Key derivation functions can be used to derive variable-length random strings that serve as cryptographic keys. They are integral to many widely-used communication protocols such as TLS, IPsec and Signal. NIST SP 800-108 specifies several key derivation functions based on pseudorandom functions such as \mode{CMAC} and \mode{HMAC}, that can be used to derive additional keys from an existing cryptographic key. This standard either explicitly or implicitly requests their KDFs to be variable...

We put forth a new paradigm for practical secure multiparty computation (MPC) in the preprocessing model, where a feasible one-time setup can enable a lifetime of efficient online secure computations. Our protocols match the security guarantees and low costs of the cheapest category of MPC solutions, namely 3-party protocols (3PC) secure against a single malicious party, with the qualitative advantages that one party communicates data sublinear in the circuit size, and can go offline after...

We were deeply impressed by the paper by Ateniese et al., published in Crypto 2019. In it, they presented a black-box construction of matchmaking encryption (ME) based on functional encryption. In our work, we propose an ME scheme based on standard assumptions in the standard model. This scheme has been proven to be secure under the learning with error (LWE) assumption. Our ME scheme is achieved through a novel framework of bilateral-policy attribute-based encryption (BP-ABE) and a new...

Abstract—Anonymous token schemes are cryptographic protocols for limiting the access to online resources to credible users. The resource provider issues a set of access tokens to the credible user that they can later redeem anonymously, i.e., without the provider being able to link their redemptions. When combined with credibility tests such as CAPTCHAs, anonymous token schemes can significantly increase user experience and provider security, without exposing user access patterns to...

Weyman and Zelevinsky generalised Vandermonde matrices to higher dimensions, which we call Vandermonde-Weyman-Zelevinsky tensors. We generalise Lagrange interpolation to higher dimensions by devising a nearly linear time algorithm that given a Vandermonde-Weyman-Zelevinsky tensor and a sparse target vector, finds a tuple of vectors that hit the target under tensor evaluation. Tensor evaluation to us means evaluating the usual multilinear form associated with the tensor in all but one...

Abstract The Singularity Random Number Generator (SRNG) represents a groundbreaking advancement in the generation of random numbers by integrating two key properties - computational irreducibility and seed independence - into a deterministic algorithm. Unlike conventional pseudorandom number generators (PRNGs) whose randomness is intrinsically linked to seed quality or chaotic sensitivity, SRNG transforms even low-entropy seeds into complex, unpredictable outputs. SRNG demonstrates...

In 2012, the Tor project expressed the need to upgrade Tor's onion encryption scheme to protect against tagging attacks and thereby strengthen its end-to-end integrity protection. Tor proposal 261, where each encryption layer is processed by a strongly secure, yet relatively expensive tweakable wide-block cipher, is the only concrete candidate replacement to be backed by formal, yet partial, security proofs (Degabriele and Stam, EUROCRYPT 2018, and Rogaway and Zhang, PoPETS 2018). We...

Yao's garbled circuits have received huge attention in both theory and practice. While garbled circuits can be constructed using minimal assumption (i.e., the existence of pseudorandom functions or one-way functions), the state-of-the-art constructions (e.g., Rosulek-Roy, Crypto 2021) are based on stronger assumptions. In particular, the ``Free-XOR'' technique (Kolesnikov-Schneider, ICALP 2008) is essential in these state-of-the-art constructions, and their security can only be proven in the...

The GCM authenticated encryption (AE) scheme is one of the most widely used AE schemes in the world, while it suffers from risk of nonce misuse, short message length per encryption and an insufficient level of security. The goal of this paper is to design new AE schemes achieving stronger provable security in the standard model and accepting longer nonces (or providing nonce misuse resistance), with the design rationale behind GCM. As a result, we propose two enhanced variants of GCM and...

Group actions have emerged as a powerful framework in post-quantum cryptography, serving as the foundation for various cryptographic primitives. The Lattice Isomorphism Problem (LIP) has recently gained attention as a promising hardness assumption for designing quantum-resistant protocols. Its formulation as a group action has opened the door to new cryptographic applications, including a commitment scheme and a linkable ring signature. In this work, we analyze the security properties of...

