The Middle-Product Learning with Errors (MPLWE) assumption is a variant of the Learning with Errors (LWE) assumption. The MPLWE assumption reduces the key size of corresponding LWE-based schemes by setting keys as sets of polynomials. Moreover, MPLWE has more robust security than other LWE variants such as Ring-LWE and Module-LWE. Lombardi et al. proposed an identity-based encryption (IBE) scheme (LVV-IBE) based on the MPLWE assumption in the random oracle model (ROM) by following Gentry et...

At CRYPTO 2015, Kirchner and Fouque claimed that a carefully tuned variant of the Blum-Kalai-Wasserman (BKW) algorithm (JACM 2003) should solve the Learning with Errors problem (LWE) in slightly subexponential time for modulus $q=\mathrm{poly}(n)$ and narrow error distribution, when given enough LWE samples. Taking a modular view, one may regard BKW as a combination of Wagner's algorithm (CRYPTO 2002), run over the corresponding dual problem, and the Aharonov-Regev distinguisher (JACM 2005)....

A (single server) private information retrieval (PIR) allows a client to read data from a public database held on a remote server, without revealing to the server which locations she is reading. In a doubly efficient PIR (DEPIR), the database is first preprocessed offline into a data structure, which then allows the server to answer any client query efficiently in sub-linear online time. Constructing DEPIR is a notoriously difficult problem, and this difficulty even extends to a weaker...

HuFu is an unstructured lattice-based signature scheme proposed during the NIST PQC standardization process. In this work, we present a side-channel analysis of HuFu's reference implementation. We first exploit the multiplications involving its two main secret matrices, recovering approximately half of their entries through a non-profiled power analysis with a few hundred traces. Using these coefficients, we reduce the dimension of the underlying LWE problem, enabling full secret key...

We present almost-optimal lattice-based attribute-based encryption (ABE) and laconic function evaluation (LFE). For depth d circuits over $\ell$-bit inputs, we obtain * key-policy (KP) and ciphertext-policy (CP) ABE schemes with ciphertext, secret key and public key size $O(1)$; * LFE with ciphertext size $\ell + O(1)$ as well as CRS and digest size $O(1)$; where O(·) hides poly(d, λ) factors. The parameter sizes are optimal, up to the poly(d) dependencies. The security of our...

Scloud+ is an unstructured LWE-based key encapsulation mechanism (KEM) with conservative quantum security, in which ternary secrets and lattice coding are incorporated for higher computational and communication efficiency. However, its efficiencies are still much inferior to those of the structured LWE-based KEM, like ML-KEM (standardized by NIST). In this paper, we present a configurable hardware architecture for Scloud+.KEM to improve the computational efficiency. Many algorithmic and...

One-shot signatures (OSS) were defined by Amos, Georgiou, Kiayias, and Zhandry (STOC'20). These allow for signing exactly one message, after which the signing key self-destructs, preventing a second message from ever being signed. While such an object is impossible classically, Amos et al observe that OSS may be possible using quantum signing keys by leveraging the no-cloning principle. OSS has since become an important conceptual tool with many applications in decentralized settings and for...

The evasive learning with errors (evasive LWE) assumption is a new assumption recently introduced by Wee (Eurocrypt 2022) and Tsabary (Crypto 2022) independently, as a significant strengthening of the standard LWE assumption. While the assumption is known to imply various strong primitives including witness encryption [Wee22,Tsabary22], the assumption in the most general case (i.e., the private coin variant) is considered quite implausible due to the obfuscation based attack mentioned in...

We study recent algebraic attacks (Briaud-Øygarden EC'23) on the Regular Syndrome Decoding (RSD) problem and the assumptions underlying the correctness of their attacks' complexity estimates. By relating these assumptions to interesting algebraic-combinatorial problems, we prove that they do not hold in full generality. However, we show that they are (asymptotically) true for most parameter sets, supporting the soundness of algebraic attacks on RSD. Further, we prove—without any heuristics...

Decentralization is a great enabler for adoption of modern cryptography in real-world systems. Widespread adoption of blockchains and secure multi-party computation protocols are perfect evidentiary examples for dramatic rise in deployment of decentralized cryptographic systems. Much of cryptographic research can be viewed as reducing (or eliminating) the dependence on trusted parties, while shielding from stronger adversarial threats. In this work, we study the problem of multi-authority...

Threshold fully homomorphic encryption (ThFHE) is an extension of FHE that can be applied to multiparty computation (MPC) with low round complexity. Recently, Passelègue and Stehlé (Asiacrypt 2024) presented a simulation-secure ThFHE scheme with polynomially small decryption shares from “yet another” learning with errors assumption (LWE), in which the norm of the secret key is leaked to the adversary. While “yet another” LWE is reduced from standard LWE, its module variant, “yet another”...

Hiding the metadata in Internet protocols serves to protect user privacy, dissuade traffic analysis, and prevent network ossification. Fully encrypted protocols require even the initial key exchange to be obfuscated: a passive observer should be unable to distinguish a protocol execution from an exchange of random bitstrings. Deployed obfuscated key exchanges such as Tor's pluggable transport protocol obfs4 are Diffie–Hellman-based, and rely on the Elligator encoding for obfuscation....

