We initiate the study of the black-box complexity of private-key functional encryption (FE). Of central importance in the private-key setting is the inner-product functionality, which is currently only known from assumptions that imply public-key encryption, such as Decisional Diffie-Hellman or Learning-with-Errors. As our main result, we rule out black-box constructions of private-key inner-product FE from random oracles. This implies a black-box separation between private-key...

In this paper, we study multi-party non-interactive key exchange (NIKE) in the fine-grained setting. More precisely, we propose three multi-party NIKE schemes in three computation models, namely, the bounded parallel-time, bounded time, and bounded storage models. Their security is based on a very mild assumption (e.g., NC1 ⊊ ⊕L/poly) or even without any complexity assumption. This improves the recent work of Afshar, Couteau, Mahmoody, and Sadeghi (EUROCRYPT 2023) that requires idealized...

The indifferentiability framework has become a standard methodology that enables us to study the security of cryptographic constructions in idealized models of computation. Unfortunately, while indifferentiability provides strong guarantees whenever the security of a construction is captured by a ``single-stage'' security game, it may generally provide no meaningful guarantees when the security is captured by a ``multi-stage'' one. In particular, the indifferentiability framework does not...

Proof-Carrying Data (PCD) is a foundational tool for ensuring the correctness of incremental distributed computations that has found numerous applications in theory and practice. The state-of-the-art PCD constructions are obtained via accumulation or folding schemes. Unfortunately, almost all known constructions of accumulation schemes rely on homomorphic vector commitments (VCs), which results in relatively high computational costs and insecurity in the face of quantum adversaries. A recent...

Multi-valued validated Byzantine agreement (MVBA), a fundamental primitive of distributed computing, enables $n$ processes to agree on a valid $\ell$-bit value, despite $t$ faulty processes behaving arbitrarily. Among hash-based protocols for the asynchronous setting with adaptive faults, the state-of-the-art HMVBA protocol has optimal $O(1)$ time complexity and near-optimal $O(n \ell + n^2 \kappa \log n)$ bit complexity, but tolerates only $t < n/5$ faults. We present REDUCER, an MVBA...

Non-interactive zero-knowledge (NIZK) proofs allow a prover to convince a verifier about the validity of an NP-statement by sending a single message and without disclosing any additional information (besides the validity of the statement). Single-message cryptographic proofs are very versatile, which has made them widely used both in theory and in practice. This is particularly true for succinct proofs, where the length of the message is sublinear in the size of the NP relation. This...

Time-lock puzzles are unique cryptographic primitives that use computational complexity to keep information secret for some period of time, after which security expires. This topic, while over 25 years old, is still in a state where foundations are not well understood: For example, current analysis techniques of time-lock primitives provide no sound mechanism to build composed multi-party cryptographic protocols which use expiring security as a building block. Further, there are analyses...

In the post-quantum migration of TLS 1.3, an ephemeral Diffie-Hellman must be replaced with a post-quantum key encapsulation mechanism (KEM). At EUROCRYPT 2022, Huguenin-Dumittan and Vaudenay [EC:HugVau22] demonstrated that KEMs with standard CPA security are sufficient for the security of the TLS1.3 handshake. However, their result is only proven in the random oracle model (ROM), and as the authors comment, their reduction is very much non-tight and not sufficient to guarantee security in...

We propose a generalization of Zhandry’s compressed oracle method to random permutations, where an algorithm can query both the permutation and its inverse. We show how to use the resulting oracle simulation to bound the success probability of an algorithm for any predicate on input-output pairs, a key feature of Zhandry’s technique that had hitherto resisted attempts at generalization to random permutations. One key technical ingredient is to use strictly monotone factorizations to...

The universal composability (UC) model provides strong security guarantees for protocols used in arbitrary contexts. While these guarantees are highly desirable, in practice, schemes with a standalone proof of security, such as the Groth16 proof system, are preferred. This is because UC security typically comes with undesirable overhead, sometimes making UC-secure schemes significantly less efficient than their standalone counterparts. We establish the UC security of Groth16 without any...

The BUFF transform, due to Cremers et al. (S&P'21), is a generic transformation for digital signature scheme, with the purpose of obtaining additional security guarantees beyond unforgeability: exclusive ownership, message-bound signatures, and non-resignability. Non-resignability (which essentially challenges an adversary to re-sign an unknown message for which it only obtains the signature) turned out to be a delicate matter, as recently Don et al. (CRYPTO'24) showed that the initial...

Byzantine broadcast is one of the fundamental problems in distributed computing. Many of its practical applications, from multiparty computation to consensus mechanisms for blockchains, require increasingly weaker trust assumptions, as well as scalability for an ever-growing number of users $n$. This rules out existing solutions which run in a linear number of rounds in $n$ or rely on trusted setup requirements. In this paper, we propose the first sublinear-round and trustless Byzantine...

The Asynchronous Common Subset (ACS) problem is a fundamental problem in distributed computing. Very recently, Das et al. (2024) developed a new ACS protocol with several desirable properties: (i) it provides optimal resilience, tolerating up to $t < n/3$ corrupt parties out of $n$ parties in total, (ii) it does not rely on a trusted set up, (iii) it utilizes only "lighweight" cryptography, which can be instantiated using just a hash function, and (iv) it has expected round complexity...