Due to their simple security assessments, permutation-based pseudo-random functions (PRFs) have become widely used in cryptography. It has been shown that PRFs using a single $n$-bit permutation achieve $n/2$ bits of security, while those using two permutation calls provide $2n/3$ bits of security in the classical setting. This paper studies the security of permutation-based PRFs within the Q1 model, where attackers are restricted to classical queries and offline quantum computations. We...

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...

In this paper, we propose a new 10-bit S-box generated from a Feistel construction. The subpermutations are generated by a 5-cell cellular automaton based on a unique well-chosen rule and bijective affine transformations. In particular, the cellular automaton rule is chosen based on empirical tests of its ability to generate good pseudorandom output on a ring cellular automaton. Similarly, Feistel's network layout is based on empirical data regarding the quality of the output S-box. We...

In this paper, we propose a new type of non-interactive zero-knowledge (NIZK), called Fine-grained Verifier NIZK (FV-NIZK), which provides more flexible and more fine-grained verifiability of proofs than standard NIZK that supports public verifiability and designated-verifier NIZK (DV-NIZK) that supports private verifiability. FV-NIZK has two statistically (or computationally) equivalent verification approaches: --- a master verification using the master secret key $msk$; --- a...

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...

Authenticated encryption (AE) provides both authenticity and privacy. Starting with Bellare's and Namprempre's work in 2000, the Encrypt-then-MAC composition of an encryption scheme for privacy and a MAC for authenticity has become a well-studied and common approach. This work investigates the security of the Encrypt-then-MAC composition in a quantum setting which means that adversarial queries as well as the responses to those queries may be in superposition. We demonstrate that the...

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...

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...

Existing secret management techniques demand users memorize complex passwords, store convoluted recovery phrases, or place their trust in a specific service or hardware provider. We have designed a novel protocol that combines existing cryptographic techniques to eliminate these complications and reduce user complexity to recalling a short PIN. Our protocol specifically focuses on a distributed approach to secret storage that leverages Oblivious Pseudorandom Functions (OPRFs) and a...

Oblivious pseudorandom functions (OPRFs) are an important primitive in privacy-preserving cryptographic protocols. The growing interest in OPRFs, both in theory and practice, has led to the development of numerous constructions and variations. However, most of these constructions rely on classical assumptions. Potential future quantum attacks may limit the practicality of those OPRFs for real-world applications. To close this gap, we introduce Leap, a novel OPRF based on heuristic...

Randomized functional encryption (rFE) generalizes functional encryption (FE) by incorporating randomized functionalities. Randomized multi-input functional encryption (rMIFE) extends rFE to accommodate multi-input randomized functionalities. In this paper, we reassess the framework of rFE/rMIFE enhancing our understanding of this primitive and laying the groundwork for more secure and flexible constructions in this field. Specifically, we make three key contributions: - New...

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...

Syndrome decoding (SD), and equivalently Learning Parity with Noise (LPN), is a fundamental problem in cryptography, which states that for a field $\mathbb{F}$, some compressing public matrix $\mathbf{G} \in \mathbb{F}^{k\times n}$, and a secret sparse vector $\mathbf{e} \in\mathbb{F}^{n}$ sampled from some noise distribution, $\mathbf{G}\mathbf{e}$ is indistinguishable from uniform. Recently, the SD has gained significant interest due to its use in pseudorandom correlation generators...

We investigate two natural relaxations of quantum cryptographic assumptions. First, we examine primitives such as pseudorandom generators (${PRG}$s) and pseudorandom states (${PRS}$s), extended with quantum input sampling, which we term ${PRG}^{qs}$ and ${PRS}^{qs}$. In these primitives, the input is sampled via a quantum algorithm rather than uniformly at random. The second relaxation, $\bot$-pseudodeterminism, allows the generator to output $\bot$ on an inverse-polynomial fraction of...

Secure computation enables mutually distrusting parties to jointly compute a function on their secret inputs, while revealing nothing beyond the function output. A long-running challenge is understanding the required communication complexity of such protocols – in particular, when communication can be sublinear in the circuit representation size of the desired function. While several techniques have demonstrated the viability of sublinear secure computation in the two-party setting, known...

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...

Publicly identifiable abort is a critical feature for ensuring accountability in outsourced computations using secure multiparty computation (MPC). Despite its importance, no prior work has specifically addressed identifiable abort in the context of outsourced computations. In this paper, we present the first MPC protocol that supports publicly identifiable abort with minimal overhead for external clients. Our approach minimizes client-side computation by requiring only a few pseudorandom...

