This study analyzes and investigates pseudorandom generation (PRG) in the context of masked cryptographic implementation. Although masking and PRGs have been distinctly studied for a long time, little literature studies how the randomness in the masked implementation should be generated. The lack of analysis on mask-bits generators makes the practical security of masked cryptographic implementation unclear, and practitioners (e.g., designers, implementers, and evaluators) may be confused about how to realize it. This study provides its systematic analysis by developing new three adversarial models, which correspond to respective practical scenarios of leakage assessment, quantitative evaluation of sidechannel security (e.g., success rate and key-lifetime), and practical deployment. We present the properties required for each scenario by a stage-by-stage analysis. In particular, we support a long-held belief/folklore with a proof: for the output of PRG for masking, cryptographic security is sufficient but unnecessary, but only a statistical uniformity (precisely, high-dimensional uniform equidistribution) is necessary. In addition, we thoroughly investigate the side-channel security of PRGs in the wild in the masking context. We conclude this study with some recommendations for practitioners and a proposal of leakage-resilient method of comparative performance.

With the threat posed by quantum computers on the horizon, systems like Ethereum must transition to cryptographic primitives resistant to quantum attacks. One of the most critical of these primitives is the non-interactive multi-signature scheme used in Ethereum's proof-of-stake consensus, currently implemented with BLS signatures. This primitive enables validators to independently sign blocks, with their signatures then publicly aggregated into a compact aggregate signature. In this work, we introduce a family of hash-based signature schemes as post-quantum alternatives to BLS. We consider the folklore method of aggregating signatures via (hash-based) succinct arguments, and our work is focused on instantiating the underlying signature scheme. The proposed schemes are variants of the XMSS signature scheme, analyzed within a novel and unified framework. While being generic, this framework is designed to minimize security loss, facilitating efficient parameter selection. A key feature of our work is the avoidance of random oracles in the security proof. Instead, we define explicit standard model requirements for the underlying hash functions. This eliminates the paradox of simultaneously treating hash functions as random oracles and as explicit circuits for aggregation. Furthermore, this provides cryptanalysts with clearly defined targets for evaluating the security of hash functions. Finally, we provide recommendations for practical instantiations of hash functions and concrete parameter settings, supported by known and novel heuristic bounds on the standard model properties.

Two-party computation has been an active area of research since Yao's breakthrough results on garbled circuits. We present secret key somewhat additive homomorphic schemes where the client has perfect privacy (server can be computationally unbounded). Our basic scheme is somewhat additive homomorphic and we extend it to support multiplication. The server handles circuit multiplication gates by returning the multiplicands to the client which updates the decryption key so that the original ciphertext vector includes the encrypted multiplication gate outputs. We give a 2-party protocol that also incorporates server inputs where the client has perfect privacy. Server privacy holds against a computationally bounded adversary since it depends on the hardness of the subset sum problem. Correctness of the server in the malicious model can be verified by a 3rd party where the client and server privacy are protected from the verifier.

Bitcoin script cannot easily access and store state information onchain without an upgrade such as BIP-347 (OP_CAT); this makes performing general (stateful) computation on Bitcoin impossible to do directly. Despite this limitation, several approaches have been proposed to bypass it, with BitVM being the closest to production. BitVM enables fraud-proof-based computation on Bitcoin, relying on a $1$-out-of-$n$ honesty assumption. This left the question of whether it is possible to achieve computation under the same honesty assumption without requiring onlookers to ensure validity through fraud proofs. In this note, we answer this question affirmatively by introducing ColliderVM, a new approach for performing computation on Bitcoin today. Crucially, this approach eliminates some capital inefficiency concerns stemming from reliance on fraud proofs. For our construction, a key point is to replace the Lamport or Winternitz signature-based storage component in contemporary protocols with a hash collision-based commitment. Our techniques are inspired by ColliderScript, but are more efficient, reducing the number of hash evaluations required by at least $\times 10000$. With it, we estimate that the Bitcoin script length for STARK proof verification becomes practical, allowing it to be used alongside other, pairing-based proof systems common today in applications.

This work describes vulnerabilities in the specification of AEAD modes and Key Wrap in two cryptographic message formats. Firstly, this applies to AEAD packets as introduced in the novel LibrePGP specification that is implemented by the widely used GnuPG application. Secondly, we describe vulnerabilities in the AES-based AEAD schemes as well as the Key Wrap Algorithm specified in the Cryptographic Message Syntax (CMS). These new attacks exploit the possibility to downgrade AEAD or AES Key Wrap ciphertexts to valid legacy CFB- or CBC-encrypted related ciphertexts and require that the attacker learns the content of the legacy decryption result. This can happen in two principal ways: either due to the human recipient returning the decryption output to the attacker as a quote or due to a programmatic decryption oracle in the receiving system that reveals information about the plaintext. The attacks effect the decryption of low-entropy plaintext blocks in AEAD ciphertexts and, in the case of LibrePGP, also the manipulation of existing AEAD ciphertexts. For AES Key Wrap in CMS, full key decryption is possible. Some of the attacks require multiple successful oracle queries. The attacks thus demonstrate that CCA2 security is not achieved by the LibrePGP and CMS AEAD or Key Wrap encryption in the presence of a legacy cipher mode decryption oracle.

The recently standardized secure group messaging protocol Messaging Layer Security (MLS) is designed to ensure asynchronous communications within large groups, with an almost-optimal communication cost and the same security level as point-to-point se- cure messaging protocols such as Signal. In particular, the core sub-protocol of MLS, a Continuous Group Key Agreement (CGKA) called TreeKEM, must generate a common group key that respects the fundamental security properties of post-compromise security and forward secrecy which mitigate the effects of user corruption over time. Most research on CGKAs has focused on how to improve these two security properties. However, post-compromise security and forward secrecy require the active participation of respectively all compromised users and all users within the group. Inactive users – who remain offline for long periods – do not update anymore their encryption keys and therefore represent a vulnerability for the entire group. This issue has already been identified in the MLS standard, but no solution, other than expelling these inactive users after some disconnection time, has been found. We propose here a CGKA protocol based on TreeKEM and fully compatible with the MLS standard, that implements a quarantine mechanism for the inactive users in order to mitigate the risk induced by these users during their inactivity period and before they are removed from the group. That mechanism indeed updates the inactive users’ encryption keys on their behalf and secures these keys with a secret sharing scheme. If some of the inactive users eventually reconnect, their quarantine stops and they are able to recover all the messages that were exchanged during their offline period. Our Quarantined-TreeKEM protocol thus increases the security of original TreeKEM, with a very limited – and sometimes negative – communication overhead.

This paper presents a Generalized BFV (GBFV) fully homomorphic encryption scheme that encrypts plaintext spaces of the form $\mathbb{Z}[x]/(\Phi_m(x), t(x))$ with $\Phi_m(x)$ the $m$-th cyclotomic polynomial and $t(x)$ an arbitrary polynomial. GBFV encompasses both BFV where $t(x) = p$ is a constant, and the CLPX scheme (CT-RSA 2018) where $m = 2^k$ and $t(x) = x - b$ is a linear polynomial. The latter can encrypt a single huge integer modulo $\Phi_m(b)$, has much lower noise growth than BFV, but it is not known to be efficiently bootstrappable. We show that by a clever choice of $m$ and higher degree polynomial $t(x)$, our scheme combines the SIMD capabilities of BFV with the low noise growth of CLPX, whilst still being efficiently bootstrappable. Moreover, we present parameter families that natively accommodate packed plaintext spaces defined by a large cyclotomic prime, such as the Fermat prime $\Phi_2(2^{16}) = 2^{16} + 1$ and the Goldilocks prime $\Phi_6(2^{32}) = 2^{64} - 2^{32} + 1$. These primes are often used in homomorphic encryption applications and zero-knowledge proof systems. Due to the lower noise growth, GBFV can evaluate much deeper circuits compared to native BFV in the same ring dimension. As a result, we can evaluate either larger circuits or work with smaller ring dimensions. In particular, we can natively bootstrap GBFV at 128-bit security already at ring dimension $n = 2^{14}$, which was impossible before. We implemented the GBFV scheme on top of the SEAL library and achieve a latency of only 2 seconds to bootstrap a ciphertext encrypting up to 8192 elements modulo $2^{16} + 1$.

