What a lovely hat

One-more problems like One-More Discrete Logarithm (OMDL) and One-More Diffie--Hellman (OMDH) have found wide use in cryptography, due to their ability to naturally model security definitions for interactive primitives like blind signatures and oblivious PRF. Furthermore, a generalization of OMDH called Threshold OMDH (TOMDH) has proven useful for building threshold versions of interactive protocols. However, due to their complexity it is often unclear how hard such problems actually are,...

Adaptor signatures (AS) extend the functionality of traditional digital signatures by enabling the generation of a pre-signature tied to an instance of a hard NP relation, which can later be turned (adapted) into a full signature upon revealing a corresponding witness. The recent work by Liu et al. [ASIACRYPT 2024] devised a generic AS scheme that can be used for any NP relation---which here we will refer to as universal adaptor signatures scheme, in short UAS---from any one-way function....

The Multi-Party Computation in the Head (MPCitH) paradigm has proven to be a versatile tool to design proofs of knowledge (PoK) based on variety of computationally hard problems. For instance, many post-quantum signatures have been designed from MPC based proofs combined with the Fiat-Shamir transformation. Over the years, MPCitH has evolved significantly with developments based on techniques such as threshold computing and other optimizations. Recently, Vector Oblivious Linear Evaluation...

We improve recent generic proof systems for isogeny knowledge by Cong, Lai, Levin [26] based on circuit satisfiability, by using radical isogeny descriptions [19, 20] to prove a path in the underlying isogeny graph. We then present a new generic construction for a verifiable random function (VRF) based on a one-more type hardness assumption and zero-knowledge proofs. We argue that isogenies fit the constraints of our construction and instantiate the VRF with a CGL walk [22] and our new...

Compressing primitives such as accumulators and vector commitments, allow to rep- resent large data sets with some compact, ideally constant-sized value. Moreover, they support operations like proving membership or non-membership with minimal, ideally also constant- sized, storage and communication overhead. In recent years, these primitives have found numerous practical applications, with many constructions based on various hardness assumptions. So far, however, it has been elusive to...

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...

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 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...

Post-quantum cryptography has gained attention due to the need for secure cryptographic systems in the face of quantum computing. Code-based and lattice-based cryptography are two promi- nent approaches, both heavily studied within the NIST standardization project. Code-based cryptography—most prominently exemplified by the McEliece cryptosystem—is based on the hardness of decoding random linear error-correcting codes. Despite the McEliece cryptosystem having been unbroken for several...

Ever since the seminal work of Diffie and Hellman, cryptographic (cyclic) groups have served as a fundamental building block for constructing cryptographic schemes and protocols. The security of these constructions can often be based on the hardness of (cyclic) group-based computational assumptions. Then, the generic group model (GGM) has been studied as an idealized model (Shoup, EuroCrypt 1997), which justifies the hardness of many (cyclic) group-based assumptions and shows the limits of...

In this article, we propose a generic hybrid encryption scheme providing entity authentication. The scheme is based on lossy trapdoor functions relying on the hardness of the Learning With Errors problem. The construction can be used on a number of different security requirements with minimal reconfiguration. It ensures entity authentication and ciphertext integrity while providing security against adaptive chosen ciphertext attacks in the standard model. As a desired characteristic of...

HAWK is a lattice-based signature scheme candidate to the fourth call of the NIST's Post-Quantum standardization campaign. Considered as a cousin of Falcon (one of the future NIST post-quantum standards) one can wonder whether HAWK shares the same drawbacks as Falcon in terms of side-channel attacks. Indeed, Falcon signature algorithm and particularly its Gaussian sampler, has shown to be highly vulnerable to power-analysis attacks. Besides, efficiently protecting Falcon's signature...

Secure sketches are designed to facilitate the recovery of originally enrolled data from inputs that may vary slightly over time. This capability is important in applications where data consistency cannot be guaranteed due to natural variations, such as in biometric systems and hardware security. Traditionally, secure sketches are constructed using error-correcting codes to handle these variations effectively. Additionally, principles of information theory ensure the security of these...

Delegatable anonymous credentials (DACs) enable a root issuer to delegate credential-issuing power, allowing a delegatee to take a delegator role. To preserve privacy, credential recipients and verifiers should not learn anything about intermediate issuers in the delegation chain. One particularly efficient approach to constructing DACs is due to Crites and Lysyanskaya (CT-RSA '19). In contrast to previous approaches, it is based on mercurial signatures (a type of equivalence-class...

In the (preprocessing) Decisional Diffie-Hellman (DDH) problem, we are given a cyclic group $G$ with a generator $g$ and a prime order $N$, and we want to prepare some advice of size $S$, such that we can efficiently distinguish $(g^{x},g^{y},g^{xy})$ from $(g^{x},g^{y},g^{z})$ in time $T$ for uniformly and independently chosen $x,y,z$ from $\mathbb{Z}_N$. This is a central cryptographic problem whose computational hardness underpins many widely deployed schemes, such as the Diffie–Hellman...