Dynamic Decentralized Functional Encryption (DDFE), introduced by Chotard et al. (CRYPTO'20), represents a robust generalization of (Multi-Client) Functional Encryption. It allows users to dynamically join and contribute private inputs to individually controlled joint functions without requiring a trusted authority. Recently, Shi et al. (PKC'23) proposed the first Multi-Client Functional Encryption scheme for function-hiding inner products (FH-IP) without relying on random oracles....

Structure-preserving signatures (SPS) have emerged as an important cryptographic building block, as their compatibility with the Groth-Sahai (GS) NIZK framework allows to construct protocols under standard assumptions with reasonable efficiency. Over the last years there has been a significant interest in the design of threshold signature schemes. However, only very recently Crites et al. (ASIACRYPT 2023) have introduced threshold SPS (TSPS) along with a fully non-interactive construction....

Weak forward secrecy (wFS) of authenticated key exchange (AKE) protocols is a passive variant of (full) forward secrecy (FS). A natural mechanism to upgrade from wFS to FS is the use of key confirmation messages which compute a message authentication code (MAC) over the transcript. Unfortunately, Gellert, Gjøsteen, Jacobson and Jager (GGJJ, CRYPTO 2023) show that this mechanism inherently incurs a loss proportional to the number of users, leading to an overall non-tight reduction, even if...

Universal computational extractors (UCEs), introduced by Bellare, Hoang, and Keelveedhi [BHK13], can securely replace random oracles in various applications, including KDM-secure encryption, deterministic encryption, RSA-OAEP, etc. Despite its usefulness, constructing UCE in the standard model is challenging. The only known positive result is given by Brzuska and Mittelbach [BM14], who construct UCE with strongly computationally unpredictable one-query source assuming indistinguishability...

The existence of "unstructured" hard languages in $\mathsf{NP} \,\cap\,\mathsf{coNP}$ is an intriguing open question. Bennett and Gill (SICOMP, 1981) asked whether $\mathsf{P}$ is separated from $\mathsf{NP} \cap \mathsf{coNP}$ relative to a random oracle, a question that remained open ever since. While a hard language in $\mathsf{NP} \,\cap\,\mathsf{coNP}$ can be constructed in a black-box way from a one-way permutation, for which only few (structured) candidates exist, Bitansky et al....

We introduce protocols for classical verification of quantum depth (CVQD). These protocols enable a classical verifier to differentiate between devices of varying quantum circuit depths, even in the presence of classical computation. The goal is to demonstrate that a classical verifier can reject a device with a quantum circuit depth of no more than $d$, even if the prover employs additional polynomial-time classical computation to deceive. Conversely, the verifier accepts a device with a...

zkSNARK is a cryptographic primitive that allows a prover to prove to a resource constrained verifier, that it has indeed performed a specified non-deterministic computation correctly, while hiding private witnesses. In this work we focus on lattice based zkSNARK, as this serves two important design goals. Firstly, we get post-quantum zkSNARK schemes with $O(\log (\mbox{Circuit size}))$ sized proofs (without random oracles) and secondly, the easy verifier circuit allows further...

The Snowden's revelations kick-started a community-wide effort to develop cryptographic tools against mass surveillance. In this work, we propose to add another primitive to that toolbox: Fail-Stop Signatures (FSS) [EC'89]. FSS are digital signatures enhanced with a forgery-detection mechanism that can protect a PPT signer from more powerful attackers. Despite the fascinating concept, research in this area stalled after the '90s. However, the ongoing transition to post-quantum...

Memory tightness of reductions in cryptography, in addition to the standard tightness related to advantage and running time, is important when the underlying problem can be solved efficiently with large memory, as discussed in Auerbach, Cash, Fersch, and Kiltz (CRYPTO 2017). Diemert, Geller, Jager, and Lyu (ASIACRYPT 2021) and Ghoshal, Ghosal, Jaeger, and Tessaro (EUROCRYPT 2022) gave memory-tight proofs for the multi-challenge security of digital signatures in the random oracle model....

Zero-Knowledge Virtual Machines (ZKVMs) have gained traction in recent years due to their potential applications in a variety of areas, particularly blockchain ecosystems. Despite tremendous progress on ZKVMs in the industry, no formal definitions or security proofs have been established in the literature. Due to this lack of formalization, existing protocols exhibit significant discrepancies in terms of problem definitions and performance metrics, making it difficult to analyze and compare...

Garbled circuit techniques that are secure in the adaptive setting -- where inputs are chosen after the garbled program is sent -- are motivated by practice, but they are notoriously difficult to achieve. Prior adaptive garbling is either impractically expensive or encrypts the entire garbled program with the output of a programmable random oracle (PRO), a strong assumption. We present a simple framework for proving adaptive security of garbling schemes in the non-programmable random...