An oblivious Top-$k$ algorithm selects the $k$ smallest elements from $d$ elements while ensuring the sequence of operations and memory accesses do not depend on the input. In 1969, Alekseev proposed an oblivious Top-$k$ algorithm with complexity $O(d \log^2{k})$, which was later improved by Yao in 1980 for small $k \ll \sqrt{d}$. In this paper, we revisit the literature on oblivious Top-$k$ and propose another improvement of Alekseev's method that outperforms both for large $k = \Omega(\sqrt{d})$. Our construction is equivalent to applying a new truncation technique to Batcher's odd-even sorting algorithm. In addition, we propose a combined network to take advantage of both Yao's and our technique that achieves the best concrete performance, in terms of the number of comparators, for any $k$. To demonstrate the efficiency of our combined Top-$k$ network, we implement a secure non-interactive $k$-nearest neighbors classifier using homomorphic encryption as an application. Compared with the work of Zuber and Sirdey (PoPETS 2021) where oblivious Top-$k$ was realized with complexity $O(d^2)$, our experimental results show a speedup of up to 47 times (not accounting for difference in CPU) for $d = 1000$.

Multi-point function secret sharing (FSS) is a building block for pseudo- random correlation generators used in the novel silent correlation generation methods for various secure multiparty computation applications. However, the main construction used so far is the naive approach to combining several single point functions. In this paper, we propose an efficient and natural generalization of the point function. FSS scheme of Boyle et al. 2016 [BGI16 ] using a tree structure, a pseudorandom generator and systems of linear equations. Our schemes are more efficient in the evaluation phase than other previously proposed multi-point FSS schemes while being also more flexible and being similar in other efficiency parameters. Our setup phase is similar in cost to previous best versions, while the full evaluation, which is by far the costliest step, is more efficient.

The advancement of succinct non-interactive argument of knowledge (SNARK) with constant proof size has significantly enhanced the efficiency and privacy of verifiable computation. Verifiable computation finds applications in distributed computing networks, particularly in scenarios where nodes cannot be generally trusted, such as blockchains. However, fully harnessing the efficiency of SNARK becomes challenging when the computing targets in the network change frequently, as the SNARK verification can involve some untrusted preprocess of the target, which is expected to be reproduced by other nodes. This problem can be addressed with two approaches: One relieves the reproduction overhead by reducing the dimensionality of preprocessing data; The other utilizes verifiable machine computation, which eliminates the dependency on preprocess at the cost of increased overhead to SNARK proving and verification. In this paper, we propose a new SNARK with constant proof size applicable to both approaches. The proposed SNARK combines the efficiency of Groth16 protocol, albeit lacking universality for new problems, and the universality of PlonK protocol, albeit with significantly larger preprocessing data dimensions. Consequently, we demonstrate that our proposed SNARK maintains the efficiency and the universality while significantly reducing the dimensionality of preprocessing data. Furthermore, our SNARK can be seamlessly applied to the verifiable machine computation, requiring a proof size smaller about four to ten times than other related works.

Stateless blockchain designs have emerged to address the challenge of growing blockchain size using succinct global states. Previous works have developed vector commitments that support proof updates and aggregation to be used as such states. However, maintaining proofs for multiple users still demands significant computational resources, particularly to update proofs with every transaction. This paper introduces Cauchyproofs, a batch-updatable vector commitment that enables proof-serving nodes to efficiently update proofs in quasi-linear time relative to the number of users and transactions, utilizing an optimized KZG scheme to achieve complexity $O\left(\left(\left|\vec{\alpha}\right| + \left|\vec{\beta}\right|\right) \log^2 \left(\left|\vec{\alpha}\right| + \left|\vec{\beta}\right|\right)\right)$ for $\left|\alpha\right|$ users and $\left|\beta\right|$ transactions, compared to the previous $O\left(\left|\vec{\alpha}\right|\cdot\left|\vec{\beta}\right|\right)$ approaches. This advancement reduces the computational burden on proof-serving nodes, allowing efficient proof maintenance across large user groups. We demonstrate that our approach is approximately eight times faster than the naive approach at the Ethereum-level transaction throughput if we perform batch update every hour. Additionally, we present a novel matrix representation for KZG proofs utilizing Cauchy matrices, enabling faster all-proof computations with reduced elliptic curve operations. Finally, we propose an algorithm for history proof query, supporting retrospective proof generation with high efficiency. Our contributions substantially enhance the scalability and practicality of proof-serving nodes in stateless blockchain frameworks.

Key separation is often difficult to enforce in practice. While key reuse can be catastrophic for security, we know of a number of cryptographic schemes for which it is provably safe. But existing formal models, such as the notions of joint security (Haber-Pinkas, CCS ’01) and agility (Acar et al., EUROCRYPT ’10), do not address the full range of key-reuse attacks—in particular, those that break the abstraction of the scheme, or exploit protocol interactions at a higher level of abstraction. This work attends to these vectors by focusing on two key elements: the game that codifies the scheme under attack, as well as its intended adversarial model; and the underlying interface that exposes secret key operations for use by the game. Our main security experiment considers the implications of using an interface (in practice, the API of a software library or a hardware platform such as TPM) to realize the scheme specified by the game when the interface is shared with other unspecified, insecure, or even malicious applications. After building up a definitional framework, we apply it to the analysis of two real-world schemes: the EdDSA signature algorithm and the Noise protocol framework. Both provide some degree of context separability, a design pattern for interfaces and their applications that aids in the deployment of secure protocols.

Recently, a number of highly optimized threshold signing protocols for Schnorr signatures have been proposed. While these proposals contain important new techniques, some of them present and analyze these techniques in very specific contexts, making it less than obvious how these techniques can be adapted to other contexts, or combined with one another. The main goal of this paper is to abstract out and extend in various ways some of these techniques, building a toolbox of techniques that can be easily combined in different ways and in different contexts. To this end, we present security results for various "enhanced" modes of attack on the Schnorr signature scheme in the non-distributed setting, and we demonstrate how to reduce the security in the distributed threshold setting to these enhanced modes of attack in the non-distributed setting. This results in a very modular approach to protocol design and analysis, which can be used to easily design new threshold Schnorr protocols that enjoy better security and/or performance properties than existing ones.

In this work, we continue the analysis of the binding properties of implicitly-rejecting key-encapsulation mechanisms (KEMs) obtained via the Fujisaki-Okamoto (FO) transform. These binding properties, in earlier literature known under the term robustness, thwart attacks that can arise when using KEMs in complex protocols. Recently, Cremers et al. (CCS'24) introduced a framework for binding notions, encompassing previously existing but also new ones. While implicitly-rejecting FO-KEMs have been analyzed with respect to multiple of these notions, there are still several gaps. We complete the picture by providing positive and negative results for the remaining notions. Further, we show how to apply our results to the code-based KEMs BIKE and HQC, which were round-4 candidates in NIST's PQC standardization process. Through this, we close a second gap as our results complete the analysis of the binding notions for the NIST round-4 KEMs. Finally, we give a modified version of the FO transform that achieves all binding notions.

Ongoing efforts to transition to post-quantum public-key cryptosystems have created the need for algorithms with a variety of performance characteristics and security assumptions. Among the candidates in NIST's post-quantum standardisation process for additional digital signatures is FAEST, a Vector Oblivious Linear Evaluation in-the-Head (VOLEitH)-based scheme, whose security relies on the one-wayness of the Advanced Encryption Standard (AES). The VOLEitH paradigm enables competitive performance and signature sizes under conservative security assumptions. However, since it was introduced recently, in 2023, its resistance to physical attacks has not yet been analysed. In this paper, we present the first security analysis of VOLEitH-based signature schemes in the context of side-channel and fault injection attacks. We demonstrate four practical attacks on a masked implementation of FAEST in ARM Cortex-M4 capable of recovering the full secret key with high probability (greater than 0.87) from a single signature. These attacks exploit vulnerabilities of components specific to VOLEitH schemes and FAEST, such as the parallel all-but-one vector commitments, the VOLE generation, and the AES proof generation. Finally, we propose countermeasures to mitigate these attacks and enhance the physical security of VOLEitH-based signature schemes.

Recently, $\mathsf{NTRU}$+$\mathsf{Sign}$ was proposed as a new compact signature scheme, following `Fiat-Shamir with Aborts' (FSwA) framework. Its compactness is mainly based on their novel NTRU-based key structure that fits well with bimodal distributions in the FSwA framework. However, despite its compactness, $\mathsf{NTRU}$+$\mathsf{Sign}$ fails to provide a diverse set of parameters that can meet some desired security levels. This limitation stems from its reliance on a ring $\mathbb{Z}_q[x]/\langle x^n+1 \rangle$, where $n$ is restricted to powers of two, limiting the flexibility in selecting appropriate security levels. To overcome this limitation, we propose a revised version of $\mathsf{NTRU}$+$\mathsf{Sign}$ by adopting a ring $\mathbb{Z}_q[x]/\langle x^n-x^{n/2}+1\rangle$ from cyclotomic trinomials, where $n=2^{i}3^{j}$ for some positive integers $i$ and $j$. Our parameterization offers three distinct security levels: approximately $120$, $190$, and $260$ bits, while preserving the compactness in $\mathbb{Z}_q[x]/\langle x^n+1 \rangle$. We implement these re-parameterized $\mathsf{NTRU}$+$\mathsf{Sign}$ schemes, showing that the performance of $\mathsf{NTRU}$+$\mathsf{Sign}$ from cyclotomic trinomials is still comparable to previous lattice-based signature schemes such as $\mathsf{Dilithium}$ and $\mathsf{HAETAE}$.