A dot-product proof (DPP) is a simple probabilistic proof system in which the input statement $\mathbf{x}$ and the proof $\boldsymbol{\pi}$ are vectors over a finite field $\mathbb{F}$, and the proof is verified by making a single dot-product query $\langle \mathbf{q},(\mathbf{x} \| \boldsymbol{\pi}) \rangle$ jointly to $\mathbf{x}$ and $\boldsymbol{\pi}$. A DPP can be viewed as a 1-query fully linear PCP. We study the feasibility and efficiency of DPPs, obtaining the following results: -...

Assuming the hardness of LWE and the existence of IO, we construct a public-key encryption scheme that is IND-CCA secure but fails to satisfy even a weak notion of indistinguishability security with respect to selective opening attacks. Prior to our work, such a separation was known only from stronger assumptions such as differing inputs obfuscation (Hofheinz, Rao, and Wichs, PKC 2016). Central to our separation is a new hash family, which may be of independent interest. Specifically,...

An adaptor signatures (AS) scheme is an extension of digital signatures that allows the signer to generate a pre-signature for an instance of a hard relation. This pre-signature can later be adapted to a full signature with a corresponding witness. Meanwhile, the signer can extract a witness from both the pre-signature and the signature. AS have recently garnered more attention due to its scalability and interoperability. Dai et al. [INDOCRYPT 2022] proved that AS can be constructed for any...

We construct a succinct non-interactive argument (SNARG) system for every NP language $\mathcal{L}$ that has a propositional proof of non-membership for each $x\notin \mathcal{L}$. The soundness of our SNARG system relies on the hardness of the learning with errors (LWE) problem. The common reference string (CRS) in our construction grows with the space required to verify the propositional proof, and the size of the proof grows poly-logarithmically in the length of the propositional...

In this work we first present an explicit forking lemma that distills the information-theoretic essence of the high-moment technique introduced by Rotem and Segev (CRYPTO '21), who analyzed the security of identification protocols and Fiat-Shamir signature schemes. Whereas the technique of Rotem and Segev was particularly geared towards two specific cryptographic primitives, we present a stand-alone probabilistic lower bound, which does not involve any underlying primitive or idealized...

Motivated by the problem of detecting AI-generated text, we consider the problem of watermarking the output of language models with provable guarantees. We aim for watermarks which satisfy: (a) undetectability, a cryptographic notion introduced by Christ, Gunn & Zamir (2024) which stipulates that it is computationally hard to distinguish watermarked language model outputs from the model's actual output distribution; and (b) robustness to channels which introduce a constant fraction of...

We revisit the construction of multiparty non-interactive key-exchange protocols with fine-grained security, which was recently studied in (Afshar et al., Eurocrypt 2023). Their work introduced a 4-party non-interactive key exchange with quadratic hardness, and proved it secure in Shoup's generic group model. This positive result was complemented with a proof that $n$-party non-interactive key exchange with superquadratic security cannot exist in Maurer's generic group model, for any $n\geq...

We define the notion of a classical commitment scheme to quantum states, which allows a quantum prover to compute a classical commitment to a quantum state, and later open each qubit of the state in either the standard or the Hadamard basis. Our notion is a strengthening of the measurement protocol from Mahadev (STOC 2018). We construct such a commitment scheme from the post-quantum Learning With Errors (LWE) assumption, and more generally from any noisy trapdoor claw-free function family...

Arora & Ge introduced a noise-free polynomial system to compute the secret of a Learning With Errors (LWE) instance via linearization. Albrecht et al. later utilized the Arora-Ge polynomial model to study the complexity of Gröbner basis computations on LWE polynomial systems under the assumption of semi-regularity. In this paper we revisit the Arora-Ge polynomial and prove that it satisfies a genericity condition recently introduced by Caminata & Gorla, called being in generic coordinates....

We provide a novel view of public-key cryptography by showing full equivalences of certain primitives to "hard" monoid actions. More precisely, we show that key exchange and two-party computation are exactly equivalent to monoid actions with certain structural and hardness properties. To the best of our knowledge, this is the first "natural" characterization of the mathematical structure inherent to any key exchange or two-party computation protocol, and the first explicit proof of the...

We study succinct non-interactive arguments (SNARGs) and succinct non-interactive arguments of knowledge (SNARKs) for the class $\mathsf{UP}$ in the reusable designated verifier model. $\mathsf{UP}$ is an expressive subclass of $\mathsf{NP}$ consisting of all $\mathsf{NP}$ languages where each instance has at most one witness; a designated verifier SNARG (dvSNARG) is one where verification of the SNARG proof requires a private verification key; and such a dvSNARG is reusable if soundness...