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...

A privately constrained pseudorandom function (pCPRF) is a PRF with the additional property that one can derive a constrained key that allows evaluating the PRF only on inputs satisfying a constraint predicate $C$, without revealing $C$ itself or leaking information about the PRF’s output on inputs that do not satisfy the constraint. Existing privately constrained PRFs face significant limitations: either (1) they rely on assumptions known to imply fully-homomorphic encryption or...

Lund et al. (JACM 1992) invented the powerful Sumcheck protocol that has been extensively used in complexity theory and in designing concretely efficient (zero-knowledge) arguments. In this work, we systematically study Sumcheck in the context of secure multi-party computation (MPC). Our main result is a new generic framework for lifting semi-honest MPC protocols to maliciously secure ones, with a {\em constant} multiplicative overhead in {\em both} computation and communication, and in the...

Correlated randomness lies at the core of efficient modern secure multi-party computation (MPC) protocols. Costs of generating such correlated randomness required for the MPC online phase protocol often constitute a bottleneck in the overall protocol. A recent paradigm of {\em pseudorandom correlation generator} (PCG) initiated by Boyle et al. (CCS'18, Crypto'19) offers an appealing solution to this issue. In sketch, each party is given a short PCG seed, which can be locally expanded into...

We propose the first $\textit{distributed}$ version of a simple, efficient, and provably quantum-safe pseudorandom function (PRF). The distributed PRF (DPRF) supports arbitrary threshold access structures based on the hardness of the well-studied Learning with Rounding (LWR) problem. Our construction (abbreviated as $\mathsf{PQDPRF}$) practically outperforms not only existing constructions of DPRF based on lattice-based assumptions, but also outperforms (in terms of evaluation time) existing...

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...

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.,...

Homomorphic secret sharing (HSS) is a distributed analogue of fully homomorphic encryption (FHE) where following an input-sharing phase, two or more parties can locally compute a function over their private inputs to obtain shares of the function output. Over the last decade, HSS schemes have been constructed from an array of different assumptions. However, all existing HSS schemes, except ones based on assumptions known to imply multi-key FHE, require a public-key infrastructure (PKI) or...

In recent development of secure multi-party computation (MPC), pseudorandom correlations of subfield vector oblivious linear evaluation (sVOLE) type become popular due to their amazing applicability in multi-dimensional MPC protocols such as privacy-preserving biometric identification and privacy-preserving machine learning protocols. In this paper, we introduce a novel way of VOLE distribution in three-party and four-party honest majority settings with the aid of a trusted server. This new...

A universal thresholdizer (UT), constructed from a threshold fully homomorphic encryption by Boneh et. al , Crypto 2018, is a general framework for universally thresholdizing many cryptographic schemes. However, their framework is insufficient to construct strongly secure threshold schemes, such as threshold signatures and threshold public-key encryption, etc. In this paper, we strengthen the security definition for a universal thresholdizer and propose a scheme which satisfies our...

Homomorphic message authentication codes (HMACs) allow users to authenticate data using a shared secret key, while supporting computation over authenticated data. Given data $(m_1, \ldots, m_n)$ and their tags $(\sigma_1, \ldots, \sigma_n)$, anyone can evaluate a circuit $C$ on the data and tags to produce a succinct tag authenticating the output $C(m_1, \ldots, m_n)$. Importantly, tags remain succinc -- of size polynomial in the security parameter $\lambda$ -- regardless of the size of $C$....

Authentication often bridges real-world individuals and their virtual public identities, like usernames, user IDs and e-mails, exposing vulnerabilities that threaten user privacy. This research introduces COCO (Coconuts and Oblivious Computations for Orthogonal Authentication), a framework that segregates roles among Verifiers, Authenticators, and Clients to achieve privacy-preserving authentication. COCO eliminates the need for Authenticators to directly access virtual public identifiers...

The growing adoption of secure multi-party computation (MPC) has driven the development of efficient symmetric key primitives tailored for MPC. Recent advancements, such as the alternating moduli paradigm, have shown promise but leave room for cryptographic and practical improvements. In this paper, we analyze a family of weak pseudorandom functions (wPRF) proposed at Crypto 2024, focusing on the One-to-One parameter sets. We demonstrate that these configurations fail to achieve their...