This survey, mostly written in the years 2022-2023, is meant as an as short as possible description of the current state-of-the-art lattice attacks on lattice-based cryptosystems, without losing the essence of the matter. The main focus is the security of the NIST finalists and alternatives that are based on lattices, namely CRYSTALS-Kyber, CRYSTALS-Dilithium and Falcon. Instead of going through these cryptosystems case by case, this survey considers attacks on the underlying hardness assumptions: in the case of the mentioned lattice-based schemes, these are (variants of) LWE (Learning With Errors) and NTRU.

More and more people take advantage of mobile apps to strike up relationships and casual contacts. This sometimes results in the sharing of self-generated nudes. While this opens a way for sexual exploration, it also raises concerns. In this paper, we review existing technology-assisted permissive proposals/features that provide security, privacy or accountability benefits when sharing nudes online. To do so, we performed a systematic literature review combing through 10,026 search results and cross-references, and we identified real-world solutions by surveying OS features and 52 dating, messaging and social network apps. We systematized knowledge by defining a sexting threat model, deriving a taxonomy of the proposals/features, discussing some of their shortcomings, organizing privacy-related concepts, and providing take-aways with some directions for future research and development. Our study found a very diverse ecosystem of academic proposals and app features, showing that safer sexting goes far beyond nude detection. None of the techniques represents the ultimate solution for all threats, but each contributes to a safer sexting in a different way.

The security and performance of many advanced protocols heavily rely on the underlying symmetric-key primitives. These primitives, known as arithmetization-oriented (\texttt{AO}) ciphers, focus on arithmetic metrics over large finite fields. Most \texttt{AO} ciphers are vulnerable to algebraic attacks, especially integral attacks. In this work, we explore integral attacks over large finite fields. By combining integral distinguishers with inner product masks, we propose inner product masked (IPM) integral distinguishers and establish a system of equations concerning the inner product mask. Additionally, we provide theoretical lower bounds on the complexity of IPM integral distinguishers in certain cases. For practical applications, we introduce IPM integral sets, which effectively characterize the integral property of sets over the finite field $\mathbb{F}_{p^n}$. Besides the IPM sets based on additive subgroups and multiplicative subgroups, we present a method to obtain sets with improved integral properties by merging existing sets. Exploring different classes of IPM integral sets can help us find lower-complexity integral distinguishers. Combining with monomial detection techniques, we propose a framework for searching for integral distinguishers based on the IPM integral set. Our framework is compatible with various monomial detection techniques, including general monomial prediction proposed by Cui et al. at ASIACRYPT 2022 and coefficient grouping invented by Liu et al. at EUROCRYPT 2023. Previous integral distinguishers over $\mathbb{F}_{2^n}$ were predominantly based on additive subgroups. With IPM integral sets based on multiplicative subgroups and merged sets, we successfully obtain IPM integral distinguishers with lower complexity for \textsf{MiMC}, \textsf{CIMINION}, and \textsf{Chaghri}. We believe that our work will provide new insights into integral attacks over large finite fields.

SCALES (Small Clients And Larger Ephemeral Servers) model is a recently proposed model for MPC (Acharya et al., TCC 2022). While the SCALES model offers several attractive features for practical large-scale MPC, the result of Acharya et al. only offered semi-honest secure protocols in this model. We present a new efficient SCALES protocol secure against malicious adversaries, for general Boolean circuits. We start with the base construction of Acharya et al. and design and use a suite of carefully defined building blocks that may be of independent interest. The resulting protocol is UC-secure without honest majority, with a CRS and bulletin-board as setups, and allows publicly identifying deviations from correct execution.

The recently proposed YOSO model is a groundbreaking approach to MPC, executable on a public blockchain, circumventing adaptive player corruption by hiding the corruption targets until they are worthless. Players are selected unpredictably from a large pool to perform MPC subtasks, in which each selected player sends a single message (and reveals their identity). While YOSO MPC has attractive asymptotic complexity, unfortunately, it is concretely prohibitively expensive due to the cost of its building blocks. We propose a modification to the YOSO model that preserves resilience to adaptive server corruption, but allows for much more efficient protocols. In SCALES (Small Clients And Larger Ephemeral Servers) only the servers facilitating the MPC computation are ephemeral (unpredictably selected and ``speak once''). Input providers (clients) publish problem instances and collect the output, but do not otherwise participate in computation. SCALES offers attractive features, and improves over YOSO protocols in outsourcing MPC to a large pool of servers under adaptive corruption. We build SCALES from rerandomizable garbling schemes, which is a contribution of independent interest, with additional applications.

In the past three decades, we have witnessed the creation of various cryptanalytic attacks. However, relatively little research has been done on their potential underlying connections. The geometric approach, developed by Beyne in 2021, shows that a cipher can be viewed as a linear operation when we treat its input and output as points in an induced \textit{free vector space}. By performing a change of basis for the input and output spaces, one can obtain various transition matrices. Linear, differential, and (ultrametic) integral attacks have been well reinterpreted by Beyne's theory in a unified way. Thus far, the geometric approach always uses the same basis for the input and output spaces. We observe here that this restriction is unnecessary and allowing different bases makes the geometric approach more flexible and able to interpret/predict more attack types. Given some set of bases for the input and output spaces, a family of basis-based attacks is defined by combining them, and all attacks in this family can be studied in a unified automatic search method. We revisit three kinds of bases from previous geometric approach papers and extend them to four extra ones by introducing new rules when generating new bases. With the final seven bases, we can obtain $7^{2d}$ different basis-based attacks in the $d$-th order spaces, where the \textit{order} is defined as the number of messages used in one sample during the attack. We then provide four examples of applications of this new framework. First, we show that by choosing a better pair of bases, Beyne and Verbauwhede's ultrametric integral cryptanalysis can be interpreted as a single element of a transition matrix rather than as a linear combination of elements. This unifies the ultrametric integral cryptanalysis with the previous linear and quasi-differential attacks. Second, we revisit the multiple-of-$n$ property with our refined geometric approach and exhibit new multiple-of-$n$ distinguishers that can reach more rounds of the \skinny-64 cipher than the state-of-the-art. Third, we study the multiple-of-$n$ property for the first-order case, which is similar to the subspace trail but it is the divisibility property that is considered. This leads to a new distinguisher for 11-round-reduced \skinny-64. Finally, we give a closed formula for differential-linear approximations without any assumptions, even confirming that the two differential-linear approximations of \simeck-32 and \simeck-48 found by Hadipour \textit{et al.} are deterministic independently of concrete key values. We emphasize that all these applications were not possible before.

Receiver anamorphic encryption (hereafter anamorphic encryption), introduced by Persiano et al. at Eurocrypt 2022, allows for a double message to be symmetrically hidden in a public-key encryption ciphertext via a pre-shared -double key-. In anamorphic encryption, confidentiality must be preserved even if the adversary (or the -dictator-) has access to all regular keys. It has been the subject of several works since its introduction that explore tweaks and extensions to the core primitive. However, this study has not been systematic, and so disparate security notions have been proposed, for which their relationships are not clear. Moreover, there are clear gaps in the literature, including in the treatment of chosen-ciphertext attacks. In this work, we conduct a systematic study of receiver anamorphic encryption. We unify existing security notions and propose several new ones, and prove implications and separations between them. Our main findings are as follows. First, we identify gaps in previous security notions against an anamorphic -sender-, namely an adversary who is given the double key, and propose three new security notions to bridge these gaps. We also identify several gaps in the treatment of chosen-ciphertext attacks, a setting only very recently considered in anamorphic cryptography (Jaeger and Stracovsky, Asiacrypt 2024). Moreover, observing that no previous construction achieves all desirable security properties in this setting, we propose a suitable construction that does. Finally, we propose several security notions for -asymmetric- anamorphic encryption, and explore the case here where the dictator and the anamorphic sender collude.