Trusted setup is commonly used for non-interactive proof and argument systems. However, there is no guarantee that the setup parameters in these systems are generated in a trustworthy manner. Building upon previous works, we conduct a systematic study of non-interactive zero-knowledge arguments in the common reference string model where the authority running the trusted setup might be corrupted. We explore both zero-knowledge and soundness properties in this setting.  - We consider a new...

Masking is one of the most popular countermeasures to side- channel attacks, because it can offer provable security. However, depend- ing on the adversary’s model, useful security guarantees can be hard to provide. At first, masking has been shown secure against t-threshold probing adversaries by Ishai et al. at Crypto’03. It has then been shown secure in the more generic random probing model by Duc et al. at Euro- crypt’14. Prouff and Rivain have introduced the noisy leakage model...

The main goal of this work is to construct authenticated encryption (AE) that is both committing and leakage-resilient. As a first approach for this we consider generic composition as a well-known method for constructing AE schemes. While the leakage resilience of generic composition schemes has already been analyzed by Barwell et al. (AC'17), for committing security this is not the case. We fill this gap by providing a separate analysis of the generic composition paradigms with respect to...

Equivalence class signatures (EQS; Asiacrypt '14), sign vectors of elements from a bilinear group. Anyone can transform a signature on a vector to a signature on any multiple of that vector; signatures thus authenticate equivalence classes. A transformed signature/message pair is indistinguishable from a random signature on a random message. EQS have been used to efficiently instantiate (delegatable) anonymous credentials, (round-optimal) blind signatures, ring and group signatures,...

Over the past few decades, we have seen a proliferation of advanced cryptographic primitives with lossy or homomorphic properties built from various assumptions such as Quadratic Residuosity, Decisional Diffie-Hellman, and Learning with Errors. These primitives imply hard problems in the complexity class $\mathcal{SZK}$ (statistical zero-knowledge); as a consequence, they can only be based on assumptions that are broken in $\mathcal{BPP}^{\mathcal{SZK}}$. This poses a barrier for building...

BIKE is a post-quantum key encapsulation mechanism (KEM) selected for the 4th round of the NIST’s standardization campaign. It relies on the hardness of the syndrome decoding problem for quasi-cyclic codes and on the indistinguishability of the public key from a random element, and provides the most competitive performance among round 4 candidates, which makes it relevant for future real-world use cases. Analyzing its side-channel resistance has been highly encouraged by the community and...

A recent line of research has introduced a systematic approach to explore the complexity of explicit construction problems through the use of meta problems, namely, the range avoidance problem (abbrev. $\textsf{Avoid}$) and the remote point problem (abbrev. $\textsf{RPP}$). The upper and lower bounds for these meta problems provide a unified perspective on the complexity of specific explicit construction problems that were previously studied independently. An interesting question largely...

The security of code-based cryptography relies primarily on the hardness of decoding generic linear codes. Until very recently, all the best algorithms for solving the decoding problem were information set decoders ($\mathsf{ISD}$). However, recently a new algorithm called RLPN-decoding which relies on a completely different approach was introduced and it has been shown that RLPN outperforms significantly $\mathsf{ISD}$ decoders for a rather large range of rates. This RLPN decoder relies on...

Driven by the open problem raised by Hofheinz and Kiltz (Journal of Cryptology, 2012), we study the formalization of lattice-based programmable hash function (PHF), and give three types of concrete constructions by using several techniques such as a novel combination of cover-free sets and lattice trapdoors. Under the Inhomogeneous Small Integer Solution (ISIS) assumption, we show that any (non-trivial) lattice-based PHF is a collision-resistant hash function, which gives a direct...

We prove a tight parallel repetition theorem for $3$-message computationally-secure quantum interactive protocols between an efficient challenger and an efficient adversary. We also prove under plausible assumptions that the security of $4$-message computationally secure protocols does not generally decrease under parallel repetition. These mirror the classical results of Bellare, Impagliazzo, and Naor [BIN97]. Finally, we prove that all quantum argument systems can be generically compiled...

$\Sigma$-protocols are a widely utilized, relatively simple and well understood type of zero-knowledge proofs. However, the well known Schnorr $\Sigma$-protocol for proving knowledge of discrete logarithm in a cyclic group of known prime order, and similar protocols working over this type of groups, are hard to generalize to dealing with other groups. In particular with hidden order groups, due to the inability of the knowledge extractor to invert elements modulo the order. In this paper,...

An hard homogeneous space (HHS) is a finite group acting on a set with the group action being hard to invert and the set lacking any algebraic structure. As such HHS could potentially replace finite groups where the discrete logarithm is hard for building cryptographic primitives and protocols in a post-quantum world. Threshold HHS-based primitives typically require parties to compute the group action of a secret-shared input on a public set element. On one hand this could be done...