In the aftermath of the Snowden revelations in 2013, concerns about the integrity and security of cryptographic systems have grown significantly. As adversaries with substantial resources might attempt to subvert cryptographic algorithms and undermine their intended security guarantees, the need for subversion-resilient cryptography has become paramount. Security properties are preserved in subversion-resilient schemes, even if the adversary implements the scheme used in the security...

We study verifiable outsourcing of computation in a model where the verifier has black-box access to the function being computed. We introduce the problem of oracle-aided batch verification of computation (OBVC) for a function class $\mathcal{F}$. This allows a verifier to efficiently verify the correctness of any $f \in \mathcal{F}$ evaluated on a batch of $n$ instances $x_1, \ldots, x_n$, while only making $\lambda$ calls to an oracle for $f$ (along with $O(n \lambda)$ calls to...

Extremely Lossy Functions (ELFs) are families of functions that, depending on the choice during key generation, either operate in injective mode or instead have only a polynomial image size. The choice of the mode is indistinguishable to an outsider. ELFs were introduced by Zhandry (Crypto 2016) and have been shown to be very useful in replacing random oracles in a number of applications. One open question is to determine the minimal assumption needed to instantiate ELFs. While all...

In Crypto 2019, Zhandry showed how to define compressed oracles, which record quantum superposition queries to the quantum random oracle. In this paper, we extend Zhandry's compressed oracle technique to non-uniformly distributed functions with independently sampled outputs. We define two quantum oracles $\mathsf{CStO}_D$ and $\mathsf{CPhsO}_D$, which are indistinguishable to the non-uniform quantum random oracle where quantum access is given to a random function $H$ whose images $H(x)$...

We revisit OCAKE (ACNS 23), a generic recipe that constructs password-based authenticated key exchange (PAKE) from key encapsulation mechanisms (KEMs), to allow instantiations with post-quantums KEM like KYBER. The ACNS23 paper left as an open problem to argue security against quantum attackers, with its security proof being in the universal composability (UC) framework. This is common for PAKE, however, at the time of this submission’s writing, it was not known how to prove (computational)...

When modelling how public key encryption can enable secure communication, we should acknowledge that secret information, such as private keys or the randomness used for encryption, could become compromised. Intuitively, one would expect unrelated communication to remain secure, yet formalizing this intuition has proven challenging. Several security notions have appeared that aim to capture said scenario, ranging from the multi-user setting with corruptions, via selective opening attacks...

We propose a generic construction of password-based authenticated key exchange (PAKE) from key encapsulation mechanisms (KEM). Assuming that the KEM is oneway secure against plaintext-checkable attacks (OW-PCA), we prove that our PAKE protocol is \textit{tightly secure} in the Bellare-Pointcheval-Rogaway model (EUROCRYPT 2000). Our tight security proofs require ideal ciphers and random oracles. The OW-PCA security is relatively weak and can be implemented tightly with the Diffie-Hellman...

In the Random Oracle Model (ROM) all parties have oracle access to a common random function, and the parties are limited in the number of queries they can make to the oracle. The Merkle’s Puzzles protocol, introduced by Merkle [CACM ’78], is a key-agreement protocol in the ROM with a quadratic gap between the query complexity of the honest parties and the eavesdropper. This quadratic gap is known to be optimal, by the works of Impagliazzo and Rudich [STOC ’89] and Barak and Mahmoody [Crypto...

The majority of fault-tolerant distributed algorithms are designed assuming a nominal corruption model, in which at most a fraction $f_n$ of parties can be corrupted by the adversary. However, due to the infamous Sybil attack, nominal models are not sufficient to express the trust assumptions in open (i.e., permissionless) settings. Instead, permissionless systems typically operate in a weighted model, where each participant is associated with a weight and the adversary can corrupt a set of...

We instantiate the hash-then-evaluate paradigm for pseudorandom functions (PRFs), $\mathsf{PRF}(k, x) := \mathsf{wPRF}(k, \mathsf{RO}(x))$, which builds a PRF $\mathsf{PRF}$ from a weak PRF $\mathsf{wPRF}$ via a public preprocessing random oracle $\mathsf{RO}$. In applications to secure multiparty computation (MPC), only the low-complexity wPRF performs secret-depending operations. Our construction replaces RO by $f(k_H , \mathsf{elf}(x))$, where $f$ is a non-adaptive PRF and the key $k_H$...

We present simple and practical protocols for generating randomness as used by asynchronous total-order broadcast. The protocols are secure in a proof-of-stake setting with dynamically changing stake. They can be plugged into existing protocols for asynchronous total-order broadcast and will turn these into asynchronous total-order broadcast with dynamic stake. Our contribution relies on two important techniques. The paper ``Random Oracles in Constantinople: Practical Asynchronous Byzantine...

In this work, we initiate a new conceptual line of attack on the fundamental question of how to generate hard problems. Motivated by the need for one-way functions in cryptography, we propose an information-theoretic framework to study the question of generating new provably hard one-way functions by composing functions that are easy to invert and evaluate, where each such easy function is modeled as a random oracles paired with another oracle that implements an inverse function.