Since the selection of the National Institute of Standards and Technology (NIST) Post-Quantum Cryptography (PQC) standardization algorithms, research on integrating PQC into security protocols such as TLS/SSL, IPSec, and DNSSEC has been actively pursued. However, PQC migration for Internet of Things (IoT) communication protocols remains largely unexplored. Embedded devices in IoT environments have limited computational power and memory, making it crucial to optimize PQC algorithms for efficient computation and minimal memory usage when deploying them on low-spec IoT devices. In this paper, we introduce KEM-MQTT, a lightweight and efficient Key Encapsulation Mechanism (KEM) for the Message Queuing Telemetry Transport (MQTT) protocol, widely used in IoT environments. Our approach applies the NIST KEM algorithm Crystals-Kyber (Kyber) while leveraging MQTT’s characteristics and sensor node constraints. To enhance efficiency, we address certificate verification issues and adopt KEMTLS to eliminate the need for Post-Quantum Digital Signatures Algorithm (PQC-DSA) in mutual authentication. As a result, KEM-MQTT retains its lightweight properties while maintaining the security guarantees of TLS 1.3. We identify inefficiencies in existing Kyber implementations on 8-bit AVR microcontrollers (MCUs), which are highly resource-constrained. To address this, we propose novel implementation techniques that optimize Kyber for AVR, focusing on high-speed execution, reduced memory consumption, and secure implementation, including Signed LookUp-Table (LUT) Reduction. Our optimized Kyber achieves performance gains of 81%,75%, and 85% in the KeyGen, Encaps, and DeCaps processes, respectively, compared to the reference implementation. With approximately 3 KB of stack usage, our Kyber implementation surpasses all state-of-the-art Elliptic Curve Diffie-Hellman (ECDH) implementations. Finally, in KEM-MQTT using Kyber-512, an 8-bit AVR device completes the handshake preparation process in 4.32 seconds, excluding the physical transmission and reception times.

We propose a new private Approximate Nearest Neighbor (ANN) search scheme named Pacmann that allows a client to perform ANN search in a vector database without revealing the query vector to the server. Unlike prior constructions that run encrypted search on the server side, Pacmann carefully offloads limited computation and storage to the client, no longer requiring computationally-intensive cryptographic techniques. Specifically, clients run a graph-based ANN search, where in each hop on the graph, the client privately retrieves local graph information from the server. To make this efficient, we combine two ideas: (1) we adapt a leading graph-based ANN search algorithm to be compatible with private information retrieval (PIR) for subgraph retrieval; (2) we use a recent class of PIR schemes that trade offline preprocessing for online computational efficiency. Pacmann achieves significantly better search quality than the state-of-the-art private ANN search schemes, showing up to 2.5$\times$ better search accuracy on real-world datasets than prior work and reaching 90\% quality of a state-of-the-art non-private ANN algorithm. Moreover on large datasets with up to 100 million vectors, Pacmann shows better scalability than prior private ANN schemes with up to $63\%$ reduction in computation time and $24\%$ reduction in overall latency.

Encrypted search schemes have been proposed to address growing privacy concerns. However, several leakage-abuse attacks have highlighted some security vulnerabilities. Recent attacks assumed an attacker's knowledge containing data "similar" to the indexed data. However, this vague assumption is barely discussed in literature: how likely is it for an attacker to obtain a "similar enough" data? Our paper provides novel statistical tools usable on any attack in this setting to analyze its sensitivity to data similarity. First, we introduce a mathematical model based on statistical estimators to analytically understand the attackers' knowledge and the notion of similarity. Second, we conceive statistical tools to model the influence of the similarity on the attack accuracy. We apply our tools on three existing attacks to answer questions such as: is similarity the only factor influencing accuracy of a given attack? Third, we show that the enforcement of a maximum index size can make the ``similar-data'' assumption harder to satisfy. In particular, we propose a statistical method to estimate an appropriate maximum size for a given attack and dataset. For the best known attack on the Enron dataset, a maximum index size of 200 guarantees (with high probability) the attack accuracy to be below 5%.

In this paper, we revisit shuffle protocol for Shamir secret sharing. Upon examining previous works, we observe that existing constructions either produce non-uniform shuffle or require large communication and round complexity, e.g. exponential in the number of parties. We propose two shuffle protocols, both of which shuffle uniformly within $O(\frac{k + l}{\log k}n^2m\log m)$ communication for shuffling rows of an $m\times l$ matrix shared among $n$ parties, where $k\leq m$ is a parameter balancing communication and computation. Our first construction is more concretely efficient, while our second construction requires only $O(nml)$ online communication within $O(n)$ round. In terms of overall communication and online communication, both shuffle protocols outperform current optimal shuffle protocols for Shamir secret sharing. At the core of our constructions is a novel permutation-sharing technique, which can be used to permute arbitrarily many vectors by computing matrix-vector products. Once shared, applying a permutation becomes much cheaper, which results in a faster online phase. Letting each party share one secret uniform permutation in the offline phase and applying them sequentially in the online phase, we obtain our first shuffle protocol. To further optimize online complexity and simplify the trade-off, we adopt the shuffle correlation proposed by Gao et al. and obtain the second shuffle protocol with $O(nml)$ online communication and $O(n^2ml)$ online computation. This brings an additional benefit that the online complexity is now independent of offline complexity, which reduces parameter optimization to optimizing offline efficiency. Our constructions require only most basic primitives in Shamir secret sharing scheme, and work for arbitrary field $\mathbb{F}$ of size larger than $n$. As shuffle is a frequent operation in algorithm design, we expect them to accelerate many other primitives in context of Shamir secret sharing MPC, such as sorting, oblivious data structure, etc.

Shuffle is a frequently used operation in secure multiparty computations, with applications including joint data analysis, anonymous communication systems, secure multiparty sorting, etc. Despite a series of ingenious works, the online (i.e. data-dependent) complexity of malicious secure $n$-party shuffle protocol remains $\Omega(n^2m)$ for shuffling data array of length $m$. This potentially slows down the application and MPC primitives built upon MPC shuffle. In this paper, we study the online complexities of MPC shuffle protocol. We observe that most existing works follow a ``permute-in-turn'' paradigm,where MPC shuffle protocol consists of $n$ sequential calls to a more basic MPC permutation protocol. We hence raise the following question: given only black-box access to an arbitrary MPC framework and permutation protocol, can we build an MPC shuffle, whose online complexities are independent of the underlying permutation protocol? We answer this question affirmatively, offering generic transformation from semi-honest/malicious MPC permutation protocolsto MPC shuffle protocols with semi-honest/malicious security and only $O(nm)$ online communication and computation. The linear online phase is obtained almost for free via the transformation, in the sense that in terms of overall complexities, the generated protocolequals the protocol generated by naive permute-in-turn paradigm. Notably, instantiating our construction with additive/Shamir secret sharing and corresponding optimal permutation protocol, we obtain the first malicious secure shuffle protocols with linear online complexities for additive/Shamir secret sharing, respectively. These results are to be compared with previous optimal online communication complexities of $O(Bn^2m)$ and $O(n^2m\log m)$ for malicious secure shuffle, for additive and Shamir secret sharing, respectively. We provide formal security proofs for both semi-honest and malicious secure transformations,showing that our malicious secure construction achieves universally composable security. Experimental results indicate that our construction significantly improves online performance while maintaining a moderate increase in offline overhead. Given that shuffle is a frequently used primitive in secure multiparty computation, we anticipate that our constructions will accelerate many real-world MPC applications.

In this paper, we present efficient SNARKs for Boolean circuits, achieving significant improvements in the prover efficiency. The core of our technique is a novel tower sumcheck protocol and a tower zero-check protocol tailored for tower fields, which enable this efficiency boost. When instantiated with Wiedemann's binary tower fields with the base field of $GF(2)$ and the top-level field $GF(2^{2^\ell})$, assuming the quadratic complexity of multiplications \(O(2^{2\ell})\) in the top-level field with $2^\ell$ bits, the prover time of our sumcheck protocol is \(O(2^{1.5\ell}N)\). It is faster than the standard sumcheck protocol over the large field with the complexity of \(O(2^{2\ell}N)\). To achieve a reasonable security level, $2^\ell$ is usually set to $128$. Leveraging this advancement, we improve the efficiency of IOP protocols over the binary or small characteristic fields for Plonkish, CCS, and GKR-based constraint systems. Moreover, to further improve the prover efficiency of the SNARKs, we introduce a basis-switching mechanism that efficiently transforms polynomial evaluations on the base-field polynomial to evaluations on the tower-field polynomial. With the basis-switching, we are able to compile the binary-field IOPs to SNARKs using large-field polynomial commitment schemes (PCS) that batch the witness over the base field. The size of the large-field PCS is only $\frac{1}{2^\ell}$ of the size of the witness over the base field. Combining the IOP and the PCS, the overall prover time of our SNARKs for Boolean circuits significantly faster than the naive approach of encoding Boolean values in a large field.