We propose a new notion of knowledge soundness, denoted rogue-instance security, for interactive and non-interactive batch knowledge proofs. Our notion, inspired by the standard notion of rogue-key security for multi-signature schemes, considers a setting in which a malicious prover is provided with an honestly-generated instance $x_1$, and may then be able to maliciously generate related "rogue" instances $x_2,\ldots,x_k$ for convincing a verifier in a batch knowledge proof of corresponding...

In this paper, we introduce $\mathsf{DeuringVUF}$, a new Verifiable Unpredictable Function (VUF) protocol based on isogenies between supersingular curves. The most interesting application of this VUF is $\mathsf{DeuringVRF}$ a post-quantum Verifiable Random Function (VRF). The main advantage of this new scheme is its compactness, with combined public key and proof size of roughly 450 bytes, which is orders of magnitude smaller than other generic purpose post-quantum VRF...

Constructing advanced cryptographic primitives such as obfuscation or broadcast encryption from standard hardness assumptions in the post quantum regime is an important area of research, which has met with limited success despite significant effort. It is therefore extremely important to find new, simple to state assumptions in this regime which can be used to fill this gap. An important step was taken recently by Wee (Eurocrypt '22) who identified two new assumptions from lattices, namely...

Anonymous or attribute-based credential (ABC) systems are a versatile and important cryptographic tool to achieve strong access control guarantees while simultaneously respecting the privacy of individuals. A major problem in the practical adoption of ABCs is their transferability, i.e., such credentials can easily be duplicated, shared or lent. One way to counter this problem is to tie ABCs to biometric features of the credential holder and to require biometric verification on every use....

Succinct arguments that rely on the Merkle-tree paradigm introduced by Kilian (STOC 92) suffer from larger proof sizes in practice due to the use of generic cryptographic primitives. In contrast, succinct arguments with the smallest proof sizes in practice exploit homomorphic commitments. However these latter are quantum insecure, unlike succinct arguments based on the Merkle-tree paradigm. A recent line of works seeks to address this limitation, by constructing quantum-safe succinct...

Non-Interactive Zero-Knowledge proofs (NIZK) allow a prover to convince a verifier that a statement is true by sending only one message and without conveying any other information. In the CRS model, many instantiations have been proposed from group-theoretic assumptions. On the one hand, some of these constructions use the group structure in a black-box way but rely on pairings, an example being the celebrated Groth-Sahai proof system. On the other hand, a recent line of research realized...

Group actions are fundamental mathematical tools, with a long history of use in cryptography. Indeed, the action of finite groups at the basis of the discrete logarithm problem is behind a very large portion of modern cryptographic systems. With the advent of post-quantum cryptography, however, the method for building protocols shifted towards a different paradigm, centered on the difficulty of discerning 'noisy' objects, as is the case for lattices, codes, and multivariate systems. This...

The generic-group model (GGM) aims to capture algorithms working over groups of prime order that only rely on the group operation, but do not exploit any additional structure given by the concrete implementation of the group. In it, it is possible to prove information-theoretic lower bounds on the hardness of problems like the discrete logarithm (DL) or computational Diffie-Hellman (CDH). Thus, since its introduction, it has served as a valuable tool to assess the concrete security provided...

In this work we first examine the hardness of solving various search problems by hybrid quantum-classical strategies, namely, by algorithms that have both quantum and classical capabilities. We then construct a hybrid quantum-classical search algorithm and analyze its success probability. Regarding the former, for search problems that are allowed to have multiple solutions and in which the input is sampled according to arbitrary distributions we establish their hybrid quantum-classical...

A sequential aggregate signature (SAS) scheme allows multiple users to sequentially combine their respective signatures in order to reduce communication costs. Historically, early proposals required the use of trapdoor permutation (e.g., RSA). In recent years, a number of attempts have been made to extend SAS schemes to post-quantum assumptions. Many post-quantum signatures have been proposed in the hash-and-sign paradigm, which requires the use of trapdoor functions and appears to be an...

This paper introduces a new family of CVE schemes built from generic errors (GE-CVE) and identifies a vulnerability therein. To introduce the problem, we generalize the concept of error sets beyond those defined by a metric, and use the set-theoretic difference operator to characterize when these error sets are detectable or correctable by codes. We prove the existence of a general, metric-less form of the Gilbert-Varshamov bound, and show that - like in the Hamming setting - a random code...

Oblivious Pseudorandom Functions (OPRFs) are an elementary building block in cryptographic and privacy-preserving applications. However, while there are numerous pre-quantum secure OPRF constructions, few options exist in a post-quantum secure setting, and of those even fewer are practical for modern-day applications. In this work, we focus on isogeny group actions, as the associated low bandwidth leads to efficient constructions. Our results focus on the Naor-Reingold OPRF. We introduce...