In PKC'24, de Saint Guilhem and Pedersen give a pseudorandom function basing on a relaxed group action assumption in the semi-honest setting. Basing on the assumption, they build an oblivious pseudorandom function (OPRF). Later, a recent paper by Levin and Pedersen uses the same function to build a verifiable random function (VRF), using the same assumption. We give a structural attack on this problem by reducing it to a few group action inverse problems (GAIP/DLog) over small subgroups....

Oblivious pseudorandom function (OPRF) is a two-party cryptographic protocol that allows the receiver to input $x$ and learn $F(x)$ for some PRF $F$, only known to the sender. For private set intersection (PSI) applications, OPRF protocols have evolved to enhance efficiency, primarily using symmetric key cryptography. Current state-of-the-art protocols, such as those by Rindal and Schoppmann (Eurocrypt '21), leverage vector oblivious linear evaluation (VOLE) and oblivious key-value store...

We present an efficient and simple multi-party private set intersection cardinality (PSI-CA) protocol that allows several parties to learn the intersection size of their private sets without revealing any other information. Our protocol is highly efficient because it only utilizes the Oblivious Key-Value Store and zero-sharing techniques, without incorporating components such as OPPRF (Oblivious Programmable Pseudorandom Function) which is the main building block of multi-party PSI-CA...

Private Set Intersection (PSI) is a cryptographic primitive that allows two parties to obtain the intersection of their private input sets while revealing nothing more than the intersection. PSI and its numerous variants, which compute on the intersection of items and their associated weights, have been widely studied. In this paper, we revisit the problem of finding the best item in the intersection according to weight sum introduced by Beauregard et al. (SCN '22), which is a special...

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...

We propose plausible post-quantum (PQ) oblivious pseudorandom functions (OPRFs) based on the Power-Residue PRF (Damgård CRYPTO’88), a generalization of the Legendre PRF. For security parameter $\lambda$, we consider the PRF $\mathsf{Gold}_k(x)$ that maps an integer $x$ modulo a public prime $p = 2^\lambda\cdot g + 1$ to the element $(k + x)^g \bmod p$, where $g$ is public and $\log g \approx 2\lambda$. At the core of our constructions are efficient novel methods for evaluating...

A group signatures allows a user to sign a message anonymously on behalf of a group and provides accountability by using an opening authority who can ``open'' a signature and reveal the signer's identity. Group signatures have been widely used in privacy-preserving applications including anonymous attestation and anonymous authentication. Fully dynamic group signatures allow new members to join the group and existing members to be revoked if needed. Symmetric-key based group signature...

One-time programs (Goldwasser, Kalai and Rothblum, CRYPTO 2008) are functions that can be run on any single input of a user's choice, but not on a second input. Classically, they are unachievable without trusted hardware, but the destructive nature of quantum measurements seems to provide a quantum path to constructing them. Unfortunately, Broadbent, Gutoski and Stebila showed that even with quantum techniques, a strong notion of one-time programs, similar to ideal obfuscation, cannot be...

Probabilistic data structures (PDS) are compact representations of high-volume data that provide approximate answers to queries about the data. They are commonplace in today's computing systems, finding use in databases, networking and more. While PDS are designed to perform well under benign inputs, they are frequently used in applications where inputs may be adversarially chosen. This may lead to a violation of their expected behaviour, for example an increase in false positive rate. In...

This paper partly solves the open problem of tight trade-off of client storage and server time in the client preprocessing setting of private information retrieval (PIR). In the client preprocessing setting of PIR, the client is allowed to store some hints generated from the database in a preprocessing phase and use the hints to assist online queries. We construct a new single-server client preprocessing PIR scheme. For a database with $n$ entries of size $w$, our protocol uses $S=O((n/T)...

Pseudorandom codes are error-correcting codes with the property that no efficient adversary can distinguish encodings from uniformly random strings. They were recently introduced by Christ and Gunn [CRYPTO 2024] for the purpose of watermarking the outputs of randomized algorithms, such as generative AI models. Several constructions of pseudorandom codes have since been proposed, but none of them are robust to error channels that depend on previously seen codewords. This stronger kind of...

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: -...

