Currently, Gasper, the implemented consensus protocol of Ethereum, takes between 64 and 95 slots to finalize blocks. Because of that, a significant portion of the chain is susceptible to reorgs. The possibility to capture MEV (Maximum Extractable Value) through such reorgs can then disincentivize honestly following the protocol, breaking the desired correspondence of honest and rational behavior. Moreover, the relatively long time to finality forces users to choose between economic security and faster transaction confirmation. This motivates the study of the so-called single slot finality protocols: consensus protocols that finalize a block in each slot and, more importantly, that finalize the block proposed at a given slot within such slot. In this work we propose a simple, non-blackbox protocol that combines a synchronous dynamically available protocol with a partially synchronous finality gadget, resulting in a consensus protocol that can finalize one block per slot, paving the way to single slot finality within Ethereum. Importantly, the protocol we present can finalize the block proposed in a slot, within such slot.

Dynamic participation has recently become a crucial requirement for devising permissionless consensus protocols. This notion, originally formalized by Pass and Shi (ASIACRYPT 2017) through their "sleepy model", captures the essence of a system's ability to handle participants joining or leaving during a protocol execution. A dynamically available consensus protocol preserves safety and liveness while allowing dynamic participation. Blockchain protocols, such as Bitcoin's consensus protocol, have implicitly adopted this concept. In the context of Ethereum's consensus protocol, Gasper, Neu, Tas, and Tse (S&P 2021) presented an attack against LMD-GHOST -- the component of Gasper designed to ensure dynamic availability. Consequently, LMD-GHOST results unable to fulfill its intended function of providing dynamic availability for the protocol. Despite attempts to mitigate this issue, the modified protocol still does not achieve dynamic availability, highlighting the need for more secure dynamically available protocols. In this work, we present RLMD-GHOST, a synchronous consensus protocol that not only ensures dynamic availability but also maintains safety during bounded periods of asynchrony. This protocol is particularly appealing for practical systems where strict synchrony assumptions may not always hold, contrary to general assumptions in standard synchronous protocols. Additionally, we present the "generalized sleepy model", within which our results are proven. Building upon the original sleepy model proposed by Pass and Shi, our model extends it with more generalized and stronger constraints on the corruption and sleepiness power of the adversary. This approach allows us to explore a wide range of dynamic participation regimes, spanning from complete dynamic participation to no dynamic participation, i.e., with every participant online. Consequently, this model provides a foundation for analyzing dynamically available protocols.

Recent years have seen many advances in designing secure messaging protocols, aiming at provably strong security properties in theory or high efficiency for real-world practical deployment. However, important trade-off areas of the design space inbetween these elements have not yet been explored. In this work we design the first provably secure protocol that at the same time achieves (i) strong resilience against finegrained compromise, (ii) temporal privacy, and (iii) immediate decryption with constant-size overhead, notably, in the postquantum (PQ) setting. Besides these main design goals, we introduce a novel definition of offline deniability suitable for our setting, and prove that our protocol meets it, notably when combined with a PQ offline deniable initial key exchange.

In this note we assess the efficiency of a SIDH-based digital signature built on a weakened variant of a recent identification protocol proposed by Basso et al. Despite the devastating attacks against (the mathematical problem underlying) SIDH, this identification protocol remains secure, as its security is backed by a different (and more standard) isogeny-finding problem. We conduct our analysis by applying some known cryptographic techniques to decrease the signature size by about $70\%$ for all parameter sets (obtaining signatures of approximately 21 KB for SIKEp434). Moreover, we propose a minor optimisation to compute many isogenies in parallel from the same starting curve. Our assessment confirms that the problem of designing a practical isogeny-based signature scheme remains largely open. However, concretely determine the current state of the art which future optimisations can compare to appears to be of relevance for a problem which has witnessed only small steps towards a solution.

Recently, significant progress has been made toward quantumly secure multi-party computation (MPC) in the stand-alone setting. In sharp contrast, the picture of concurrently secure MPC (or even 2PC), for both classical and quantum functionalities, still remains unclear. Quantum information behaves in a fundamentally different way, making the job of adversary harder and easier at the same time. Thus, it is unclear if the positive or negative results from the classical setting still apply. This work initiates a systematic study of concurrent secure computation in the quantum setting. We obtain a mix of positive and negative results. We first show that assuming the existence of post-quantum one-way functions (PQ-OWFs), concurrently secure 2PC (and thus MPC) for quantum functionalities is impossible. Next, we focus on the bounded-concurrent setting, where we obtain simulation-sound zero-knowledge arguments for both NP and QMA, assuming PQ-OWFs. This is obtained by a new design of simulation-sound gadget, relying on the recent post-quantum non-malleable commitments by Liang, Pandey, and Yamakawa [FOCS'23], and the quantum rewinding strategy recently developed by Ananth, Chung, and La Placa [CRYPTO'21] for bounded-concurrent post-quantum ZK. Moreover, we show that our technique is general enough---It also leads to quantum-secure bounded-concurrent coin-flipping protocols, and eventually general-purpose 2PC and MPC, for both classical and quantum functionalities. All these constructions can be based on the quantum hardness of Learning with Errors.