Abdalla et al. (ASIACRYPT 2020) introduced a notion of identity-based inner-product functional encryption (IBIPFE) that combines identity-based encryption and inner-product functional encryption (IPFE). Thus far, several pairing-based and lattice-based IBIPFE schemes have been proposed. However, there are two open problems. First, there are no known IBIPFE schemes that satisfy the adaptive simulation-based security. Second, known IBIPFE schemes that satisfy the adaptive...

At Crypto 2021, May presented an algorithm solving the ternary Learning-With-Error problem, where the solution is a ternary vector $s\in\{0,\pm 1\}^{n}$ with a known number of $(+1)$ and $(-1)$ entries. This attack significantly improved the time complexity of $\mathcal{S}^{0.5}$ from previously known algorithms to $\mathcal{S}^{0.25}$, where $\mathcal{S}$ is the size of the key space. Therefore, May exploited that using more representations, i.e., allowing ternary interim results with...

Indistinguishability obfuscation (iO) stands out as a powerful cryptographic primitive but remains notoriously difficult to realize under simple-to-state, post-quantum assumptions. Recent works have proposed lattice-inspired iO constructions backed by new “LWE-with-hints” assumptions, which posit that certain distributions of LWE samples retain security despite auxiliary information. However, subsequent cryptanalysis has revealed structural vulnerabilities in these assumptions, leaving us...

Evasive LWE (Wee, Eurocrypt 2022 and Tsabary, Crypto 2022) is a recently introduced, popular lattice assumption which has been used to tackle long-standing problems in lattice based cryptography. In this work, we develop new counter-examples against Evasive LWE, in both the private and public-coin regime, propose counter-measures that define safety zones, and finally explore modifications to construct full compact FE/iO. Attacks: Our attacks are summarized as follows. - The recent...

We present a simple counterexample to all known variants of the private-coin evasive learning with errors (LWE) assumption. Unlike prior works, our counterexample is direct, it does not use heavy cryptographic machinery (such as obfuscation or witness encryption), and it applies to all variants of the assumption. Our counterexample can be seen as a "zeroizing" attack against evasive LWE, calling into question the soundness of the underlying design philosophy.

Lattice trapdoor algorithms allow us to sample hard random lattices together with their trapdoors, given which short lattice vectors can be sampled efficiently. This enables a wide range of advanced cryptographic primitives. In this work, we ask: can we distribute lattice trapdoor algorithms non-interactively? We study a natural approach to sharing lattice trapdoors: splitting them into partial trapdoors for different lower-rank sublattices which allow the local sampling of short...

Updatable Public-Key Encryption (UPKE) augments the security of PKE with Forward Secrecy properties. While requiring more coordination between parties, UPKE enables much more efficient constructions than full-fledged Forward-Secret PKE. Alwen, Fuchsbauer and Mularczyk (AFM, Eurocrypt’24) presented the strongest security notion to date. It is the first to meet the needs of UPKE’s most important applications: Secure Group Messaging and Continuous Group Key Agreement. The authors provide a very...

Updatable public-key encryption (UPKE) allows anyone to update a public key while simultaneously producing an update token, given which the secret key holder could consistently update the secret key. Furthermore, ciphertexts encrypted under the old public key remain secure even if the updated secret key is leaked -- a property much desired in secure messaging. All existing lattice-based constructions of UPKE update keys by a noisy linear shift. As the noise accumulates, these schemes either...

We propose a new method to construct a public-key encryption scheme, where one can homomorphically transform a ciphertext encrypted under a key $\mathbf{x}$ into a ciphertext under $(P, P(\mathbf{x}))$, for any polynomial-time RAM program $P: \mathbf{x} \mapsto \mathbf{y}$ with runtime $T$ and memory $L$. Combined with other lattice techniques, this allows us to construct: 1) Succinct-randomised encodings from RAM programs with encoder complexity $(|\mathbf{x}| + |\mathbf{y}|)\cdot...

We propose the notion of succinct oblivious tensor evaluation (OTE), where two parties compute an additive secret sharing of a tensor product of two vectors $\mathbf{x} \otimes \mathbf{y}$, exchanging two simultaneous messages. Crucially, the size of both messages and of the CRS is independent of the dimension of $\mathbf{x}$. We present a construction of OTE with optimal complexity from the standard learning with errors (LWE) problem. Then we show how this new technical tool enables a...

As introduced by Persiano {\it et al.} (Eurocrypt'22), anamorphic encryption (AE) is a primitive enabling private communications against a dictator that forces users to surrender their decryption keys. In its fully asymmetric flavor (defined by Catalano {\it et al.}, Eurocrypt'24), anamorphic channels can work as hidden public-key mechanisms in the sense that anamorphic encryptors are not necessarily able to decrypt anamorphic ciphertexts. Unfortunately, fully asymmetric AE is hard to come...

Broadcast encryption allows a user to encrypt a message to $N$ recipients with a ciphertext whose size scales sublinearly with $N$. The natural security notion for broadcast encryption is adaptive security which allows an adversary to choose the set of recipients after seeing the public parameters. Achieving adaptive security in broadcast encryption is challenging, and in the plain model, the primary technique is the celebrated dual-systems approach, which can be implemented over groups with...

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...