The random oracle model is an instrument used for proving that protocol has no structural flaws when settling with standard hash properties is impossible or fairly difficult. In practice, however, random oracles have to be instantiated with some specific hash functions, which are not random oracles. Hence, in the real world, an adversary has broader capabilities than considered in the random oracle proof — it can exploit the peculiarities of a specific hash function to achieve its goal. In a...

With applications in secure messaging, Updatable Public Key Encryption (UPKE) was proposed by Jost et al. (EUROCRYPT '19) and Alwen et al. (CRYPTO '20). It is a natural relaxation of forward-secure public-key encryption. In UPKE, we can update secret keys by using update ciphertexts which any sender can generate. The UPKE schemes proposed so far that satisfy the strong CCA security are Haidar et al.'s concrete construction (CCS '22) and Dodis et al's generic construction that use...

Time-lock puzzles wrap a solution $\mathrm{s}$ inside a puzzle $\mathrm{P}$ in such a way that ``solving'' $\mathrm{P}$ to find $\mathrm{s}$ requires significantly more time than generating the pair $(\mathrm{s},\mathrm{P})$, even if the adversary has access to parallel computing; hence it can be thought of as sending a message $\mathrm{s}$ to the future. It is known [Mahmoody, Moran, Vadhan, Crypto'11] that when the source of hardness is only a random oracle, then any puzzle generator with...

A distributed sampler is a way for several mutually distrusting parties to non-interactively generate a common reference string (CRS) that all parties trust. Previous work constructs distributed samplers in the random oracle model, or in the standard model with very limited security guarantees. This is no accident, as standard model distributed samplers with full security were shown impossible. In this work, we provide new definitions for distributed samplers which we show achieve...

A large number of works prove lower bounds on space-time trade-offs in preprocessing attacks, i.e., trade-offs between the size of the advice and the time needed to break a scheme given such advice. We contend that the question of how much {\em time} is needed to produce this advice is equally important, and often highly non-trivial. However, this question has received significantly less attention. In this paper, we present lower bounds on the complexity of preprocessing attacks that depend...

Chameleon hash (CH) is a trapdoor hash function. Generally it is hard to find collisions, but with the help of a trapdoor, finding collisions becomes easy. CH plays an important role in converting a conventional blockchain to a redactable one. However, most of existing CH schemes are too weak to support redactable blockchains. The currently known CH schemes serving for redactable blockchains have the best security of so-called ``full collision resistance (f-CR)'', but they are built either...

Compressed oracles (Zhandry, Crypto 2019) are a powerful technique to reason about quantum random oracles, enabling a sort of lazy sampling in the presence of superposition queries. A long-standing open question is whether a similar technique can also be used to reason about random (efficiently invertible) permutations. In this work, we make a step towards answering this question. We first define the compressed permutation oracle and illustrate its use. While the soundness of this...

In 2013, the Snowden revelations have shown subversion of cryptographic implementations to be a relevant threat. Since then, the academic community has been pushing the development of models and constructions to defend against adversaries able to arbitrarily subvert cryptographic implementations. To capture these strong capabilities of adversaries, Russell, Tang, Yung, and Zhou (CCS'17) proposed CPA-secure encryption in a model that utilizes a trusted party called a watchdog testing an...

In a Multi-Client Functional Encryption (MCFE) scheme, $n$ clients each obtain a secret encryption key from a trusted authority. During each time step $t$, each client $i$ can encrypt its data using its secret key. The authority can use its master secret key to compute a functional key given a function $f$, and the functional key can be applied to a collection of $n$ clients’ ciphertexts encrypted to the same time step, resulting in the outcome of $f$ on the clients’ data. In this paper, we...

Proof-carrying data (PCD) is a powerful cryptographic primitive that allows mutually distrustful parties to perform distributed computation in an efficiently verifiable manner. Known constructions of PCD are obtained by recursively-composing SNARKs or related primitives. SNARKs with desirable properties such as transparent setup are constructed in the random oracle model. However, using such SNARKs to construct PCD requires heuristically instantiating the oracle and using it in a...

In this work, we initiate a study of $K$-NIKE protocols in the fine-grained setting, in which there is a polynomial gap between the running time of the honest parties and that of the adversary. Our goal is to show the possibility, or impossibility, of basing such protocols on weaker assumptions than those of $K$-NIKE for $K \geq 3$. Our contribution is threefold. - We show that random oracles can be used to obtain fine-grained $K$-NIKE protocols for every constant $K$. In particular,...

Commitments are fundamental in cryptography. In the classical world, commitments are equivalent to the existence of one-way functions. It is also known that the most desired form of commitments in terms of their round complexity, i.e., non-interactive commitments, cannot be built from one-way functions in a black-box way [Mahmoody-Pass, Crypto'12]. However, if one allows the parties to use quantum computation and communication, it is known that non-interactive commitments (to classical bits)...

We study sufficient conditions for compiling simulation-extractable zkSNARKs from information-theoretic interactive oracle proofs (IOP) using a simulation-extractable commit-and-prove system for its oracles. Specifically, we define simulation extractability for opening and evaluation proofs of polynomial commitment schemes, which we then employ to prove the security of zkSNARKS obtained from polynomial IOP prove systems, such as Plonk and Marlin. To instantiate our methodology we...