Recent active studies have demonstrated that cryptography without one-way functions (OWFs) could be possible in the quantum world. Many fundamental primitives that are natural quantum analogs of OWFs or pseudorandom generators (PRGs) have been introduced, and their mutual relations and applications have been studied. Among them, pseudorandom function-like state generators (PRFSGs) [Ananth, Qian, and Yuen, Crypto 2022] are one of the most important primitives. PRFSGs are a natural quantum...

In this paper, we investigate whether the privacy mechanism of periodically changing the pseudorandom identities of Bluetooth Low Energy (BLE) beacons is sufficient to ensure privacy. We consider a new natural privacy notion for BLE broadcasting beacons which we call ``Timed-sequence- indistinguishability'' of beacons. This new privacy definition is stronger than the well-known indistinguishability, since it considers not just the advertisements' content, but also the advertisements'...

Ensuring fairness in blockchain-based data trading presents significant challenges, as the transparency of blockchain can expose sensitive details and compromise fairness. Fairness ensures that the seller receives payment only if they provide the correct data, and the buyer gains access to the data only after making the payment. Existing approaches face limitations in efficiency particularly when applied to large-scale data. Moreover, preserving privacy has also been a significant challenge...

We study the (in)feasibility of quantum pseudorandom notions in a quantum analog of the random oracle model, where all the parties, including the adversary, have oracle access to the same Haar random unitary. In this model, we show the following: • (Unbounded-query secure) pseudorandom unitaries (PRU) exist. Moreover, the PRU construction makes two calls to the Haar oracle. • We consider constructions of PRUs making a single call to the Haar oracle. In this setting, we show that...

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...

This is a survey on the One Time Pad (OTP) and its derivatives, from its origins to modern times. OTP, if used correctly, is (the only) cryptographic code that no computing power, present or future, can break. Naturally, the discussion shifts to the creation of long random sequences, starting from short ones, which can be easily shared. We could call it the Short Key Dream. Many problems inevitably arise, which affect many fields of computer science, mathematics and knowledge in general....

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 construct a quantum oracle relative to which $\mathbf{BQP}=\mathbf{QCMA}$ but quantum-computation-classical-communication (QCCC) key exchange, QCCC commitments, and two-round quantum key distribution exist. We also construct an oracle relative to which $\mathbf{BQP}=\mathbf{QMA}$, but quantum lightning (a stronger variant of quantum money) exists. This extends previous work by Kretschmer [Kretschmer, TQC22], which showed that there is a quantum oracle relative to which...

Fundamental principles of quantum mechanics have inspired many new research directions, particularly in quantum cryptography. One such principle is quantum no-cloning which has led to the emerging field of revocable cryptography. Roughly speaking, in a revocable cryptographic primitive, a cryptographic object (such as a ciphertext or program) is represented as a quantum state in such a way that surrendering it effectively translates into losing the capability to use this cryptographic...

Software watermarking allows for embedding a mark into a piece of code, such that any attempt to remove the mark will render the code useless. Provably secure watermarking schemes currently seems limited to programs computing various cryptographic operations, such as evaluating pseudorandom functions (PRFs), signing messages, or decrypting ciphertexts (the latter often going by the name ``traitor tracing''). Moreover, each of these watermarking schemes has an ad-hoc construction of its...

The existence of pseudorandom unitaries (PRUs)---efficient quantum circuits that are computationally indistinguishable from Haar-random unitaries---has been a central open question, with significant implications for cryptography, complexity theory, and fundamental physics. In this work, we close this question by proving that PRUs exist, assuming that any quantum-secure one-way function exists. We establish this result for both (1) the standard notion of PRUs, which are secure against any...

Quantum pseudorandomness has found applications in many areas of quantum information, ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum systems, and, more recently, in the foundations of quantum cryptography. Kretschmer (TQC '21) showed that both pseudorandom states and pseudorandom unitaries exist even in a world without classical one-way functions. To this day, however, all known constructions require classical cryptographic building blocks which are...

An involution is a permutation that is the inverse of itself. Involutions have attracted plenty attentions in cryptographic community due to their advantage regarding hardware implementations. In this paper, we reconsider constructing {\it pseudorandom involutions}. We demonstrate two constructions. First, the 4-round Feistel network {\it using the same random function (Feistel-SF) in every round} is a pseudorandom involution. This shows the Feistel-SF construction still provides...