Public-key encryption with keyword search (PEKS) was first proposed by Boneh et al. (EUROCRYPT 2004), achieving the ability to search for ciphertext files. Nevertheless, it is vulnerable to inside keyword guessing attacks (IKGA). Public-key authenticated encryption with keyword search (PAEKS), introduced by Huang et al. (Inf. Sci. 2017), on the other hand, is secure against IKGA. Nonetheless, it is susceptible to quantum computing attacks. Liu et al. and Cheng et al. addressed this problem...

Secure Multi-Party Computation (MPC) is continuously becoming more and more practical. Many optimizations have been introduced, making MPC protocols more suitable for solving real-world problems. However, the MPC protocols and optimizations are usually implemented as a standalone proof of concept or in an MPC framework and are tightly coupled with special-purpose circuit formats, such as Bristol Format. This makes it very hard and time-consuming to re-use algorithmic advances and implemented...

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...

This is the second update of this report. In this update, we partially solve Open problem 2 and completely solve Open problem 3 from the previous version. By doing this we address one modification of the Panny's attack done by Nils Langius. In the first update we introduced conditions for choosing the parameters that render the attacks (both classical and quantum algorithms attacks) proposed by Lorenz Panny in March 2023 on the first variant, inapplicable. For the classical attack, we...

Is it possible to prove the deletion of a computer program after having executed it? While this task is clearly impossible using classical information alone, the laws of quantum mechanics may admit a solution to this problem. In this work, we propose a new approach to answer this question, using quantum information. In the interactive settings, we present the first fully-secure solution for blind delegation with certified deletion, assuming post-quantum hardness of the learning with errors...

We define the Generic Group Action Model (GGAM), an adaptation of the Generic Group Model to the setting of group actions (such as CSIDH). Compared to a previously proposed definition by Montgomery and Zhandry (ASIACRYPT'22), our GGAM more accurately abstracts the security properties of group actions. We are able to prove information-theoretic lower bounds in the GGAM for the discrete logarithm assumption, as well as for non-standard assumptions recently introduced in the setting of...

We introduce CorrGapCDH, the Gap Computational Diffie-Hellman problem in the multi-user setting with Corruptions. In the random oracle model, our assumption tightly implies the security of the authenticated key exchange protocols NAXOS in the eCK model and (a simplified version of) X3DH without ephemeral key reveal. We prove hardness of CorrGapCDH in the generic group model, with optimal bounds matching the one of the discrete logarithm problem. We also introduce CorrCRGapCDH, a stronger...

Adaptor signatures have seen wide applications in layer-2 and peer-to-peer blockchain ap- plications such as atomic swaps and payment channels. We first identify two shortcomings of previous literature on adaptor signatures. (1) Current aim of “script-less” adaptor signatures restricts instantiability, limiting designs based on BLS or current NIST PQC candidates. (2) We identify gaps in current formulations of security. In particular, we show that current notions do not rule out a class of...

Post-quantum signature schemes based on the MPC-in-the-Head (MPCitH) paradigm are recently attracting significant attention as their security solely depends on the one-wayness of the underlying primitive, providing diversity for the hardness assumption in post-quantum cryptography. Recent MPCitH-friendly ciphers have been designed using simple algebraic S-boxes operating on a large field in order to improve the performance of the resulting signature schemes. Due to their simple algebraic...

A *functional commitment* scheme enables a user to concisely commit to a function from a specified family, then later concisely and verifiably reveal values of the function at desired inputs. Useful special cases, which have seen applications across cryptography, include vector commitments and polynomial commitments. To date, functional commitments have been constructed (under falsifiable assumptions) only for functions that are essentially *linear*, with one recent exception that works...

A hash-and-sign signature based on a preimage-sampleable function (Gentry et al., STOC 2008) is secure in the quantum random oracle model if the preimage-sampleable function is collision-resistant (Boneh et al., ASIACRYPT 2011) or one-way (Zhandry, CRYPTO 2012). However, trapdoor functions in code-based and multivariate-quadratic-based signatures are not preimage-sampleable functions; for example, underlying trapdoor functions of the Courtois-Finiasz-Sendrier, Unbalanced Oil and Vinegar...

Impossible differential (ID), zero-correlation (ZC), and integral attacks are a family of important attacks on block ciphers. For example, the impossible differential attack was the first cryptanalytic attack on 7 rounds of AES. Evaluating the security of block ciphers against these attacks is very important but also challenging: Finding these attacks usually implies a combinatorial optimization problem involving many parameters and constraints that is very hard to solve using manual...