We revisit the problem of {\em reusable} non-interactive secure computation (NISC). A standard NISC protocol for a sender-receiver functionality $f$ enables the receiver to encrypt its input $x$ such that any sender, on input $y$, can send back a message revealing only $f(x,y)$. Security should hold even when either party can be malicious. A {\em reusable} NISC protocol has the additional feature that the receiver's message can be safely reused for computing multiple outputs $f(x,y_i)$. Here...

Computationally sound protocol verification tools promise to deliver full-strength cryptographic proofs for security protocols. Unfortunately, current tools lack either modularity or automation. We propose a new approach based on a novel use of information flow and refinement types for sound cryptographic proofs. Our framework, Owl, allows type-based modular descriptions of security protocols, wherein disjoint subprotocols can be programmed and automatically proved secure separately....

We prove adaptive security of a simple three-round threshold Schnorr signature scheme, which we call Sparkle+. The standard notion of security for threshold signatures considers a static adversary – one who must declare which parties are corrupt at the beginning of the protocol. The stronger adaptive adversary can at any time corrupt parties and learn their state. This notion is natural and practical, yet not proven to be met by most schemes in the literature. In this paper, we...

The introduction of time-lock puzzles initiated the study of publicly “sending information into the future.” For time-lock puzzles, the underlying security-enabling mechanism is the computational complexity of the operations needed to solve the puzzle, which must be tunable to reveal the solution after a predetermined time, and not before that time. Time-lock puzzles are typically constructed via a commitment to a secret, paired with a reveal algorithm that sequentially iterates a basic...

Trick-taking games are traditional card games played all over the world. There are many such games, and most of them can be played online through dedicated applications, either for fun or for betting money. However, these games have an intrinsic drawback: each player plays its cards according to several secret constraints (unknown to the other players), and if a player does not respect these constraints, the other players will not realize it until much later in the game. In 2019, X....

This paper gives new constructions of two-round multi-signatures and threshold signatures for which security relies solely on either the hardness of the (plain) discrete logarithm problem or the hardness of RSA, in addition to assuming random oracles. Their signing protocol is partially non-interactive, i.e., the first round of the signing protocol is independent of the message being signed. We obtain our constructions by generalizing the most efficient discrete- logarithm based schemes,...

Lyubashevky's signatures are based on the Fiat-Shamir with Aborts paradigm. It transforms an interactive identification protocol that has a non-negligible probability of aborting into a signature by repeating executions until a loop iteration does not trigger an abort. Interaction is removed by replacing the challenge of the verifier by the evaluation of a hash function, modeled as a random oracle in the analysis. The access to the random oracle is classical (ROM), resp. quantum (QROM), if...

The notion of Endemic Oblivious Transfer (EOT) was introduced by Masny and Rindal (CCS'19). EOT offers a weaker security guarantee than the conventional random OT; namely, the malicious parties can fix their outputs arbitrarily. The authors presented a 1-round UC-secure EOT protocol under a tailor-made and non-standard assumption, Choose-and-Open DDH, in the RO model. In this work, we systematically study EOT in the UC/GUC framework. We present a new 1-round UC-secure EOT construction...

Byzantine broadcast is one of the fundamental problems in distributed computing. Many practical applications from secure multiparty computation to consensus mechanisms for blockchains require increasingly weaker trust assumptions, as well as scalability for an ever-growing number of users, which rules out existing solutions with linear number of rounds or trusted setup requirements. In this paper, we propose the first sublinear-round and trustless Byzantine broadcast protocol. Unlike...

The most compact quantum-safe proof systems for large circuits are PCP-type systems such as Ligero, Aurora, and Shockwave, that only use weak cryptographic assumptions, namely hash functions modeled as random oracles. One would expect that by allowing for stronger assumptions, such as the hardness of Module-SIS, it should be possible to design more compact proof systems. But alas, despite considerable progress in lattice-based proofs, no such proof system was known so far. We rectify this...

We give round-optimal {\em black-box} constructions of two-party and multiparty protocols in the common random/reference string (CRS) model, with security against malicious adversaries, based on any two-round oblivious transfer (OT) protocol in the same model. Specifically, we obtain two types of results. \begin{enumerate} \item {\bf Two-party protocol.} We give a (two-round) {\it two-sided NISC} protocol that makes black-box use of two-round (malicious-secure) OT in the CRS model....

Ring signatures allow a user to sign messages on behalf of an ad hoc set of users - a ring - while hiding her identity. The original motivation for ring signatures was whistleblowing [Rivest et al. ASIACRYPT'01]: a high government employee can anonymously leak sensitive information while certifying that it comes from a reliable source, namely by signing the leak. However, essentially all known ring signature schemes require the members of the ring to publish a structured verification key...

The random oracle methodology is central to the design of many practical cryptosystems. A common challenge faced in several systems is the need to have a random oracle that outputs from a structured distribution $\mathcal{D}$, even though most heuristic implementations such as SHA-3 are best suited for outputting bitstrings. Our work explores the problem of sampling from discrete Gaussian (and related) distributions in a manner that they can be programmed into random oracles. We...