Quantum computing is considered one of the next big leaps in computational science. While a fully functional quantum computer is still in the future, there is an ever-growing need to evaluate the security of the symmetric key ciphers against a potent quantum adversary. Keeping this in mind, our work explores the key recovery attack using the Grover's search on the three variants of AES (-128, -192, -256). We develop a pool of 26 implementations per AES variant (thus totaling 78), by taking the state-of-the-art advancements in the relevant fields into account. In a nutshell, we present the least Toffoli depth and full depth implementations of AES, thereby improving from Zou et al.'s Asiacrypt'20 paper by more than 97 percent for each variant of AES. We show that the qubit count - Toffoli depth product is reduced from theirs by more than 87 percent. Furthermore, we analyze the Jaques et al.'s Eurocrypt'20 implementations in detail, fix the bugs (arising from some problem of the quantum computing tool used and not related to their coding), and report corrected benchmarks. To the best of our finding, our work improves from all the previous works (including the Asiacrypt'22 paper by Huang and Sun, the Asiacrypt'23 paper by Liu et al. and the Asiacrypt'24 paper by Shi and Feng) in terms of various quantum circuit complexity metrics (Toffoli depth, full depth, Toffoli/full depth - qubit count product, full depth - gate count product, etc.). Also, our bug-fixing of Jaques et al.'s Eurocrypt'20 implementations seems to improve from the authors' own bug-fixing, thanks to our architecture consideration. Equipped with the basic AES implementations, we further investigate the prospect of the Grover's search. We propose four new implementations of the S-box, one new implementation of the MixColumn; as well as five new architecture (one is motivated by the architecture by Jaques et al. in Eurocrypt'20, and the rest four are entirely our innovation). Under the MAXDEPTH constraint (specified by NIST), the circuit depth metrics (Toffoli depth, T-depth and full depth) become crucial factors and parallelization for often becomes necessary. We provide the least depth implementation in this respect that offers the best performance in terms of metrics for circuit complexity (like, depth-squared - qubit count product, depth - gate count product). Thus, to our knowledge, we estimate the currently best-known quantum attack complexities for AES-128 ($2^{156.2630}$), AES-192 ($2^{221.5801}$) and AES-256 ($2^{286.0731}$); these provide the NIST-specified quantum security levels 1, 3 and 5 respectively. Additionally, we achieve the least Toffoli depth - qubit count product for AES-128 ($121920$, improving from $130720$ by Shi and Feng in Asiacrypt'24), AES-192 ($161664$, improving from $188880$ by Liu et al. in Asiacrypt'23) and AES-256 ($206528$, improving from $248024$ by Liu et al. in Asiacrypt'23) so far.

Recent constructions of vector commitments and non-interactive zero-knowledge (NIZK) proofs from LWE implicitly solve the following shifted multi-preimage sampling problem: given matrices $\mathbf{A}_1, \ldots, \mathbf{A}_\ell \in \mathbb{Z}_q^{n \times m}$ and targets $\mathbf{t}_1, \ldots, \mathbf{t}_\ell \in \mathbb{Z}_q^n$, sample a shift $\mathbf{c} \in \mathbb{Z}_q^n$ and short preimages $\boldsymbol{\pi}_1, \ldots, \boldsymbol{\pi}_\ell \in \mathbb{Z}_q^m$ such that $\mathbf{A}_i \boldsymbol{\pi}_i = \mathbf{t}_i + \mathbf{c}$ for all $i \in [\ell]$. In this work, we introduce a new technique for sampling $\mathbf{A}_1, \ldots, \mathbf{A}_\ell$ together with a succinct public trapdoor for solving the multi-preimage sampling problem with respect to $\mathbf{A}_1, \ldots, \mathbf{A}_\ell$. This enables the following applications: * We provide a dual-mode instantiation of the hidden-bits model (and by correspondence, a dual-mode NIZK proof for $\mathsf{NP}$) with (1) a linear-size common reference string (CRS); (2) a transparent setup in hiding mode (which yields statistical NIZK arguments); and (3) hardness from LWE with a polynomial modulus-to-noise ratio. This improves upon the work of Waters (STOC 2024) which required a quadratic-size structured reference string (in both modes) and LWE with a super-polynomial modulus-to-noise ratio. * We give a statistically-hiding vector commitment with transparent setup and polylogarithmic-size CRS, commitments, and openings from SIS. This simultaneously improves upon the vector commitment schemes of de Castro and Peikert (EUROCRYPT 2023) as well as Wee and Wu (EUROCRYPT 2023). At a conceptual level, our work provides a unified view of recent lattice-based vector commitments and hidden-bits model NIZKs through the lens of the shifted multi-preimage sampling problem.

The SM4 block cipher is a Chinese national standard and an ISO international standard. Since white-box cryptography has many real-life applications nowadays, a few white-box implementations of SM4 has been proposed, among which a type of constructions is dominated, that uses a linear or affine diagonal block encoding to protect the original three 32-bit branches entering a round function and uses its inverse as the input encoding to the S-box layer. In this paper, we analyse the security of this type of constructions against Lepoint et al.'s collision-based attack method, our experiment under a small fraction of (encodings, round key) combinations shows that the rank of the concerned linear system is much less than the number of the involved unknowns, meaning these white-box SM4 implementations should resist Lepoint et al.'s method, but we leave it as an open problem whether there are such encodings that the rank of the corresponding linear system is slightly less than the number of the involved unknowns, in which scenario Lepoint et al.'s method may be used to recover a round key for the case with linear encodings and to remove most white-box operations until mainly some Boolean masks for the case with affine encodings.

The Signal Protocol is a two-party secure messaging protocol used in applications such as Signal, WhatsApp, Google Messages and Facebook Messenger and is used by billions daily. It consists of two core components, one of which is the Double Ratchet protocol that has been the subject of a line of work that aims to understand and formalise exactly what security it provides. Existing models capture strong guarantees including resilience to state exposure in both forward security (protecting past secrets) and post-compromise security (restoring security), adaptive state corruptions, message injections and out-of-order message delivery. Due to this complexity, prior work has failed to provide security guarantees that do not degrade in the number of interactions, even in the single-session setting. Given the ubiquity of the Double Ratchet in practice, we explore tight security bounds for the Double Ratchet in the multi-session setting. To this end, we revisit the modelling of Alwen, Coretti and Dodis (EUROCRYPT 2019) who decompose the protocol into modular, abstract components, notably continuous key agreement (CKA) and forward-secure AEAD (FS-AEAD). To enable a tight security proof, we propose a CKA security model that provides one-way security under key checking attacks. We show that multi-session security of the Double Ratchet can be tightly reduced to the multi-session security of CKA and FS-AEAD, capturing the same strong security guarantees as Alwen et al. Our result improves upon the bounds of Alwen et al. in the random oracle model. Even so, we are unable to provide a completely tight proof for the Double Ratchet based on standard Diffie-Hellman assumptions, and we conjecture it is not possible. We thus go a step further and analyse CKA based on key encapsulation mechanisms (KEMs). In contrast to previous works, our new analysis allows for tight constructions based on the DDH and post-quantum assumptions.

Quantum no-cloning is one of the most fundamental properties of quantum information. In this work, we introduce a new toolkit for analyzing cloning games; these games capture more quantitative versions of no-cloning and are central to unclonable cryptography. Previous works rely on the framework laid out by Tomamichel, Fehr, Kaniewski and Wehner to analyze both the $n$-qubit BB84 game and the subspace coset game. Their constructions and analysis face the following inherent limitations: - The existing bounds on the values of these games are at least $2^{-0.25n}$; on the other hand, the trivial adversarial strategy wins with probability $2^{-n}$. Not only that, the BB84 game does in fact admit a highly nontrivial winning strategy. This raises the natural question: are there cloning games which admit no non-trivial winning strategies? - The existing constructions are not multi-copy secure; the BB84 game is not even $2 \mapsto 3$ secure, and the subspace coset game is not $t \mapsto t+1$ secure for a polynomially large $t$. Moreover, we provide evidence that the existing technical tools do not suffice to prove multi-copy security of even completely different constructions. This raises the natural question: can we design new cloning games that achieve multi-copy security, possibly by developing a new analytic toolkit? Inspired by the literature on pseudorandom states, we study a new cloning game based on binary phase states and show that it is $t$-copy secure when $t=o(n/\log n)$. Moreover, for constant $t$, we obtain the first asymptotically optimal bounds of $O(2^{-n})$. To accomplish this, we introduce a new analytic toolkit based on of binary subtypes and combine this with novel bounds on the operator norms of block-wise tensor products of matrices. We also show a worst-case to average-case reduction for a large class of cloning games, which allows us to show the same quantitative results for Haar cloning games. These technical ingredients together enable two new applications which have previously been out of reach: - In the area of black-hole physics, our cloning games reveal that, in an idealized model of a black hole which features Haar random (or pseudorandom) scrambling dynamics, the information from infalling qubits can only be recovered from either the interior or the exterior of the black hole---but never from both places at the same time. To demonstrate this result, it turns out to be crucial to prove an asymptotically optimal bound and to overcome the first limitation above. - In the area of quantum cryptography, our worst-case to average-case reduction helps us construct succinct unclonable encryption schemes from the existence of pseudorandom unitaries, thereby, for the first time, bridging the gap between ``MicroCrypt'' and unclonable cryptography. We also propose and provide evidence for the security of multi-copy unclonable encryption schemes, which requires us to overcome the second limitation above.