Although privately programmable pseudorandom functions (PPPRFs) are known to have numerous applications, so far, the only known constructions rely on Learning with Error (LWE) or indistinguishability obfuscation. We show how to construct a relaxed PPPRF with only one-way functions (OWF). The resulting PPPRF satisfies $1/\textsf{poly}$ security and works for polynomially sized input domains. Using the resulting PPPRF, we can get new results for preprocessing Private Information Retrieval...

We present the first construction for adaptively secure HIBE, that does not rely on bilinear pairings or random oracle heuristics. Notably, we design an adaptively secure HIBE from any selectively secure IBE system in the standard model. Combining this with known results, this gives the first adaptively secure HIBE system from a wide variety of standard assumptions such as CDH/Factoring/LWE/LPN. We also extend our adaptively secure HIBE system to satisfy full anonymity, giving the first...

Dynamic Decentralized Functional Encryption (DDFE) is a generalization of Functional Encryption which allows multiple users to join the system dynamically without interaction and without relying on a trusted third party. Users can independently encrypt their inputs for a joint evaluation under functions embedded in functional decryption keys; and they keep control on these functions as they all have to contribute to the generation of the functional keys. In this work, we present new...

Garbling schemes are a fundamental cryptographic tool for enabling private computations and ensuring that nothing leaks beyond the output. As a widely studied primitive, significant efforts have been made to reduce their size. Until recently, all such schemes followed the Lindell and Pinkas paradigm for Boolean circuits (JoC 2009), where each gate is represented as a set of ciphertexts computed using only symmetric-key primitives. However, this approach is inherently limited to 𝑂(𝜆) bits per...

The study of attack algorithms for the Learning with Errors (LWE) problem is crucial for the cryptanalysis of LWE-based cryptosystems. The BKW algorithm has gained significant attention as an important combinatorial attack for solving LWE. However, its exponential time and memory requirements severely limit its practical applications, even with medium-sized parameters. In this paper, we present a memory-efficient BKW algorithm for LWE, which extends Bogos's work [Asiacrypt'16] on the...

Software watermarking for cryptographic functionalities enables embedding an arbitrary message (a mark) into a cryptographic function. An extraction algorithm, when provided with a (potentially unauthorized) circuit, retrieves either the embedded mark or a special symbol unmarked indicating the absence of a mark. It is difficult to modify or remove the embedded mark without destroying the functionality of a marked function. Previous works have primarily employed black-box extraction...

Secure key leasing (SKL) is an advanced encryption functionality that allows a secret key holder to generate a quantum decryption key and securely lease it to a user. Once the user returns the quantum decryption key (or provides a classical certificate confirming its deletion), they lose their decryption capability. Previous works on public key encryption with SKL (PKE-SKL) have only considered the single-key security model, where the adversary receives at most one quantum decryption key....

We propose a new incrementally computable proof system, called Incrementally Verifiable $\textit{Streaming}$ Computation (IVsC). IVsC enables computing incremental proofs of correct execution for any RAM program $\mathcal{M}$ on a $\textit{streaming}$ input $x$. Input $x$ is called a $\textit{streaming}$ input if it is only available on-the-fly as part of an ongoing data generation/streaming process, and not available at once. We also propose a new notion of zero-knowledge features for IVsC...

Indistinguishability obfuscation (iO) has seen remarkable theoretical progress, yet it remains impractical due to its high complexity and inefficiency. A common bottleneck in recent iO schemes is the reliance on bootstrapping techniques from functional encryption (FE) into iO, which requires recursively invoking the FE encryption algorithm for each input bit—creating a significant barrier to practical iO schemes. In this work, we propose diamond iO, a new lattice-based iO construction...

Can a sender commit to a long input without even reading all of it? Can a prover convince a verifier that an NP statement holds without even reading the entire witness? Can a set of parties run a multiparty computation (MPC) protocol in the RAM model, without necessarily even reading their entire inputs? We show how to construct such "doubly efficient" schemes in a setting where parties can preprocess their input offline, but subsequently they can engage in many different protocol...

We study error detection and correction in a computationally bounded world, where errors are introduced by an arbitrary $\textit{polynomial-time}$ adversarial channel. Our focus is on $\textit{seeded}$ codes, where the encoding and decoding procedures can share a public random seed, but are otherwise deterministic. We can ask for either $\textit{selective}$ or $\textit{adaptive}$ security, depending on whether the adversary can choose the message being encoded before or after seeing the...

The Stealth Address Protocol (SAP) allows users to receive assets through stealth addresses that are unlinkable to their stealth meta-addresses. The most widely used SAP, Dual-Key SAP (DKSAP), and the most performant SAP, Elliptic Curve Pairing Dual-Key SAP (ECPDKSAP), are based on elliptic curve cryptography, which is vulnerable to quantum attacks. These protocols depend on the elliptic curve discrete logarithm problem, which could be efficiently solved on a sufficiently powerful quantum...

Quantum key leasing, also known as public key encryption with secure key leasing (PKE-SKL), allows a user to lease a (quantum) secret key to a server for decryption purpose, with the capability of revoking the key afterwards. In the pioneering work by Chardouvelis et al (arXiv:2310.14328), a PKE-SKL scheme utilizing classical channels was successfully built upon the noisy trapdoor claw-free (NTCF) family. This approach, however, relies on the superpolynomial hardness of learning with...

