with optimal download rate and client-to-server communication $M^d\cdot \lambda^3$.
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