In order for a client to securely connect to a server on the web, the client must trust certificate authorities (CAs) only to issue certificates to the legitimate operator of the server. If a certificate is miss-issued, it is possible for an attacker to impersonate the server to the client. The goal of Certificate Transparency (CT) is to log every certificate issued in a manner that allows anyone to audit the logs for miss-issuance. A client can even audit a CT log itself, but this would leak sensitive browsing data to the log operator. As a result, client-side audits are rare in practice. In this work, we revisit private CT auditing from a real-world perspective. Our study is motivated by recent changes to the CT ecosystem and advancements in Private Information Retrieval (PIR). First, we find that checking for inclusion of Signed Certificate Timestamps (SCTs) in a log — the audit performed by clients — is now possible with PIR in under a second and under 100kb of communication with minor adjustments to the protocol that have been proposed previously. Our results also show how to scale audits by using existing batching techniques and the algebraic structure of the PIR protocols, in particular to obtain certificate hashes by included in the log. Since PIR protocols are more performant with smaller databases, we also suggest a number of strategies to lower the size of the SCT database for audits. Our key observation is that the web will likely transition to a new model for certificate issuance. While this transition is primarily motivated by the need to adapt the PKI to larger, post-quantum signature schemes, it also removes the need for SCT audits in most cases. We present the first estimates of how this transition may impact SCT auditing, based on data gathered from public CT logs. We find that large scale deployment of the new issuance model may reduce the number of SCT audits needed by a factor of 1,000, making PIR-based auditing practical to deploy.

A wide range of countermeasures have been proposed to defend against side-channel attacks, with masking being one of the most effective and commonly used techniques. While theoretical models provide formal security proofs, these often rely on assumptions—sometimes implicit—that can be difficult to assess in practice. As a result, the design of secure masked implementations frequently combines proven theoretical arguments with heuristic and empirical validation. Despite the significant body of work, the literature still lacks a cohesive and well-defined framework for translating theoretical security guarantees into practical implementations on physical devices. Specifically, there remains a gap in connecting provable results from abstract models to quantitative security guarantees at the implementation level. In this Systematization of Knowledge (SoK), we aim to provide a comprehensive methodology to transform abstract cryptographic algorithms into physically secure implementations against side-channel attacks on microcontrollers. We introduce new tools to adapt the ideal noisy leakage model to practical, real-world scenarios, and we integrate state-of-the-art techniques to build secure implementations based on this model. Our work systematizes the design objectives necessary for achieving high security levels in embedded devices and identifies the remaining challenges in concretely applying security reductions. By bridging the gap between theory and practice, we seek to provide a foundation for future research that can develop implementations with proven security against side-channel attacks, based on well- understood leakage assumptions.

Homomorphic encryption allows for computations on encrypted data without exposing the underlying plaintext, enabling secure and private data processing in various applications such as cloud computing and machine learning. This paper presents a comprehensive mathematical foundation for three prominent homomorphic encryption schemes: Brakerski-Gentry-Vaikuntanathan (BGV), Brakerski-Fan-Vercauteren (BFV), and Cheon-Kim-Kim-Song (CKKS), all based on the Ring Learning with Errors (RLWE) problem. We align our discussion with the functionalities proposed in the recent homomorphic encryption standard, providing detailed algorithms and correctness proofs for each scheme. Additionally, we propose improvements to the current schemes focusing on noise management and optimization of public key encryption and leveled homomorphic computation. Our modifications ensure that the noise bound remains within a fixed function for all levels of computation, guaranteeing correct decryption and maintaining efficiency comparable to existing methods. The proposed enhancements reduce ciphertext expansion and storage requirements, making these schemes more practical for real-world applications.

Non-Interactive Timed Commitment schemes (NITC) allow to open any commitment after a specified delay $t_{\mathrm{fd}}$. This is useful for sealed bid auctions and as primitive for more complex protocols. We present the first NITC without repeated squaring or theoretical black box algorithms like NIZK proofs or one-way functions. It has fast verification, almost arbitrary delay and satisfies IND-CCA hiding and perfect binding. Our protocol is based on isogenies between supersingular elliptic curves making it presumably quantum secure, and all algorithms have been implemented as part of SQISign or other well-known isogeny-based cryptosystems. Additionally, it needs no trusted setup and can use known primes for SIKE or SQISign.

We propose efficient, post-quantum threshold ring signatures constructed from one-wayness of AES encryption and the VOLE-in-the-Head zero-knowledge proof system. Our scheme scales efficiently to large rings and extends the linkable ring signatures paradigm. We define and construct key-binding deterministic tags for signature linkability, that also enable succinct aggregation with approximate lower bound arguments of knowledge; this allows us to achieve succinct aggregation of our signatures without SNARKs. Finally, we extend our threshold ring signatures to realize post-quantum anonymous ledger transactions in the spirit of Monero. Our constructions assume symmetric key primitives only. Whilst it is common to build post-quantum signatures from the one-wayness property of AES and a post-quantum NIZK scheme, we extend this paradigm to define and construct novel security properties from AES that are useful for advanced signature applications. We introduce key-binding and pseudorandomness of AES to establish linkability and anonymity of our threshold ring signatures from deterministic tags, and similarly establish binding and hiding properties of block ciphers modeled as ideal permutations to build commitments from AES, a crucial building block for our proposed post-quantum anonymous ledger scheme.

We consider the problem of constructing efficient pseudorandom functions with Beyond-Birthday-Bound (BBB) security from blockciphers. More specifically, we are interested in variable-output-length pseudorandom functions (PRF) whose domain is twice that of the underlying blockcipher. We present two such constructions, $\textsf{Pencil}$ and $\sharp\textsf{Pencil}$, which provide weak PRF and full PRF security, respectively, where both achieve full $n$-bit security. While several recent works have focused on constructing BBB PRFs from blockciphers, much less attention has been given to weak PRF constructions which can potentially be constructed more efficiently and still serve as a useful primitive. Another understudied problem in this domain, is that of extending the domain of a BBB PRF, which turns out to be rather challenging. Besides being of theoretical interest in itself, this is also a very practical problem. Often, the input to the BBB PRF is a nonce, but random nonces are much easier to handle in practice as they do not require maintaining state---which can be very cumbersome in distributed systems and encrypted cloud storage. Accordingly, in order to maintain a BBB security bound, one requires random nonces of size between $1.5n$ and $2n$ bits long and corresponding BBB (weak) PRF constructions that admit matching input sizes. NIST has recently announced a pre-draft call for comments to standardise AEAD schemes that can encrypt larger amounts of data and admit larger nonces. The call lists two approaches. The first is to define an analogue of GCM using a 256-bit blockcipher, and the second is based on a recent proposal by Gueron, to extend GCM with a key derivation function (KDF) called DNDK to increase its security. In essence, DNDK is a BBB-secure expanding weak pseudorandom function with a domain size of 192 bits that is realised from AES. Our work makes relevant contributions to this domain in two important ways. Firstly, an immediate consequence of our work is that one can construct a GCM analogue with BBB security from $\sharp\textsf{Pencil}$, without resorting to a 256-bit blockcipher. Our second contribution is that $\sharp\textsf{Pencil}$ can be used as a KDF in combination with GCM in an analogous manner to DNDK-GCM. However, $\sharp\textsf{Pencil}$ being a full PRF as opposed to DNDK which is only a weak PRF, allows one to prove the KDF-GCM composition secure as an AEAD scheme. Finally, when contrasting $\textsf{Pencil}$ and DNDK as weak PRFs with comparable parameters, our construction requires only half the blockcipher calls.

Kyber was selected by NIST as a Post-Quantum Cryptography Key Encapsulation Mechanism standard. This means that the industry now needs to transition and adopt these new standards. One of the most demanding operations in Kyber is the modular arithmetic, making it a suitable target for optimization. This work offers a novel modular reduction design with the lowest area on Xilinx FPGA platforms. This novel design, through K-reduction and LUT-based reduction, utilizes 49 LUTs and 1 DSP as opposed to Xing and Li’s 2021 CHES design requiring 90 LUTs and 1 DSP for one modular multiplication. Our design is the smallest modular multiplier reported as of today.