We put forth and instantiate a new primitive we call simultaneous-message and succinct (SMS) secure computation. An SMS scheme enables a minimal communication pattern for secure computation in the following scenario: Alice has a large private input X, Bob has a small private input y, and Charlie wants to learn $f(X, y)$ for some public function $f$. Given a common reference string (CRS) setup phase, an SMS scheme for a function f is instantiated with two parties holding inputs $X$ and...

Distributed Point Functions (DPFs) are a useful cryptographic primitive enabling a dealer to distribute short keys to two parties, such that the keys encode additive secret shares of a secret point function. However, in many applications of DPFs, no single dealer entity has full knowledge of the secret point function, necessitating the parties to run an interactive protocol to emulate the setup. Prior works have aimed to minimize complexity metrics of such distributed setup protocols, e.g.,...

Hybrid Homomorphic Encryption (HHE) is considered a promising solution for key challenges that emerge when adopting Homomorphic Encryption (HE). In cases such as communication and computation overhead for clients and storage overhead for servers, it combines symmetric cryptography with HE schemes. However, despite a decade of advancements, enhancing HHE usability, performance, and security for practical applications remains a significant stake. This work contributes to the field by...

This paper presents the first black-box registered ABE for circuit from lattices. The selective security is based on evasive LWE assumption [EUROCRYPT'22, CRYPTO'22]. The unique prior Reg-ABE scheme from lattices is derived from non-black-box construction based on function-binding hash and witness encryption [CRYPTO'23]. Technically, we first extend the black-box registration-based encryption from standard LWE [CRYPTO'23] so that we can register a public key with a function; this yields a...

Time-lock puzzles (TLP) are a cryptographic tool that allow one to encrypt a message into the future, for a predetermined amount of time $T$. At present, we have only two constructions with provable security: One based on the repeated squaring assumption and the other based on obfuscation. Basing TLP on any other assumption is a long-standing question, further motivated by the fact that known constructions are broken by quantum algorithms. In this work, we propose a new approach to...

Fully Homomorphic Encryption (FHE) allows a server to perform computations directly over the encrypted data. In general FHE protocols, the client is tasked with decrypting the computation result using its secret key. However, certain FHE applications benefit from the server knowing this result, especially without the aid of the client. Providing the server with the secret key allows it to decrypt all the data, including the client's private input. Protocols such as Goldwasser et. al....

Registered attribute-based encryption (ABE) is a generalization of public-key encryption that enables fine-grained access control to encrypted data (like standard ABE), but without needing a central trusted authority. In a key-policy registered ABE scheme, users choose their own public and private keys and then register their public keys together with a decryption policy with an (untrusted) key curator. The key curator aggregates all of the individual public keys into a short master public...

We provide the first attribute based encryption (ABE) scheme for Turing machines supporting unbounded collusions from lattice assumptions. In more detail, the encryptor encodes an attribute $\mathbf{x}$ together with a bound $t$ on the machine running time and a message $m$ into the ciphertext, the key generator embeds a Turing machine $M$ into the secret key and decryption returns $m$ if and only if $M(\mathbf{x})=1$. Crucially, the input $\mathbf{x}$ and machine $M$ can be of unbounded...

We construct a provably-secure structured variant of Learning with Errors (LWE) using nonassociative cyclic division algebras, assuming the hardness of worst-case structured lattice problems, for which we are able to give a full search-to-decision reduction, improving upon the construction of Grover et al. named `Cyclic Learning with Errors' (CLWE). We are thus able to create structured LWE over cyclic algebras without any restriction on the size of secret spaces, which was required for CLWE...

Garbled circuits are a foundational primitive in both theory and practice of cryptography. Given $(\hat{C}, K[x])$, where $\hat{C}$ is the garbling of a circuit C and $K[x] = \{K[i, x_i]\}$ are the input labels for an input $x$, anyone can recover $C(x)$, but nothing else about the input $x$. Most research efforts focus on minimizing the size of the garbled circuit $\hat{C}$. In contrast, the work by Applebaum, Ishai, Kushilevitz, and Waters (CRYPTO' 13) initiated the study of minimizing the...

We give new constructions of succinct non-interactive arguments ($\mathsf{SNARG}$s) for $\mathsf{NP}$ in the settings of both non-adaptive and adaptive soundness. Our construction of non-adaptive $\mathsf{SNARG}$ is universal assuming the security of a (leveled or unleveled) fully homomorphic encryption ($\mathsf{FHE}$) scheme as well as a batch argument ($\mathsf{BARG}$) scheme. Specifically, for any choice of parameters $\ell$ and $L$, we construct a candidate $\mathsf{SNARG}$ scheme...

Sparse Learning With Errors (sLWE) is a novel problem introduced at Crypto 2024 by Jain et al., designed to enhance security in lattice-based cryptography against quantum attacks while maintaining computational efficiency. This paper presents the first third-party analysis of the ternary variant of sLWE, where both the secret and error vectors are constrained to ternary values. We introduce a combinatorial attack that employs a subsystem extraction technique followed by a Meet-in-the-Middle...