Searchable encryption is a cryptographic primitive that allows us to perform searches on encrypted data. Searchable encryption schemes require that ciphertexts do not leak information about keywords. However, most of the existing schemes do not achieve the security notion that trapdoors do not leak information. Shen et al. (TCC 2009) proposed a security notion called full security, which includes both ciphertext privacy and trapdoor privacy, but there are few fully secure constructions. Full...

Oblivious Pseudorandom Functions (OPRFs) allow a client to evaluate a pseudorandom function (PRF) on her secret input based on a key that is held by a server. In the process, the client only learns the PRF output but not the key, while the server neither learns the input nor the output of the client. The arguably most popular OPRF is due to Naor, Pinkas and Reingold (Eurocrypt 2009). It is based on an Oblivious Exponentiation by the server, with passive security under the Decisional...

Multiple Matrix congruential generators is an important class of pseudorandom number generators. This paper studies the predictability of a class of truncated multiple matrix congruential generators with unknown parameters. Given a few truncated digits of high-order bits or low-order bits output by a multiple matrix congruential generator, we give a method based on lattice reduction to recover the parameters and the initial state of the generator.

We present the first undetectable watermarking scheme for generative image models. Undetectability ensures that no efficient adversary can distinguish between watermarked and un-watermarked images, even after making many adaptive queries. In particular, an undetectable watermark does not degrade image quality under any efficiently computable metric. Our scheme works by selecting the initial latents of a diffusion model using a pseudorandom error-correcting code (Christ and Gunn, 2024), a...

We introduce a powerful attack, termed the bit-fixing correlation attack, on Goldreich's pseudorandom generators (PRGs), specifically focusing on those based on the $\mathsf{XOR}\text{-}\mathsf{THR}$ predicate. By exploiting the bit-fixing correlation property, we derive correlation equations with high bias by fixing certain bits. Utilizing two solvers to handle these high-bias correlation equations, we present inverse attacks on $\mathsf{XOR}\text{-}\mathsf{THR}$ based PRGs within the...

In quantum cryptography, there could be a new world, Microcrypt, where cryptography is possible but one-way functions (OWFs) do not exist. Although many fundamental primitives and useful applications have been found in Microcrypt, they lack ``OWFs-free'' concrete hardness assumptions on which they are based. In classical cryptography, many hardness assumptions on concrete mathematical problems have been introduced, such as the discrete logarithm (DL) problems or the decisional...

In this paper, we construct the first asymptotically efficient two-round $n$-out-of-$n$ and multi-signature schemes from lattices in the quantum random oracle model (QROM), using the Fiat-Shamir with Aborts (FSwA) paradigm. Our protocols can be viewed as the QROM~variants of the two-round protocols by Damgård et al. (JoC 2022). A notable feature of our protocol, compared to other counterparts in the classical random oracle model, is that each party performs an independent abort and still...

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...

Peer-to-peer energy trading markets enable users to exchange electricity, directly offering them increased financial benefits. However, discrepancies often arise between the electricity volumes committed to in trading auctions and the volumes actually consumed or injected. Solutions designed to address this issue often require access to sensitive information that should be kept private. This paper presents a novel, fully privacy-preserving billing protocol designed to protect users'...

Tweakable enciphering modes (TEMs) provide security in a variety of storage and space-critical applications like disk and file-based encryption, and packet-based communication protocols, among others. XCB-AES (known as XCBv2) is specified in the IEEE 1619.2 standard for encryption of sector-oriented storage media and it comes with a proof of security for block-aligned input messages. In this work, we demonstrate the $\textit{first}$ and most efficient plaintext recovery attack on...

In classical cryptography, one-way functions (OWFs) are the minimal assumption, while recent active studies have demonstrated that OWFs are not necessarily the minimum assumption in quantum cryptography. Several new primitives have been introduced such as pseudorandom unitaries (PRUs), pseudorandom function-like state generators (PRFSGs), pseudorandom state generators (PRSGs), one-way state generators (OWSGs), one-way puzzles (OWPuzzs), and EFI pairs. They are believed to be weaker than...

The planted random subgraph detection conjecture of Abram et al. (TCC 2023) asserts the pseudorandomness of a pair of graphs $(H, G)$, where $G$ is an Erdos-Renyi random graph on $n$ vertices, and $H$ is a random induced subgraph of $G$ on $k$ vertices. Assuming the hardness of distinguishing these two distributions (with two leaked vertices), Abram et al. construct communication-efficient, computationally secure (1) 2-party private simultaneous messages (PSM) and (2) secret sharing for...