Boolean functions play an important role in designing and analyzing many cryptographic systems, such as block ciphers, stream ciphers, and hash functions, due to their unique cryptographic properties such as nonlinearity, correlation immunity, and algebraic properties. The secure evaluation of Boolean functions or Secure Boolean Evaluation (SBE) is an important area of research. SBE allows parties to jointly compute Boolean functions without exposing their private inputs. SBE finds applications in privacy-preserving protocols and secure multi-party computations. In this manuscript, we present an efficient and generic two-party protocol (namely BooleanEval) for the secure evaluation of Boolean functions by utilizing a 1-out-of-2 Oblivious Transfer (OT) as a building block. BooleanEval only employs hash evaluations and XOR operations as the core computational step, thus making it lightweight and fast. Unlike other lightweight state-of-the-art designs of SBE, BooleanEval avoids the use of additional cryptographic primitives, such as commitment schemes to reduce the computational overhead.

This work proposes an encrypted hybrid database framework that combines vectorized data search and relational data query over quantized fully homomorphic encryption (FHE). We observe that, due to the lack of efficient encrypted data ordering capabilities, most existing encrypted database (EDB) frameworks do not support hybrid queries involving both vectorized and relational data. To further enrich query expressiveness while retaining evaluation efficiency, we propose Engorgio, a hybrid EDB framework based on quantized data ordering techniques over FHE. Specifically, we design a new quantized data encoding scheme along with a set of novel comparison and permutation algorithms to accurately generate and apply orders between large-precision data items. Furthermore, we optimize specific query types, including full table scan, batched query, and Top-k query to enhance the practical performance of the proposed framework. In the experiment, we show that, compared to the state-of-the-art EDB frameworks, Engorgio is up to 28x--854x faster in homomorphic comparison, 65x--687x faster in homomorphic sorting and 15x--1,640x faster over a variety of end-to-end relational, vectorized, and hybrid SQL benchmarks. Using Engorgio, the amortized runtime for executing a relational and hybrid query on a 48-core processor is under 3 and 75 seconds, respectively, over a 10K-row hybrid database.

How could quantum cryptography help us achieve what are not achievable in classical cryptography? In this work we study the classical cryptographic problem that two parties would like to perform secure computations with long outputs. As a basic primitive and example, we first consider the following problem which we call secure function sampling with long outputs: suppose $f:\{0,1\}^n\rightarrow \{0,1\}^m$ is a public, efficient classical function, where $m$ is big; Alice would like to sample $x$ from its domain and sends $f(x)$ to Bob; what Bob knows should be no more than $f(x)$ even if it behaves maliciously. Classical cryptography, like FHE and succinct arguments [Gen09,Kil92,HW15], allows us to achieve this task within communication complexity $O(n+m)$; could we achieve this task with communication complexity independent of $m$? In this work, we first design a quantum cryptographic protocol that achieves secure function sampling with approximate security, within $O(n)$ communication (omitting the dependency on the security parameter and error tolerance). We also prove the classical impossibility using techniques in [HW15], which means that our protocol indeed achieves a type of quantum advantage. Building on the secure function sampling protocol, we further construct protocols for general secure two-party computations [Yao86,GB01] with approximate security, with communication complexity only depending on the input length and the targeted security. In terms of the assumptions, we construct protocols for these problems assuming only the existence of collapsing hash functions [Unr16]; what's more, we also construct a classical-channel protocol for these problems additionally assuming the existence of noisy trapdoor claw-free functions [BCMVV,BKVV].

Secure graph computation enables computing on graphs while hiding the graph topology as well as the associated node/edge data. This facilitates collaborative analysis among multiple data owners, who may only hold a private partial view of the global graph. Several works address this problem using the technique of secure multiparty computation (MPC) in the presence of 2 or 3 parties. However, when moving to the multiparty setting, as required for collaborative analysis among multiple data owners, these solutions are no longer scalable. This remains true with respect to the state-of-the-art framework of $\mathsf{Graphiti}$ (Koti et al., CCS 2024) as well. Specifically, $\mathsf{Graphiti}$ incurs a round complexity linear in the number of parties or data owners. This is due to its reliance on secure shuffle protocol, constituting a bottleneck in the multiparty setting. Additionally, $\mathsf{Graphiti}$ has a prohibitively expensive initialisation phase due to its reliance on secure sort, with a round complexity dependent on both the graph size and the number of parties. We propose $\mathsf{emGraph}$, a generic framework for secure graph computation in the multiparty setting that eliminates the need of shuffle and instead, relies on a weaker primitive known as $\mathsf{Permute+Share}$. Further $\mathsf{emGraph}$ is designed to have a lightweight initialisation, that eliminates the need for sorting, making its round complexity independent of the graph size and number of parties. Unlike any of the prior works, achieving a round complexity independent of the number of parties is what makes $\mathsf{emGraph}$ scalable. Finally, we implement and benchmark the performance of $\mathsf{emGraph}$ for the application of PageRank computation and showcase its efficiency and scalability improvements over $\mathsf{Graphiti}$. Concretely, we witness improvements of up to $80\times$ in runtime in comparison to state-of-the-art framework $\mathsf{Graphiti}$. Further, we observe that $\mathsf{emGraph}$ takes under a minute to perform 10 iterations of PageRank computation on a graph of size $10^6$ that is distributed among $25$ parties/data owners, making it highly practical for secure graph computation in the multiparty setting.

Zero-Knowledge (ZK) protocols have been a subject of intensive study due to their fundamental importance and versatility in modern cryptography. However, the inherently different nature of quantum information significantly alters the landscape, necessitating a re-examination of ZK designs. A crucial aspect of ZK protocols is their round complexity, intricately linked to $\textit{simulation}$, which forms the foundation of their formal definition and security proofs. In the $\textit{post-quantum}$ setting, where honest parties and their communication channels are all classical but the adversaries could be quantum, Chia, Chung, Liu, and Yamakawa [FOCS'21] demonstrated the non-existence of constant-round $\textit{black-box-simulatable}$ ZK arguments (BBZK) for $\mathbf{NP}$ unless $\mathbf{NP} \subseteq \mathbf{BQP}$. However, this problem remains widely open in the full-fledged quantum future that will eventually arrive, where all parties (including the honest ones) and their communication are naturally quantum. Indeed, this problem is of interest to the broader theory of quantum computing. It has been an important theme to investigate how quantum power fundamentally alters traditional computational tasks, such as the $\textit{unconditional}$ security of Quantum Key Distribution and the incorporation of Oblivious Transfers in MiniQCrypt. Moreover, quantum communication has led to round compression for commitments and interactive arguments. Along this line, the above problem is of great significance in understanding whether quantum computing could also change the nature of ZK protocols in some fundamentally manner. We resolved this problem by proving that only languages in $\mathbf{BQP}$ admit constant-round $\textit{fully-quantum}$ BBZK. This result holds significant implications. Firstly, it illuminates the nature of quantum zero-knowledge and provides valuable insights for designing future protocols in the quantum realm. Secondly, it relates ZK round complexity with the intriguing problem of $\mathbf{BQP}$ vs $\mathbf{QMA}$, which is out of the reach of previous analogue impossibility results in the classical or post-quantum setting. Lastly, it justifies the need for the $\textit{non-black-box}$ simulation techniques or the relaxed security notions employed in existing constant-round fully-quantum BBZK protocols.

zkVMs are SNARKs for verifying CPU execution. They allow an untrusted prover to show that it correctly ran a specified program on a witness, where the program is given as bytecode conforming to an instruction set architecture like RISC-V. Existing zkVMs still struggle with high prover resource costs, notably large runtime and memory usage. We show how to implement Jolt—an advanced, sum-check- based zkVM—with a significantly reduced memory footprint, without relying on SNARK recursion, and with only modest runtime overhead (potentially well below a factor of two). We discuss benefits of this approach compared to prevailing recursive techniques.

We introduce a general template for building garbled circuits with low communication, under the decisional composite residuosity (DCR) assumption. For the case of layered Boolean circuits, we can garble a circuit of size $s$ with communication proportional to $O(s/\log\log s)$ bits, plus an additive factor that is polynomial in the security parameter. For layered arithmetic circuits with $B$-bounded integer computation, we obtain a similar result: the garbled arithmetic circuit has size $O(s/\log\log s) \cdot (\lambda + \log B)$ bits, where $\lambda$ is the security parameter. These are the first constructions of general-purpose, garbled circuits with sublinear size, without relying on heavy tools like indistinguishability obfuscation or attribute-based and fully homomorphic encryption. To achieve these results, our main technical tool is a new construction of a form of homomorphic secret sharing where some of the inputs are semi-private, that is, known to one of the evaluating parties. Through a new relinearisation technique that allows performing arbitrary additions and multiplications on semi-private shares, we build such an HSS scheme that supports evaluating any function of the form $C(x) \cdot C'(y)$, where $C$ is any polynomially-sized circuit applied to the semi-private input $y$, and $C'$ is a restricted-multiplication (or, NC1) circuit applied to the private input $x$. This significantly broadens the expressiveness of prior known HSS constructions.