The evasive LWE assumption, proposed by Wee [Eurocrypt'22 Wee] for constructing a lattice-based optimal broadcast encryption, has shown to be a powerful assumption, adopted by subsequent works to construct advanced primitives ranging from ABE variants to obfuscation for null circuits. However, a closer look reveals significant differences among the precise assumption statements involved in different works, leading to the fundamental question of how these assumptions compare to each other. In...

Evaluating the security of LWE-based KEMs involves two crucial metrics: the hardness of the underlying LWE problem and resistance to decryption failure attacks, both significantly influenced by the secret key and error distributions. To mitigate the complexity and timing vulnerabilities of Gaussian sampling, modern LWE-based schemes often adopt either the uniform or centered binomial distribution (CBD). This work focuses on Kyber to evaluate its security under both distributions. Compared...

Password Authenticated Key Exchange (PAKE) is a fundamental cryptographic component that allows two parties to establish a shared key using only (potentially low-entropy) passwords. The interest in realizing generic KEM-based PAKEs has increased significantly in the last few years as part of the global migration effort to quantum-resistant cryptography. One such PAKE is the CAKE protocol, proposed by Beguinet et al. (ACNS ’23). However, despite its simple design based on the...

Multi-input Attribute-Based Encryption (ABE) is a generalization of key-policy ABE where attributes can be independently encrypted across several ciphertexts, and a joint decryption of these ciphertexts is possible if and only if the combination of attributes satisfies the policy of the decryption key. We extend this model by introducing a new primitive that we call Multi-Client ABE (MC-ABE), which provides the usual enhancements of multi-client functional encryption over multi-input...

We consider a generalization of the Learning With Error problem, referred to as the white-box learning problem: You are given the code of a sampler that with high probability produces samples of the form $y,f(y)+\epsilon$ where is small, and $f$ is computable in polynomial-size, and the computational task consist of outputting a polynomial-size circuit $C$ that with probability, say, $1/3$ over a new sample $y$? according to the same distributions, approximates $f(y)$ (i.e., $|C(y)-f(y)$ ...

This paper focuses on the issue of reducing the bandwidth requirement for FHE ciphertext transmission. While this issue has been extensively studied from the uplink viewpoint (transmission of encrypted inputs towards a FHE calculation) where several approaches exist to essentially cancel FHE ciphertext expansion, the downlink case (transmission of encrypted results towards an end-user) has been the object of much less attention. In this paper, we address this latter issue with a particular...

Recent attacks on NTRU lattices given by Ducas and van Woerden (ASIACRYPT 2021) showed that for moduli $q$ larger than the so-called fatigue point $n^{2.484+o(1)}$, the security of NTRU is noticeably less than that of (ring)-LWE. Unlike NTRU-based PKE with $q$ typically lying in the secure regime of NTRU lattices (i.e., $q<n^{2.484+o(1)}$), the security of existing NTRU-based multi-key FHEs (MK-FHEs) requiring $q=O(n^k)$ for $k$ keys could be significantly affected by those...

The field of fully homomorphic encryption (FHE) has seen many theoretical and computational advances in recent years, bringing the technology closer to practicality than ever before. For this reason, practitioners in related fields, such as machine learning, are increasingly interested in using FHE to provide privacy to their applications. Despite this progress, selecting secure and efficient parameters for FHE remains a complex and challenging task due to the intricate interdependencies...

In this work, we present a new paradigm for constructing Group Authenticated Key Exchange (GAKE). This result is the first tightly secure GAKE scheme in a strong security model that allows maximum exposure attacks (MEX) where the attacker is allowed to either reveal the secret session state or the long-term secret of all communication partners. Moreover, our protocol features the strong and realistic notion of (full) perfect forward secrecy (PFS), that allows the attacker to actively modify...

We put forth Oblivious State Preparation (OSP) as a cryptographic primitive that unifies techniques developed in the context of a quantum server interacting with a classical client. OSP allows a classical polynomial-time sender to input a choice of one out of two public observables, and a quantum polynomial-time receiver to recover an eigenstate of the corresponding observable -- while keeping the sender's choice hidden from any malicious receiver. We obtain the following results: - The...

In this paper we introduce the notion of encrypted RAM delegation. In an encrypted RAM delegation scheme, the prover creates a succinct proof for a group of two input strings $x_\mathsf{pb}$ and $x_\mathsf{pr}$, where $x_\mathsf{pb}$ corresponds to a large \emph{public} input and $x_\mathsf{pr}$ is a \emph{private} input. A verifier can check correctness of computation of $\mathcal{M}$ on $(x_\mathsf{pb}, x_\mathsf{pr})$, given only the proof $\pi$ and $x_\mathsf{pb}$. We design encrypted...

Discrete Gaussian sampling on lattices is a fundamental problem in lattice-based cryptography. In this paper, we revisit the Markov chain Monte Carlo (MCMC)-based Metropolis-Hastings-Klein (MHK) algorithm proposed by Wang and Ling and study its complexity under the Geometric Series Assuption (GSA) when the given basis is BKZ-reduced. We give experimental evidence that the GSA is accurate in this context, and we give a very simple approximate formula for the complexity of the sampler that is...