Private set intersection (PSI) is a type of private set operation (PSO) for which concretely efficient linear-complexity protocols do exist. However, the situation is currently less satisfactory for other relevant PSO problems such as private set union (PSU): For PSU, the most promising protocols either rely entirely on computationally expensive public-key operations or suffer from substantial communication overhead. In this work, we present the first PSU protocol that is mainly based on...

Proofs of partial knowledge, first considered by Cramer, Damgård and Schoenmakers (CRYPTO'94) and De Santis et al. (FOCS'94), allow for proving the validity of $k$ out of $n$ different statements without revealing which ones those are. In this work, we present a new approach for transforming certain proofs system into new ones that allows for proving partial knowledge. The communication complexity of the resulting proof system only depends logarithmically on the total number of statements...

Quantum pseudorandom state generators (PRSGs) have stimulated exciting developments in recent years. A PRSG, on a fixed initial (e.g., all-zero) state, produces an output state that is computationally indistinguishable from a Haar random state. However, pseudorandomness of the output state is not guaranteed on other initial states. In fact, known PRSG constructions provably fail on some initial states. In this work, we propose and construct quantum Pseudorandom State Scramblers (PRSSs),...

We revisit the lattice-based verifiable oblivious PRF construction from PKC'21 and remove or mitigate its central three sources of inefficiency. First, applying Rényi divergence arguments, we eliminate one superpolynomial factor from the ciphertext modulus \(q\), allowing us to reduce the overall bandwidth consumed by RLWE samples by about a factor of four. This necessitates us introducing intermediate unpredictability notions to argue PRF security of the final output in the Random Oracle...

The Feistel construction is a fundamental technique for building pseudorandom permutations and block ciphers. This paper shows that a simple adaptation of the construction is resistant, even to algorithm substitution attacks---that is, adversarial subversion---of the component round functions. Specifically, we establish that a Feistel-based construction with more than $337n/\log(1/\epsilon)$ rounds can transform a subverted random function---which disagrees with the original one at a small...

We revisit the notion of threshold Password-Authenticated Key Exchange (tPAKE), and we extend it to augmented tPAKE (atPAKE), which protects password information even in the case all servers are compromised, except for allowing an (inevitable) offline dictionary attack. Compared to prior notions of tPAKE this is analogous to replacing symmetric PAKE, where the server stores the user's password, with an augmented (or asymmetric) PAKE, like OPAQUE [JKX18], where the server stores a password...

Introduced in [CG24], pseudorandom error-correcting codes (PRCs) are a new cryptographic primitive with applications in watermarking generative AI models. These are codes where a collection of polynomially many codewords is computationally indistinguishable from random, except to individuals with the decoding key. In this work, we examine the assumptions under which PRCs with robustness to a constant error rate exist. 1. We show that if both the planted hyperloop assumption...

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...

In this paper, we study the security definitions of various threshold symmetric primitives. Namely, we analyze the security definitions for threshold pseudorandom functions, threshold message authentication codes and threshold symmetric encryption. In each case, we strengthen the existing security definition, and we present a scheme that satisfies our stronger notion of security. In particular, we propose indifferentiability definition and IND-CCA2 definition for a threshold pseudorandom...

Privacy set intersection (PSI) and private information retrieval (PIR) are important areas of research in privacy protection technology. One of the key tools for both is the oblivious pseudorandom function (OPRF). Currently, existing oblivious pseudorandom functions either focus solely on efficiency without considering quantum attacks, or are too complex, resulting in low efficiency. The aim of this paper is to achieve a balance: to ensure that the oblivious pseudorandom function can...

For secure multi-party computation in the line of the secret-sharing based SPDZ protocol, actively secure multiplications consume correlated randomness in the form of authenticated Beaver triples, which need to be generated in advance. Although it is a well-studied problem, the generation of Beaver triples is still a bottleneck in practice. In the two-party setting, the best solution with low communication overhead is the protocol by Boyle et al. (Crypto 2020), which is derived from...