CRLite is a low-bandwidth, low-latency, privacy-preserving mechanism for distributing certificate revocation data. A CRLite aggregator periodically encodes revocation data into a compact static hash set, or membership test, which can can be downloaded by clients and queried privately. We present a novel data-structure for membership tests, which we call a clubcard, and we evaluate the encoding efficiency of clubcards using data from Mozilla's CRLite infrastructure. As of November 2024, the WebPKI contains over 900 million valid certificates and over 8 million revoked certificates. We describe an instantiation of CRLite that encodes the revocation status of these certificates in a 6.7 MB package. This is $54\%$ smaller than the original instantiation of CRLite presented at the 2017 IEEE Symposium on Security and Privacy, and it is $21\%$ smaller than the lower bound claimed in that work. A sequence of clubcards can encode a dynamic dataset like the WebPKI revocation set. Using data from late 2024 again, we find that clubcards encoding 6 hour delta updates to the WebPKI can be compressed to 26.8 kB on average---a size that makes CRLite truly practical. We have extended Mozilla's CRLite infrastructure so that it can generate clubcards, and we have added client-side support for this system to Firefox. We report on some performance aspects of our implementation, which is currently the default revocation checking mechanism in Firefox Nightly, and we propose strategies for further reducing the bandwidth requirements of CRLite.

A Random Oracle Combiner (ROC), introduced by Dodis et al. (CRYPTO ’22), takes two hash functions $h_1, h_2$ from m bits to n bits and outputs a new hash function $C$ from $m$' to $n$' bits. This function C is guaranteed to be indifferentiable from a fresh random oracle as long as one of $h_1$ and $h_2$ (say, $h_1$) is a random oracle, while the other h2 can “arbitrarily depend” on $h_1$. The work of Dodis et al. also built the first length-preserving ROC, where $n$′ = $n$. Unfortunately, despite this feasibility result, this construction has several deficiencies. From the practical perspective, it could not be directly applied to existing Merkle-Damgård-based hash functions, such as SHA2 or SHA3. From the theoretical perspective, it required $h_1$ and $h_2$ to have input length $m$ > 3λ, where λ is the security parameter. To overcome these limitations, Dodis et al. conjectured — and left as the main open question — that the following (salted) construction is a length-preserving ROC: $C^{h1,h2}_{\mathcal{Z}_1,\mathcal{Z}_2} (M ) = h_1^*(M, \mathcal{Z}_1) \oplus h^*_2(M,\mathcal{Z}_2),$ where $\mathcal{Z}_1, \mathcal{Z}_2$ are random salts of appropriate length, and $f^*$ denotes the Merkle-Damgård-extension of a given compression function $f$. As our main result, we resolve this conjecture in the affirmative. For practical use, this makes the resulting combiner applicable to existing, Merkle-Damgård-based hash functions. On the theory side, it shows the existence of ROCs only requiring optimal input length $m$ = λ+O(1).

This paper presents new results that establish connections between isogeny graphs and nonlinear recurrences over finite fields. Specifically, we prove several theorems that link these two areas, offering deeper insights into the structure of isogeny graphs and their relationship with nonlinear recurrence sequences. We further provide two related conjectures which may be worth of further research. These findings contribute to a better understanding of the endomorphism ring of a curve, advancing progress toward the resolution of the Endomorphism Ring Problem, which aims to provide a computational characterization of the endomorphism ring of a supersingular elliptic curve.

Physically Unclonable Constants (PUCs) are a special type of Physically Unclonable Constants and they can be used to embed secret bit-strings in chips. Most PUCs are an array of cells where each cell is a digital circuit that evolve spontaneously toward one of two states, the chosen state being function of random manufacturing process variations. In this paper we propose an Analog Physically Unclonable Constant (APUC) whose output is an analog value to be transformed in digital by a digitizer circuit. The ratio behind this proposal is that an APUC cell has the potential of providing more than one bit, reducing the required footprint. Preliminary theoretical analysis and simulation results are presented. The proposed APUC has interesting performances (e.g., it can provide up to 5 bits per cell) that grant for further investigation.

BFT protocols usually have a waterfall-like degradation in performance in the face of crash faults. Some BFT protocols may not experience sudden performance degradation under crash faults. They achieve this at the expense of increased communication and round complexity in fault-free scenarios. In a nutshell, existing protocols lack the adaptability needed to perform optimally under varying conditions. We propose TockOwl, the first asynchronous consensus protocol with fault adaptability. TockOwl features quadratic communication and constant round complexity, allowing it to remain efficient in fault-free scenarios. TockOwl also possesses crash robustness, enabling it to maintain stable performance when facing crash faults. These properties collectively ensure the fault adaptability of TockOwl. Furthermore, we propose TockOwl+ that has network adaptability. TockOwl+ incorporates both fast and slow tracks and employs hedging delays, allowing it to achieve low latency comparable to partially synchronous protocols without waiting for timeouts in asynchronous environments. Compared to the latest dual-track protocols, the slow track of TockOwl+ is simpler, implying shorter latency in fully asynchronous environments.

The security of ML-DSA, like most signature schemes, is partially based on the fact that the nonce used to generate the signature is unknown to any attacker. In this work, we exhibit a lattice-based attack that is possible if the nonces share implicit or explicit information. From a collection of signatures whose nonces share certain coefficients, it is indeed possible to build a collection of non full-rank lattices. Intersecting them, we show how to create a low-rank lattice that contains one of the polynomials of the secret key, which in turn can be recovered using lattice reduction techniques. There are several interpretations of this result: firstly, it can be seen as a generalization of a fault-based attack on BLISS presented at SAC'16 by Thomas Espitau et al. Alternatively, it can be understood as a side-channel attack on ML-DSA, in the case where an attacker is able to recover only one of the coefficients of the nonce used during the generation of the signature. For ML-DSA-II, we show that $4 \times 160$ signatures and few hours of computation are sufficient to recover the secret key on a desktop computer. Lastly, our result shows that simple countermeasures, such as permuting the generation of the nonce coefficients, are not sufficient.

Secure two-party computation (2PC) allows two distrustful parties to jointly compute some functions while keeping their private secrets unrevealed. Adversaries are often categorized as semi-honest and malicious, depending on whether they follow the protocol specifications or not. While a semi-honest secure protocol is fast but strongly assumed that all participants will follow the protocol, a malicious protocol often requires heavy verification steps and preprocessing phase to prohibit any cheat. Covert security [10] was first introduced by Aumann and Lindell, which looks into the "middle ground" between semi-honest security and malicious security, such that active adversaries who cheat will be caught with a predefined probability. However, it is still an open question that how to properly determine such a probability before protocol execution, and the misbehavior detection must be made by other honest participants with cut-and-choose in current constructions. To achieve public verifiability and meanwhile outsource the verification steps, [12] presented publicly auditable security to enable an external auditor to verify the result correctness. Essentially, an additional existence assumption of a bulletin board functionality is required to keep tracking the broadcasted messages for the auditor. And moreover, the auditor cannot identify the cheater, but only points out the incorrect result. The (robust) accountability family [40, 62, 76] achieves both output delivery guarantee and public verifiability, which relies on heavy offline and online constructions with zero knowledge proofs. In this paper, we propose a new security notion called honorific security, where an external arbiter can find the cheater with overwhelming probability under the malicious corruption. With honorific security, we do not prohibit cheat of a corrupted party during the online stage, but enable the honest party to detect and punish the cheater later on in public. We show that a maliciously secure garbled circuit (GC) [83] protocol can thus be constructed with only slightly more overhead than a passively secure protocol. Our construction performs up to 2.37 times and 13.30 times as fast as the state-of-the-art protocols with covert and malicious security, respectively.

Laconic cryptography focuses on designing two-message protocols that allow secure computation on large datasets while minimizing communication costs. While laconic cryptography protocols achieve asymptotically optimal communication complexity for many tasks, their concrete efficiency is prohibitively expensive due to the heavy use of public-key techniques or the non-black-box of cryptographic primitives. In this work, we initiate the study of "laconic cryptography with preprocessing", introducing a model that includes an offline phase to generate database-dependent correlations, which are then used in a lightweight online phase. These correlations are conceptually simple, relying on linear-algebraic techniques. This enables us to develop a protocol for private laconic vector oblivious linear evaluation (plvOLE). In such a protocol, the receiver holds a large database $\mathsf{DB}$, and the sender has two messages $v$ and $w$, along with an index $i$. The receiver learns the value $v \cdot \mathsf{DB}_i + w$ without revealing other information. Our protocol, which draws from ideas developed in the context of private information retrieval with preprocessing, serves as the backbone for two applications of interest: laconic private set intersection (lPSI) for large universes and laconic function evaluation for RAM-programs (RAM-LFE). Based our plvOLE protocol, we provide efficient instantiations of these two primitives in the preprocessing model.