The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of information set decoders (ISD). A while ago, a generic decoding algorithm which does not belong to this family was proposed: statistical decoding. It is a randomized algorithm that requires the computation of a large set of parity-checks of moderate...

Blind signatures are a fascinating primitive which allow a user to obtain signatures from a signer, while hiding the message. Tremendously useful, these have been studied extensively for decades. Yet, to the best of our knowledge, all concretely practical blind signatures rely on non-standard assumptions and/or achieve sub-optimal round complexity. In this work, we provide an efficient, round-optimal (two-round) blind signature scheme from the hardness of the discrete log (DL) problem...

Introduced by von Ahn et al. (STOC’05), covert two-party computation is an appealing cryptographic primitive that allows Al- ice and Bob to securely evaluate a function on their secret inputs in a steganographic manner, i.e., even the existence of a computation is oblivious to each party - unless the output of the function is favourable to both. A prominent form of covert computation is covert authentica- tion, where Alice and Bob want to authenticate each other based on their credentials,...

In recent years, the number of applications of the repeated squaring assumption has been growing rapidly. The assumption states that, given a group element $x$, an integer $T$, and an RSA modulus $N$, it is hard to compute $x^{2^T} \mod N$---or even decide whether $y\stackrel{?}{=}x^{2^T} \mod N$---in parallel time less than the trivial approach of computing $T$ sequential squarings. This rise has been driven by efficient interactive proofs for repeated squaring, opening the door to more...

Verifiable random functions (VRFs) are a useful extension of pseudorandom functions for which it is possible to generate a proof that a certain image is indeed the correct function value (relative to a public verification key). Due to their strong soundness requirements on such proofs, VRFs are notoriously hard to construct, and existing constructions suffer either from complex proofs (for function images), or rely on complex and non-standard assumptions. In this work, we attempt to...

We propose MoNet, the first bi-directional payment channel network with unlimited lifetime for Monero. It is fully compatible with Monero without requiring any modification of the current Monero blockchain. MoNet preserves transaction fungibility, i.e., transactions over MoNet and Monero are indistinguishable, and guarantees anonymity of Monero and MoNet users by avoiding any potential privacy leakage introduced by the new payment channel network. We also propose a new crypto primitive,...

The dream of software obfuscation is to take programs, as they are, and then generically compile them into obfuscated versions that hide their secret inner workings. In this work we investigate notions of obfuscations weaker than virtual black-box (VBB) but which still allow obfuscating cryptographic primitives preserving their original functionalities as much as possible. In particular we propose two new notions of obfuscations, which we call oracle-differing-input obfuscation (odiO) and...

Identifying the concrete hardness of the discrete logarithm problem is crucial for instantiating a vast range of cryptographic schemes. Towards this goal, Corrigan-Gibbs and Kogan (EUROCRYPT '18) extended the generic-group model for capturing "preprocessing" algorithms, offering a tradeoff between the space $S$ required for storing their preprocessing information, the time $T$ required for their online phase, and their success probability. Corrigan-Gibbs and Kogan proved an upper bound of ...

The increasing use of blockchain-based cryptocurrencies like Bitcoin has run into inherent scalability limitations of blockchains. Payment channel networks, or PCNs, promise to greatly increase scalability by conducting the vast majority of transactions outside the blockchain while leveraging it as a final settlement protocol. Unfortunately, first-generation PCNs have significant privacy flaws. In particular, even though transactions are conducted off-chain, anonymity guarantees are very...

In known security reductions for the Fujisaki-Okamoto transformation, decryption failures are handled via a reduction solving the rather unnatural task of finding failing plaintexts \emph{given the private key}, resulting in a Grover search bound. Moreover, they require an implicit rejection mechanism for invalid ciphertexts to achieve a reasonable security bound in the QROM. We present a reduction that has neither of these deficiencies: We introduce two security games related to finding...

The algebraic group model (AGM), formalized by Fuchsbauer, Kiltz, and Loss, has recently received significant attention. One of the appealing properties of the AGM is that it is viewed as being (strictly) weaker than the generic group model (GGM), in the sense that hardness results for algebraic algorithms imply hardness results for generic algorithms, and generic reductions in the AGM (namely, between the algebraic formulations of two problems) imply generic reductions in the GGM. We...

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...

Blind signature schemes are one of the best-studied tools for privacy-preserving authentication. Unfortunately, known constructions of provably secure blind signatures either rely on non-standard hardness assumptions, or require parameters that grow linearly with the number of concurrently issued signatures, or involve prohibitively inefficient general techniques such as general secure two-party computation. Recently, Katz, Loss and Rosenberg (ASIACRYPT'21) gave a technique that, for the...