The Legendre sequence of an integer $x$ modulo a prime $p$ with respect to offsets $\vec a = (a_1, \dots, a_\ell)$ is the string of Legendre symbols $(\frac{x+a_1}{p}), \dots, (\frac{x+a_\ell}{p})$. Under the quadratic-residuosity assumption, we show that the function that maps the pair $(x,p)$ to the Legendre sequence of $x$ modulo $p$, with respect to public random offsets $\vec a$, is a pseudorandom generator. This answers an open question of Damgård (CRYPTO 1988), up to the choice of the...

This paper introduces the Koala PRF, which maps a variable-length sequence of $64$-bit input blocks to a single $257$-bit output block. Its design focuses on achieving low latency in its implementation in ASIC. To construct Koala, we instantiate the recently introduced Kirby construction with the Koala-P permutation and add an input encoding layer. The Koala-P permutation is obtained as the $8$-fold iteration of a simple round function inspired by that of Subterranean. Based on...

At EUROCRYPT'20, Bao et al. have shown that three-round cascading of $\textsf{LRW1}$ construction, which they dubbed as $\textsf{TNT}$, is a strong tweakable pseudorandom permutation that provably achieves $2n/3$-bit security bound. Jha et al. showed a birthday bound distinguishing attack on $\textsf{TNT}$ and invalidated the proven security bound and proved a tight birthday bound security on the $\textsf{TNT}$ construction in EUROCRYPT'24. In a recent work, Datta et al. have...

Matrix congruential generators is an important class of pseudorandom number generators. In this paper we show how to predict a class of Matrix congruential generators matrix congruential generators with unknown parameters. Given a few truncated digits of high-order bits output by a matrix congruential generator, we give a method based on lattice reduction to recover the parameters and the initial state of the generator.

Strike-lists are a common technique for rollback and replay prevention in protocols that require that clients remain anonymous or that their current position in a state machine remain confidential. Strike-lists are heavily used in anonymous credentials, e-cash schemes, and trusted execution environments, and are widely deployed on the web in the form of Privacy Pass (PoPETS '18) and Google Private State Tokens. In such protocols, clients submit pseudorandom tokens associated with each...

We address the black-box complexity of constructing pseudorandom functions (PRF) from pseudorandom generators (PRG). The celebrated GGM construction of Goldreich, Goldwasser, and Micali (Crypto 1984) provides such a construction, which (even when combined with Levin's domain-extension trick) has super-logarithmic depth. Despite many years and much effort, this remains essentially the best construction we have to date. On the negative side, one step is provided by the work of Miles and Viola...

Oblivious Transfer (OT) is at the heart of secure computation and is a foundation for many applications in cryptography. Over two decades of work have led to extremely efficient protocols for evaluating OT instances in the preprocessing model, through a paradigm called OT extension. A few OT instances generated in an offline phase can be used to perform many OTs in an online phase efficiently, i.e., with very low communication and computational overheads. Specifically, traditional OT...

Common random string model is a popular model in classical cryptography. We study a quantum analogue of this model called the common Haar state (CHS) model. In this model, every party participating in the cryptographic system receives many copies of one or more i.i.d Haar random states. We study feasibility and limitations of cryptographic primitives in this model and its variants: - We present a construction of pseudorandom function-like states with security against computationally...

An oblivious pseudorandom function (OPRF) is a two-party protocol in which a party holds an input and the other party holds the PRF key, such that the party having the input only learns the PRF output and the party having the key would not learn the input. Now, in a threshold oblivious pseudorandom function (TOPRF) protocol, a PRF key K is initially shared among T servers. A client can obtain a PRF value by interacting with t(≤ T) servers but is unable to compute the same with up to (t − 1)...

In this note, we introduce structured-seed local pseudorandom generators, a relaxation of local pseudorandom generators. We provide constructions of this primitive under the sparse-LPN assumption, and explore its implications.

In this paper, we propose the Differential Fault Attack (DFA) on three Homomorphic Encryption (HE) friendly stream ciphers \textsf{Masta}, \textsf{Pasta}, and \textsf{Elisabeth}. Both \textsf{Masta} and \textsf{Pasta} are \textsf{Rasta}-like ciphers with publicly derived and pseudorandom affine layers. The design of \textsf{Elisabeth} is an extension of \textsf{FLIP} and \textsf{FiLIP}, following the group filter permutator paradigm. All these three ciphers operate on elements over...