A Timed Commitment (TC) with time parameter $t$ is hiding for time at most $t$, that is, commitments can be force-opened by any third party within time $t$. In addition to various cryptographic assumptions, the security of all known TC schemes relies on the sequentiality assumption of repeated squarings in hidden-order groups. The repeated squaring assumption is therefore a security bottleneck. In this work, we give a black-box construction of TCs from any time-lock puzzle (TLP) by...

We present a key-policy attribute-based encryption (ABE) scheme for circuits based on the Learning With Errors (LWE) assumption whose key size is independent of the circuit depth. Our result constitutes the first improvement for ABE for circuits from LWE in almost a decade, given by Gorbunov, Vaikuntanathan, and Wee (STOC 2013) and Boneh, et al. (EUROCRYPT 2014) -- we reduce the key size in the latter from $\mathsf{poly}(\mbox{depth},\lambda)$ to $\mathsf{poly}(\lambda)$. The starting point...

We present a new compact and tightly secure (anonymous) identity-based encryption (IBE) scheme based on structured lattices. This is the first IBE scheme that is (asymptotically) as compact as the most practical NTRU-based schemes and tightly secure under the module learning with errors (MLWE) assumption, known as the standard lattice assumption, in the (quantum) random oracle model. In particular, our IBE scheme is the most compact lattice-based scheme (except for NTRU-based schemes). We...

We introduce the notion of pseudorandom obfuscation, a way to obfuscate (keyed) pseudorandom functions $f_K$ in an average-case sense. We study several variants of pseudorandom obfuscation and show a number of applications. 1. Applications in the iO World: Our weakest variant of pseudorandom obfuscation, named obfuscation for identical pseudorandom functions (iPRO), is weaker than indistinguishability obfuscation (iO): rather than obfuscating arbitrary circuits as in iO, iPRO only...

We construct the first multi-input functional encryption (MIFE) and indistinguishability obfuscation (iO) schemes for pseudorandom functionalities, where the output of the functionality is pseudorandom for every input seen by the adversary. Our MIFE scheme relies on LWE and evasive LWE (Wee, Eurocrypt 2022 and Tsabary, Crypto 2022) for constant arity functions, and a strengthening of evasive LWE for polynomial arity. Thus, we obtain the first MIFE and iO schemes for a nontrivial...

We provide the first construction of compact Functional Encryption (FE) for pseudorandom functionalities from the evasive LWE and LWE assumptions. Intuitively, a pseudorandom functionality means that the output of the circuit is indistinguishable from uniform for every input seen by the adversary. This yields the first compact FE for a nontrivial class of functions which does not rely on pairings. We demonstrate the power of our new tool by using it to achieve optimal parameters for both...

We give the first construction of a rate-1 statistical non-interactive zero-knowledge argument of knowledge. For the $\mathsf{circuitSAT}$ language, our construction achieves a proof length of $|w| + |w|^\epsilon \cdot \mathsf{poly}(\lambda)$ where $w$ denotes the witness, $\lambda$ is the security parameter, $\epsilon$ is a small constant less than 1, and $\mathsf{poly}(\cdot)$ is a fixed polynomial that is independent of the instance or the witness size. The soundness of our construction...

The Shortest Vector Problem (SVP) is a cornerstone of lattice-based cryptography, underpinning the security of numerous cryptographic schemes like NTRU. Given its NP-hardness, efficient solutions to SVP have profound implications for both cryptography and computational complexity theory. This paper presents an innovative framework that integrates concepts from quantum gravity, noncommutative geometry, spectral theory, and post-supersymmetry (post-SUSY) particle physics to address SVP. By...

This work conducts a comprehensive investigation on determining the entropic hardness of (R/M)LWR under polynomial modulus. Particularly, we establish the hardness of (M)LWR for general entropic secret distributions from (Module) LWE assumptions based on a new conceptually simple framework called rounding lossiness. By combining this hardness result and a trapdoor inversion algorithm with asymptotically the most compact parameters, we obtain a compact lossy trapdoor function (LTF) with...

We give a new approach for constructing statistical ZAP arguments (a two-message public-coin statistically witness indistinguishable argument) from quasi-polynomial hardness of the learning with errors (LWE) assumption with a polynomial modulus-to-noise ratio. Previously, all ZAP arguments from lattice-based assumptions relied on correlation-intractable hash functions. In this work, we present the first construction of a ZAP from LWE via the classic hidden-bits paradigm. Our construction...

Cryptographic group actions are a leading contender for post-quantum cryptography, and have also been used in the development of quantum cryptographic protocols. In this work, we explore quantum group actions, which consist of a group acting on a set of quantum states. We show the following results: 1. In certain settings, statistical (even query bounded) security is impossible, analogously to post-quantum classical group actions. 2. We construct quantum state group actions and prove that...

Much work has been done recently on developing password-authenticated key exchange (PAKE) mechanisms with post-quantum security. However, modern guidance recommends the use of hybrid schemes—schemes which rely on the combined hardness of a post-quantum assumption, e.g., learning with Errors (LWE), and a more traditional assumption, e.g., decisional Diffie-Hellman. To date, there is no known hybrid PAKE construction, let alone a general method for achieving such. In this paper, we present...