In this paper, we give the first formal security analysis on the one-more unforgeability of blind ECDSA. We start with giving a general attack on blind ECDSA, which is similar to the ROS attack on the blind Schnorr signature. We formulate the ECDSA-ROS problem to capture this attack. Next, we give a generic construction of blind ECDSA based on an additive homomorphic encryption and a corresponding zero-knowledge proof. Our concrete instantiation is about 40 times more bandwidth efficient...

Minimizing the energy cost and carbon footprint of the Bitcoin blockchain and related protocols is one of the most widely identified open questions in the cryptocurrency space. Substituting the proof-of-work (PoW) primitive in Nakamoto's longest chain protocol with a {\em proof of useful work} (PoUW) has been long theorized as an ideal solution in many respects but, to this day, the concept still lacks a convincingly secure realization. In this work we put forth Ofelimos, a novel PoUW-based...

We construct an efficient dynamic group signature (or more generally an accountable ring signature) from isogeny and lattice assumptions. Our group signature is based on a simple generic construction that can be instantiated by cryptographically hard group actions such as the CSIDH group action or an MLWE-based group action. The signature is of size $O(\log N)$, where $N$ is the number of users in the group. Our idea builds on the recent efficient OR-proof by Beullens, Katsumata, and...

A recent work of Benhamouda and Lin (TCC~'20) identified a dream version of secure multiparty computation (MPC), termed **Multiparty reusable Non-Interactive Secure Computation** (MrNISC), that combines at the same time several fundamental aspects of secure computation with standard simulation security into one primitive: round-optimality, succinctness, concurrency, and adaptivity. In more detail, MrNISC is essentially a two-round MPC protocol where the first round of messages serves as a...

Ring signatures enable a signer to sign a message on behalf of a group anonymously, without revealing her identity. Similarly, threshold ring signatures allow several signers to sign the same message on behalf of a group; while the combined signature reveals that some threshold $t$ of the group members signed the message, it does not leak anything else about the signers' identities. Anonymity is a central feature in threshold ring signature applications, such as whistleblowing, e-voting...

A ring signature allows a party to sign messages anonymously on behalf of a group, which is called ring. Traceable ring signatures are a variant of ring signatures that limits the anonymity guarantees, enforcing that a member can sign anonymously at most one message per tag. Namely, if a party signs two different messages for the same tag, it will be de-anomymized. This property is very useful in decentralized platforms to allow members to anonymously endorse statements in a...

The Schnorr identification and signature schemes have been amongst the most influential cryptographic protocols of the past three decades. Unfortunately, although the best-known attacks on these two schemes are via discrete-logarithm computation, the known approaches for basing their security on the hardness of the discrete logarithm problem encounter the ``square-root barrier''. In particular, in any group of order $p$ where Shoup's generic hardness result for the discrete logarithm problem...

In this work we introduce a new (circuit-dependent) homomorphic secret sharing (HSS) scheme for any $\log/\log\log$-local circuit, with communication proportional only to the width of the circuit and polynomial computation, which is secure assuming the super-polynomial hardness of learning parity with noise (LPN). At the heart of our new construction is a pseudorandom correlation generator (PCG) which allows two parties to locally stretch short seeds into pseudorandom instances of an...

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...

Starting with the work of Rivest et al. in 1996, timed assumptions have found many applications in cryptography, building e.g. the foundation of the blockchain technology. They also have been used in the context of classical MPC, e.g. to enable fairness. We follow this line of research to obtain composable generic MPC in the plain model. This approach comes with a major advantage regarding environmental friendliness, a property coined by Canetti et al. (FOCS 2013). Informally, this means...

The existence of one-way functions implies secure digital signatures, but not public-key encryption (at least in a black-box setting). Somewhat surprisingly, though, efficient public-key encryption schemes appear to be much easier to construct from concrete algebraic assumptions (such as the factoring of Diffie-Hellman-like assumptions) than efficient digital signature schemes. In this work, we provide one reason for this apparent difficulty to construct efficient signature...

Macroeconomic policy in a blockchain system concerns the algorithm that decides the payment schedule for miners and thus its money mint rate. It governs the amounts, distributions, beneficiaries and conditions required for money supply payments to participants by the system. While most chains today employ simple policies such as a constant amount per block, several cryptocurrencies have sprung up that put forth more interesting policies. As blockchains become a more popular form of money,...

The security of code-based cryptography usually relies on the hardness of the syndrome decoding (SD) problem for the Hamming weight. The best generic algorithms are all improvements of an old algorithm by Prange, and they are known under the name of Information Set Decoding (ISD) algorithms. This work aims to extend ISD algorithms’ scope by changing the underlying weight function and alphabet size of SD. More precisely, we show how to use Wagner’s algorithm in the ISD framework to solve SD...