We say a public-key encryption is plaintext-extractable in the random oracle model if there exists an algorithm that given access to all inputs/outputs queries to the random oracles can simulate the decryption oracle. We argue that plaintext-extractability is enough to show the indistinguishably under chosen ciphertext attack (IND-CCA) of OAEP+ transform (Shoup, Crypto 2001) when the underlying trapdoor permutation is one-way. We extend the result to the quantum random oracle model...

Attribute-based encryption (ABE) extends public-key encryption to enable fine-grained control to encrypted data. However, this comes at the cost of needing a central trusted authority to issue decryption keys. A multi-authority ABE (MA-ABE) scheme decentralizes ABE and allows anyone to serve as an authority. Existing constructions of MA-ABE only achieve security in the random oracle model. In this work, we develop new techniques for constructing MA-ABE for the class of subset policies...

We present a new template for building oblivious transfer from quantum information that we call the ``fixed basis'' framework. Our framework departs from prior work (eg., Crepeau and Kilian, FOCS '88) by fixing the correct choice of measurement basis used by each player, except for some hidden trap qubits that are intentionally measured in a conjugate basis. We instantiate this template in the quantum random oracle model (QROM) to obtain simple protocols that implement, with security...

In the UC framework, protocols must be subroutine respecting; therefore, shared trusted setup might cause security issues. To address this drawback, Generalized UC (GUC) framework is introduced by Canetti \emph{et al.} (TCC 2007). In this work, we investigate the impossibility and feasibility of GUC-secure commitments using global random oracles (GRO) as the trusted setup. In particular, we show that it is impossible to have a 2-round (1-round committing and 1-round opening) GUC-secure...

Quantum copy-protection, introduced by Aaronson (CCC'09), uses the no-cloning principle of quantum mechanics to protect software from being illegally distributed. Constructing copy-protection has been an important problem in quantum cryptography. Since copy-protection is shown to be impossible to achieve in the plain model, we investigate the question of constructing copy-protection for arbitrary classes of unlearnable functions in the random oracle model. We present an impossibility...

We give the first constructions in the plain model of 1) nonmalleable digital lockers (Canetti and Varia, TCC 2009) and 2) robust fuzzy extractors (Boyen et al., Eurocrypt 2005) that secure sources with entropy below 1/2 of their length. Constructions were previously only known for both primitives assuming random oracles or a common reference string (CRS). Along the way, we define a new primitive called a nonmalleable point function obfuscation with associated data. The associated data is...

In this paper it is shown that PSPACE is equal to 4th level in the polynomial hierarchy. A lot of important consequences are also deduced. True quantified Boolean formula is indeed a generalisation of the Boolean Satisfiability Problem, where determining of interpretation that satisfies a given Boolean formula is replaced by existence of Boolean functions that makes a given QBF to be tautology. Such functions are called the Skolem functions. The essential idea is to skolemize, and...

We introduce the notion of a universal random oracle. Analogously to a classical random oracle it idealizes hash functions as random functions. However, as opposed to a classical random oracle which is created freshly and independently for each adversary, the universal random oracle should provide security of a cryptographic protocol against all adversaries simultaneously. This should even hold if the adversary now depends on the random function. This reflects better the idea that the strong...

Unclonable encryption, first introduced by Broadbent and Lord (TQC'20), is a one-time encryption scheme with the following security guarantee: any non-local adversary (A, B, C) cannot simultaneously distinguish encryptions of two equal length messages. This notion is termed as unclonable indistinguishability. Prior works focused on achieving a weaker notion of unclonable encryption, where we required that any non-local adversary (A, B, C) cannot simultaneously recover the entire message m....

We propose a new paradigm for justifying the security of random oracle-based protocols, which we call the Augmented Random Oracle Model (AROM). We show that the AROM captures a wide range of important random oracle impossibility results. Thus a proof in the AROM implies some resiliency to such impossibilities. We then consider three ROM transforms which are subject to impossibilities: Fiat-Shamir (FS), Fujisaki-Okamoto (FO), and Encrypt-with-Hash (EwH). We show in each case how to obtain...

In the first part of the paper, we show a generic compiler that transforms any oracle algorithm that can query multiple oracles adaptively, i.e., can decide on which oracle to query at what point dependent on previous oracle responses, into a static algorithm that fixes these choices at the beginning of the execution. Compared to naive ways of achieving this, our compiler controls the blow-up in query complexity for each oracle individually, and causes a very mild blow-up only. In the...

Hashing arbitrary values to points on an elliptic curve is a required step in many cryptographic constructions, and a number of techniques have been proposed to do so over the years. One of the first ones was due to Shallue and van de Woestijne (ANTS-VII), and it had the interesting property of applying to essentially all elliptic curves over finite fields. It did not, however, have the desirable property of being indifferentiable from a random oracle when composed with a random oracle to...

Selective opening (SO) security is one of the most important security notions of public key encryption (PKE) in a multi-user setting. Even though messages and random coins used in some ciphertexts are leaked, SO security guarantees the confidentiality of the other ciphertexts. Actually, it is shown that there exist PKE schemes which meet the standard security such as indistinguishability against chosen ciphertext attacks (IND-CCA security) but do not meet SO security against chosen...