In Noncommutative Ring Learning With Errors From Cyclic Algebras, a variant of Learning with Errors from cyclic division algebras, dubbed ‘Cyclic LWE', was developed, and security reductions similar to those known for the ring and module case were given, as well as a Regev-style encryption scheme. In this work, we make a number of improvements to that work: namely, we describe methods to increase the number of cryptographically useful division algebras, demonstrate the hardness of CLWE from...

Certified deletion, an inherently quantum capability, allows a party holding a quantum state to prove that they have deleted the information contained in that state. Bartusek and Raizes (Crypto 2024) recently studied certified deletion in the context of secret sharing schemes, and showed constructions with privately verifiable proofs of deletion that can be verified only by the dealer who generated the shares. We give two constructions of secret sharing schemes with publicly verifiable...

The MPC-in-the-Head framework has been pro- posed as a solution for Non-Interactive Zero-Knowledge Arguments of Knowledge (NIZKAoK) due to its efficient proof generation. However, most existing NIZKAoK constructions using this approach require multiple MPC evaluations to achieve negligible soundness error, resulting in proof size and time that are asymptotically at least λ times the size of the circuit of the NP relation. In this paper, we propose a novel method to eliminate the need for...

In this work, we introduce the sparse LWE assumption, an assumption that draws inspiration from both Learning with Errors (Regev JACM 10) and Sparse Learning Parity with Noise (Alekhnovich FOCS 02). Exactly like LWE, this assumption posits indistinguishability of $(\mathbf{A}, \mathbf{s}\mathbf{A}+\mathbf{e} \mod p)$ from $(\mathbf{A}, \mathbf{u})$ for a random $\mathbf{u}$ where the secret $\mathbf{s}$, and the error vector $\mathbf{e}$ is generated exactly as in LWE. However, the...

As an emerging primitive, Registered Functional Encryption (RFE) eliminates the key-escrow issue that threatens numerous works for functional encryption, by replacing the trusted authority with a transparent key curator and allowing each user to sample their decryption keys locally. In this work, we present a new black-box approach to construct RFE for all polynomial-sized circuits. It considers adaptive simulation-based security in the bounded collusion model (Gorbunov et al. - CRYPTO'12),...

Secure key leasing (a.k.a. key-revocable cryptography) enables us to lease a cryptographic key as a quantum state in such a way that the key can be later revoked in a verifiable manner. We propose a simple framework for constructing cryptographic primitives with secure key leasing via the certified deletion property of BB84 states. Based on our framework, we obtain the following schemes. - A public key encryption scheme with secure key leasing that has classical revocation based on any...

In this work we construct fully succinct arguments of knowledge for computations over the infinite ring $\mathbb{Z}$. We are motivated both by their practical applications—e.g. verifying cryptographic primitives based on RSA groups or Ring-LWE; field emulation and field "switching"; arbitrary precision-arithmetic—and by theoretical questions of techniques for constructing arguments over the integers in general. Unlike prior works constructing arguments for $\mathbb{Z}$ or...

To date, the strongest notions of security achievable for two-round publicly-verifiable cryptographic proofs for $\mathsf{NP}$ are witness indistinguishability (Dwork-Naor 2000, Groth-Ostrovsky-Sahai 2006), witness hiding (Bitansky-Khurana-Paneth 2019, Kuykendall-Zhandry 2020), and super-polynomial simulation (Pass 2003, Khurana-Sahai 2017). On the other hand, zero-knowledge and even weak zero-knowledge (Dwork-Naor-Reingold-Stockmeyer 1999) are impossible in the two-round publicly-verifiable...

We present a new approach for constructing non-interactive zero-knowledge (NIZK) proof systems from vector trapdoor hashing (VTDH) -- a generalization of trapdoor hashing [Döttling et al., Crypto'19]. Unlike prior applications of trapdoor hash to NIZKs, we use VTDH to realize the hidden bits model [Feige-Lapidot-Shamir, FOCS'90] leading to black-box constructions of NIZKs. This approach gives us the following new results: - A statistically-sound NIZK proof system based on the hardness of...

We introduce new lattice-based techniques for building ABE for circuits with unbounded attribute length based on the LWE assumption, improving upon the previous constructions of Brakerski and Vaikuntanathan (CRYPTO 16) and Goyal, Koppula, and Waters (TCC 16). Our main result is a simple and more efficient unbounded ABE scheme for circuits where only the circuit depth is fixed at set-up; this is the first unbounded ABE scheme for circuits that rely only on black-box access to cryptographic...

Multi-key fully homomorphic encryption (MKFHE), a generalization of fully homomorphic encryption (FHE), enables a computation over encrypted data under multiple keys. The first MKFHE schemes were based on the NTRU primitive, however these early NTRU based FHE schemes were found to be insecure due to the problem of over-stretched parameters. Recently, in the case of standard (non-multi key) FHE a secure version, called FINAL, of NTRU has been found. In this work we extend FINAL to an...

Attribute-based encryption (ABE) enables fine-grained control over which ciphertexts various users can decrypt. A master authority can create secret keys $sk_f$ with different functions (circuits) $f$ for different users. Anybody can encrypt a message under some attribute $x$ so that only recipients with a key $sk_f$ for a function such that $f(x)=1$ will be able to decrypt. There are a number of different approaches toward achieving selectively secure ABE, where the adversary has to decide...