Schnorr's signature scheme provides an elegant method to derive signatures with security rooted in the hardness of the discrete logarithm problem, which is a well-studied assumption and conducive to efficient cryptography. However, unlike pairing-based schemes which allow arbitrarily many signatures to be aggregated to a single constant sized signature, achieving significant non-interactive compression for Schnorr signatures and their variants has remained elusive. This work shows how to...

Secure function evaluation (SFE) allows Alice to publish an encrypted version of her input $m$ such that Bob (holding a circuit $C$) can send a single message that reveals $C(m)$ to Alice, and nothing more. Security is required to hold against malicious parties, that may behave arbitrarily. In this work we study the notion of SFE in the quantum setting, where Alice outputs an encrypted quantum state $|\psi>$ and learns $C(|\psi>)$ after receiving Bob's message. We show that, assuming the...

A hash function family $\mathcal{H}$ is correlation intractable for a $t$-input relation $\mathcal{R}$ if, given a random function $h$ chosen from $\mathcal{H}$, it is hard to find $x_1,\ldots,x_t$ such that $\mathcal{R}(x_1,\ldots,x_t,h(x_1),\ldots,h(x_t))$ is true. Among other applications, such hash functions are a crucial tool for instantiating the Fiat-Shamir heuristic in the plain model, including the only known NIZK for NP based on the learning with errors (LWE) problem (Peikert and...

Succinct non-interactive arguments (SNARGs) enable proofs of NP statements with very low communication. Recently, there has been significant work in both theory and practice on constructing SNARGs with very short proofs. Currently, the state-of-the-art in succinctness is due to Groth (Eurocrypt 2016) who constructed a SNARG from bilinear maps where the proof consists of just 3 group elements. In this work, we first construct a concretely-efficient designated-verifier (preprocessing) SNARG...

Attribute-based encryption (ABE) is an advanced form of encryption scheme allowing for access policies to be embedded within the secret keys and ciphertexts. By now, we have ABEs supporting numerous types of policies based on hardness assumptions over bilinear maps and lattices. However, one of the distinguishing differences between ABEs based on these two breeds of assumptions is that the former can achieve adaptive security for quite expressible policies (e.g., inner-products, boolean...

Although they have been studied for a long time, distributed signature protocols have garnered renewed interest in recent years in view of novel applications to topics like blockchains. Most recent works have focused on distributed versions of ECDSA or variants of Schnorr signatures, however, and in particular, little attention has been given to constructions based on post-quantum secure assumptions like the hardness of lattice problems. A few lattice-based threshold signature and...

We prove a tight lower bound on the number of group operations required for batch verification by any generic-group accumulator that stores a less-than-trivial amount of information. Specifically, we show that $\Omega(t \cdot (\lambda / \log \lambda))$ group operations are required for the batch verification of any subset of $t \geq 1$ elements, where $\lambda \in \mathbb{N}$ is the security parameter, thus ruling out non-trivial batch verification in the standard non-interactive...

We introduce the notion of a Succinct Parallelizable Argument of Knowledge (SPARK). This is an argument of knowledge with the following three efficiency properties for computing and proving a (non-deterministic, polynomial time) parallel RAM computation that can be computed in parallel time T with at most p processors: (1) The prover’s (parallel) running time is T + polylog(T * p). (In other words, the prover’s running time is essentially T for large computation times!) (2) The prover uses...

The Fiat-Shamir transform is a general method for reducing interaction in public-coin protocols by replacing the random verifier messages with deterministic hashes of the protocol transcript. The soundness of this transformation is usually heuristic and lacks a formal security proof. Instead, to argue security, one can rely on the random oracle methodology, which informally states that whenever a random oracle soundly instantiates Fiat-Shamir, a hash function that is ``sufficiently...

We present a generic forgery attack on signature schemes constructed from 5-round identification schemes made non-interactive with the Fiat-Shamir transform. The attack applies to ID schemes that use parallel repetition to decrease the soundness error. The attack can be mitigated by increasing the number of parallel repetitions, and our analysis of the attack facilitates parameter selection. We apply the attack to MQDSS, a post-quantum signature scheme relying on the hardness of the...

Despite the fundamental importance of delay functions, repeated squaring in RSA groups (Rivest, Shamir and Wagner '96) is the main candidate offering both a useful structure and a realistic level of practicality. Somewhat unsatisfyingly, its sequentiality is provided directly by assumption (i.e., the function is assumed to be a delay function). We prove sharp thresholds on the sequentiality of all generic-ring delay functions relative to an RSA modulus based on the hardness of factoring in...

Today's most compact zero-knowledge arguments are based on the hardness of the discrete logarithm problem and related classical assumptions. If one is interested in quantum-safe solutions, then all of the known techniques stem from the PCP-based framework of Kilian (STOC 92) which can be instantiated based on the hardness of any collision-resistant hash function. Both approaches produce asymptotically logarithmic sized arguments but, by exploiting extra algebraic structure, the discrete...