Authenticated Key Exchange (AKE) is a cryptographic protocol to share a common session key among multiple parties. Usually, PKI-based AKE schemes are designed to guarantee secrecy of the session key and mutual authentication. However, in practice, there are many cases where mutual authentication is undesirable such as in anonymous networks like Tor and Riffle, or difficult to achieve due to the certificate management at the user level such as the Internet. Goldberg et al. formulated a model...

We construct the first non-interactive zero-knowledge (NIZK) proof systems in the fine-grained setting where adversaries’ resources are bounded and honest users have no more resources than an adversary. More concretely, our setting is the NC1-fine-grained setting, namely, all parties (including adversaries and honest participants) are in NC1. Our NIZK systems are for circuit satisfiability (SAT) under the worst-case assumption, NC1 being unequal to Parity-L/poly. As technical contributions,...

In his landmark paper at TCC 2008 Paul Valiant introduced the notion of ``incrementally verifiable computation'' which enables a prover to incrementally compute a succinct proof of correct execution of a (potentially) long running process. The paper later won the 2019 TCC test of time award. The construction was proven secure in the random oracle model without any further computational assumptions. However, the overall proof was given using a non-standard version of the random-oracle...

We show the following hold, unconditionally unless otherwise stated, relative to a random oracle: - There are NP search problems solvable by quantum polynomial-time machines but not classical probabilistic polynomial-time machines. - There exist functions that are one-way, and even collision resistant, against classical adversaries but are easily inverted quantumly. Similar separations hold for digital signatures and CPA-secure public key encryption (the latter requiring the assumption...

Succinct non-interactive arguments of knowledge (SNARKs) are cryptographic proofs with strong efficiency properties. Applications of SNARKs often involve proving computations that include the SNARK verifier, a technique called recursive composition. Unfortunately, SNARKs with desirable features such as a transparent (public-coin) setup are known only in the random oracle model (ROM). In applications this oracle must be heuristically instantiated and used in a non-black-box way. In this...

First of all we take a thorough look at an error in a paper by Daemen et al. (ToSC 2018) which looks at minimal requirements for tree-based hashing based on multiple primitives, including block ciphers. This reveals that the error is more fundamental than previously shown by Gunsing et al. (ToSC 2020), which is mainly interested in its effect on the security bounds. It turns out that the cause for the error is due to an essential oversight in the interaction between the different oracles...

The pre-shared key (PSK) handshake modes of TLS 1.3 allow for the performant, low-latency resumption of previous connections and are widely used on the Web and by resource-constrained devices, e.g., in the Internet of Things. Taking advantage of these performance benefits with optimal and theoretically-sound parameters requires tight security proofs. We give the first tight security proofs for the TLS 1.3 PSK handshake modes. Our main technical contribution is to address a gap in prior...

We study the following question, first publicly posed by Hosoyamada and Yamakawa in 2018. Can parties Alice and Bob with quantum computing power and classical communication rely only on a random oracle (that can be queried in quantum superposition) to agree on a key that is private from eavesdroppers? We make the first progress on the question above and prove the following. When only one of the parties is classical and the other party is quantum powered, as long as they ask a total of $d$...

Succinct non-interactive arguments (SNARGs) have become a fundamental primitive in the cryptographic community. The focus of this work is constructions of SNARGs in the Random Oracle Model (ROM). Such SNARGs enjoy post-quantum security and can be deployed using lightweight cryptography to heuristically instantiate the random oracle. A ROM-SNARG is \emph{$(t,\varepsilon)$-sound} if no $t$-query malicious prover can convince the verifier to accept a false statement with probability larger...

The task of combining cryptographic keys, some of which may be maliciously formed, into one key, which is (pseudo)random is a central task in cryptographic systems. For example, it is a crucial component in the widely used TLS and Signal protocols. From an analytical standpoint, current security proofs model such key combiners as dual-PRFs -- a function which is a PRF when keyed by either of its two inputs -- guaranteeing pseudo-randomness if one of the keys is compromised or even...

This paper proposes the first practical pairing-free three-move blind signature schemes that (1) are concurrently secure, (2) produce short signatures (i.e., three or four group elements/scalars), and (3) are provably secure either in the generic group model (GGM) or the algebraic group model (AGM) under the (plain or one-more) discrete logarithm assumption (beyond additionally assuming random oracles). We also propose a partially blind version of one of our schemes. Our schemes do not rely...

Identity-based matchmaking encryption (IB-ME) is a generalization of identity-based encryption where the sender and the receiver can both specify a target identity: if both the chosen target identities match the one of the other party, the plaintext is revealed, and otherwise the sender’s identity, the target identity, and the plaintext remain hidden. Previous work showed how to construct IB-ME in the random oracle model. We give the first construction in the plain model, based on standard...