A broadcast encryption scheme allows a user to encrypt a message to $N$ recipients with a ciphertext whose size scales sublinearly with $N$. While broadcast encryption enables succinct encrypted broadcasts, it also introduces a strong trust assumption and a single point of failure; namely, there is a central authority who generates the decryption keys for all users in the system. Distributed broadcast encryption offers an appealing alternative where there is a one-time (trusted) setup...

We present new lattice-based attribute-based encryption (ABE) and laconic function evaluation (LFE) schemes for circuits with *sublinear* ciphertext overhead. For depth $d$ circuits over $\ell$-bit inputs, we obtain * an ABE with ciphertext and secret key size $O(1)$; * a LFE with ciphertext size $\ell + O(1)$ and digest size $O(1)$; * an ABE with public key and ciphertext size $O(\ell^{2/3})$ and secret key size $O(1)$, where $O(\cdot)$ hides $\mbox{poly}(d,\lambda)$...

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...

With the rapid advance in quantum computing, quantum security is now an indispensable property for any cryptographic system. In this paper, we study how to prove the security of a complex cryptographic system in the quantum random oracle model. We first give a variant of Zhandry's compressed quantum random oracle (${\bf CStO}$), called compressed quantum random oracle with adaptive special points ({\bf CStO}$_s$). Then, we extend the on-line extraction technique of Don et al...

We present Scloud+, an LWE-based key encapsulation mechanism (KEM). The key feature of Scloud+ is its use of the unstructured-LWE problem (i.e., without algebraic structures such as rings or modules) and its incorporation of ternary secrets and lattice coding to enhance performance. A notable advantage of the unstructured-LWE problem is its resistance to potential attacks exploiting algebraic structures, making it a conservative choice for constructing high-security schemes. However, a...

The recent works of Ananth et al. (ITCS 2022) and Bartusek et al. (Eurocrypt 2023) initiated the study of pre-constrained cryptography which achieves meaningful security even against the system authority. In this work we significantly expand this area by defining several new primitives and providing constructions from simple, standard assumptions as follows. - Pre-Constrained Encryption. We define a weaker notion of pre-constrained encryption (PCE), as compared to the work of Ananth et...

With the potential arrival of quantum computers, it is essential to build cryptosystems resistant to attackers with the computing power of a quantum computer. With Shor's algorithm, cryptosystems based on discrete logarithms and factorization become obsolete. Reason why NIST has launching two competitions in 2016 and 2023 to standardize post-quantum cryptosystems (such as KEM and signature ) based on problems supposed to resist attacks using quantum computers. EagleSign was prosed to NIT...

Lattice cryptography schemes based on the learning with errors (LWE) hardness assumption have been standardized by NIST for use as post-quantum cryptosystems, and by HomomorphicEncryption.org for encrypted compute on sensitive data. Thus, understanding their concrete security is critical. Most work on LWE security focuses on theoretical estimates of attack performance, which is important but may overlook attack nuances arising in real-world implementations. The sole existing concrete...

Lattice-based cryptography is in the process of being standardized. Several proposals to deal with side-channel information using lattice reduction exist. However, it has been shown that algorithms based on Bayesian updating are often more favorable in practice. In this work, we define distribution hints; a type of hint that allows modelling probabilistic information. These hints generalize most previously defined hints and the information obtained in several attacks. We define two...

Lattice cryptography is currently a major research focus in public-key encryption, renowned for its ability to resist quantum attacks. The introduction of ideal lattices (ring lattices) has elevated the theoretical framework of lattice cryptography. Ideal lattice cryptography, compared to classical lattice cryptography, achieves more acceptable operational efficiency through fast Fourier transforms. However, to date, issues of impracticality or insecurity persist in ideal lattice problems....

Resource-constrained devices such as wireless sensors and Internet of Things (IoT) devices have become ubiquitous in our digital ecosystem. These devices generate and handle a major part of our digital data. However, due to the impending threat of quantum computers on our existing public-key cryptographic schemes and the limited resources available on IoT devices, it is important to design lightweight post-quantum cryptographic (PQC) schemes suitable for these devices. In this work, we...

Servan-Schreiber et al. (S&P 2023) presented a new notion called private access control lists (PACL) for function secret sharing (FSS), where the FSS evaluators can ensure that the FSS dealer is authorized to share the given function. Their construction relies on costly non-interactive secret-shared proofs and is not secure in post-quantum setting. We give a construction of PACL from publicly verifiable secret sharing (PVSS) under short integer solution (SIS). Our construction adapts the...

Attribute-based signatures (ABS) allow users to simultaneously sign messages and prove their possession of some attributes while hiding the attributes and revealing only the fact that they satisfy a public policy. In this paper, we propose a generic construction of ABS for circuits of unbounded depth and size, with optimal parameter size—meaning the lengths of public parameters, keys, and signatures are all constant. Our construction can be instantiated from various standard assumptions,...

A threshold signature scheme splits the signing key among $\ell$ parties, such that any $t$-subset of parties can jointly generate signatures on a given message. Designing concretely efficient post-quantum threshold signatures is a pressing question, as evidenced by NIST's recent call. In this work, we propose, implement, and evaluate a lattice-based threshold signature scheme, Ringtail, which is the first to achieve a combination of desirable properties: (i) The signing...