This article makes an important contribution to solving the long-standing problem of whether all elliptic curves can be equipped with a hash function (indifferentiable from a random oracle) whose running time amounts to one exponentiation in the basic finite field $\mathbb{F}_{\!q}$. More precisely, we construct a new indifferentiable hash function to any ordinary elliptic $\mathbb{F}_{\!q}$-curve $E_a$ of $j$-invariant $1728$ with the cost of extracting one quartic root in...

The ability to verifiably retrieve transaction or state data stored off-chain is crucial to blockchain scaling techniques such as rollups or sharding. We formalize the problem and design a storage- and communication-efficient protocol using linear erasure-correcting codes and homomorphic vector commitments. Motivated by application requirements for rollups, our solution Semi-AVID-PR departs from earlier Verifiable Information Dispersal schemes in that we do not require comprehensive...

An average-case variant of the $k$-SUM conjecture asserts that finding $k$ numbers that sum to 0 in a list of $r$ random numbers, each of the order $r^k$, cannot be done in much less than $r^{\lceil k/2 \rceil}$ time. On the other hand, in the dense regime of parameters, where the list contains more numbers and many solutions exist, the complexity of finding one of them can be significantly improved by Wagner's $k$-tree algorithm. Such algorithms for $k$-SUM in the dense regime have many...

In this paper, we study the round complexity of concurrently secure computation protocols in the plain model, without random oracles or assuming the presence of a trusted setup. In the plain model, it is well known that concurrently secure two-party computation with polynomial simulation is impossible to achieve in two rounds. For this reason, we focus on the well-studied notion of security with super-polynomial simulation (SPS). Our main result is the first construction of two-round SPS...

Constructing an efficient CCA-secure KEM is generally done by first constructing a passively-secure PKE scheme, and then applying the Fujisaki-Okamoto (FO) transformation. The original FO transformation was designed to offer security in a single user setting. A stronger notion, known as multi-user security, considers the attacker's advantage in breaking one of many user's ciphertexts. Bellare et al.~(EUROCRYPT 2020) showed that standard single user security implies multi-user security with...

Robust (fuzzy) extractors are very useful for, e.g., authenticated exchange from shared weak secret and remote biometric authentication against active adversaries. They enable two parties to extract the same uniform randomness with the ``helper'' string. More importantly, they have an authentication mechanism built in that tampering of the ``helper'' string will be detected. Unfortunately, as shown by Dodis and Wichs, in the information-theoretic setting, a robust extractor for an...

We construct a short and adaptively secure identity-based signature scheme tightly based on the well-known Short Integer Solution (SIS) assumption. Although identity-based signature schemes can be tightly constructed from either standard signature schemes against adaptive corruptions in the multi-user setting or a two-level hierarchical identity-based encryption scheme, neither of them is known with short signature size and tight security based on the SIS assumption. Here ``short'' means the...

A two-party authenticated key exchange (AKE) protocol allows each of the two parties to share a common secret key over insecure channels even in the presence of active adversaries who can actively control and modify the exchanged messages. To capture the various kind of malicious behaviors of the adversaries, there have been lots of efforts to define the security models. Amongst them, the extended Canetti-Krawczyk (eCK) security model is considered as one of the strongest ones and widely...

We construct the first authenticated key exchange protocols that achieve tight security in the standard model. Previous works either relied on techniques that seem to inherently require a random oracle, or achieved only “Multi-Bit-Guess” security, which is not known to compose tightly, for instance, to build a secure channel. Our constructions are generic, based on digital signatures and key encapsulation mechanisms (KEMs). The main technical challenges we resolve is to determine suitable...

We formally introduce, define, and construct memory-hard puzzles. Intuitively, for a difficulty parameter $t$, a cryptographic puzzle is memory-hard if any parallel random access machine (PRAM) algorithm with "small" cumulative memory complexity ($\ll t^2$) cannot solve the puzzle; moreover, such puzzles should be both "easy" to generate and be solvable by a sequential RAM algorithm running in time $t$. Our definitions and constructions of memory-hard puzzles are in the standard model,...

HMAC and NMAC are the most basic and important constructions to convert Merkle-Damgård hash functions into message authentication codes (MACs) or pseudorandom functions (PRFs). In the quantum setting, at CRYPTO 2017, Song and Yun showed that HMAC and NMAC are quantum pseudorandom functions (qPRFs) under the standard assumption that the underlying compression function is a qPRF. Their proof guarantees security up to $O(2^{n/5})$ or $O(2^{n/8})$ quantum queries when the output length of HMAC...

We consider the task of learning a function via oracle queries, where the queries and responses are monitored (and perhaps also modified) by an untrusted intermediary. Our goal is twofold: First, we would like to prevent the intermediary from gaining any information about either the function or the learner's intentions (e.g. the particular hypothesis class the learner is considering). Second, we would like to curb the intermediary's ability to meaningfully interfere with the learning...

Should quantum computers become available, they will reduce the effective key length of basic secret-key primitives, such as blockciphers. To address this we will either need to use blockciphers with inherently longer keys or develop key-length extension techniques to amplify the security of a blockcipher to use longer keys. We consider the latter approach and revisit the FX and double encryption constructions. Classically, FX was proven to be a secure key-length extension technique, while...