Video conferencing apps like Zoom have hundreds of millions of daily users, making them a high-value target for surveillance and subversion. While such apps claim to achieve some forms of end-to-end encryption, they usually assume an incorruptible server that is able to identify and authenticate all the parties in a meeting. Concretely this means that, e.g., even when using the “end-to-end encrypted” setting, malicious Zoom servers could eavesdrop or impersonate in arbitrary groups. In this work, we show how security against malicious servers can be improved by changing the way in which such protocols use passwords (known as passcodes in Zoom) and integrating a password-authenticated key exchange (PAKE) protocol. To formally prove that our approach achieves its goals, we formalize a class of cryptographic protocols suitable for this setting, and define a basic security notion for them, in which group security can be achieved assuming the server is trusted to correctly authorize the group members. We prove that Zoom indeed meets this notion. We then propose a stronger security notion that can provide security against malicious servers, and propose a transformation that can achieve this notion. We show how we can apply our transformation to Zoom to provably achieve stronger security against malicious servers, notably without introducing new security elements.

In this paper we give nearly tight reductions for modern implicitly authenticated Diffie-Hellman protocols in the style of the Signal and Noise protocols, which are extremely simple and efficient. Unlike previous approaches, the combination of nearly tight proofs and efficient protocols enables the first real-world instantiations for which the parameters can be chosen in a theoretically sound manner, i.e., according to the bounds of the reductions. Specifically, our reductions have a security loss which is only linear in the number of users $\mu$ and constant in the number of sessions per user $\ell$. This is much better than most other key exchange proofs which are typically quadratic in the product $\mu \ell$. Combined with the simplicity of our protocols, this implies that our protocols are more efficient than the state of the art when soundly instantiated. We also prove that our security proofs are optimal: a linear loss in the number of users is unavoidable for our protocols for a large and natural class of reductions.

A Single Secret Leader Election (SSLE) enables a group of parties to randomly choose exactly one leader from the group with the restriction that the identity of the leader will be known to the chosen leader and nobody else. At a later time, the elected leader should be able to publicly reveal her identity and prove that she is the elected leader. The election process itself should work properly even if many registered users are passive and do not send any messages. SSLE is used to strengthen the security of proof-of-stake consensus protocols by ensuring that the identity of the block proposer remains unknown until the proposer publishes a block. Boneh, Eskandarian, Hanzlik, and Greco (AFT'20) defined the concept of an SSLE and gave several constructions. Their most efficient construction is based on the difficulty of the Decision Diffie-Hellman problem in a cyclic group. In this work we construct the first efficient SSLE protocols based on the standard Learning With Errors (LWE) problem on integer lattices, as well as the Ring-LWE problem. Both are believed to be post-quantum secure. Our constructions generalize the paradigm of Boneh et al. by introducing the concept of a re-randomizable commitment (RRC). We then construct several post-quantum RRC schemes from lattice assumptions and prove the security of the derived SSLE protocols. Constructing a lattice-based RRC scheme is non-trivial, and may be of independent interest.

Off-chain channel networks} are one of the most promising technologies for dealing with blockchain scalability and delayed finality issues. Parties connected within such networks can send coins to each other without interacting with the blockchain. Moreover, these payments can be ``routed'' over the network. Thanks to this, even the parties that do not have a channel in common can perform payments between each other with the help of intermediaries. In this paper, we introduce a new notion that we call ``Non-Atomic Payment Splitting (NAPS)'' protocols that allow the intermediaries in the network to split the payments recursively into several subpayments in such a way that the payment can be successful ``partially'' (i.e.~not all the requested amount may be transferred). This contrasts with the existing splitting techniques that are ``atomic'' in that they did not allow such partial payments (we compare the ``atomic'' and ``non-atomic'' approaches in the paper). We define NAPS formally and then present a protocol that we call ``EthNA'', that satisfies this definition. EthNA is based on very simple and efficient cryptographic tools; in particular, it does not use expensive cryptographic primitives. We implement a simple variant of EthNA in Solidity and provide some benchmarks. We also report on some experiments with routing using EthNA.

Digital Covid certificates are the first widely deployed end-user cryptographic certificates. For service providers, such as airlines or event ticket vendors, that needed to check that their (global) customers satisfy certain health policies, the verification of such Covid certificates was challenging though - not because of the cryptography involved, but due to the multitude of issuers, different certificate types and the evolving nature of country-specific policies that had to be supported. As Covid certificates contain sensitive health information, their (online) presentation to non-health related entities also poses clear privacy risk. To address both challenges, the EU proposed a specification for outsourcing the verification process to a validator service, that executes the process and informs service providers of the result. The WHO announced to adopt this approach for general vaccination credentials beyond Covid-19. While being beneficial to improve security and privacy for service providers, their solution requires strong trust assumption for the (central) validation service that learns all health-related details of the users. In our work, we propose and formally model a privacy-preserving variant of such an outsourced validation service. Therein the validator learns the attributes it is supposed to verify, but not the users identity. Still, the validator's assertion is blindly bound to the user's identity to ensure the desired user-binding. We analyze the EU specification in our model and show that it only meets a subset of those goals. Our analysis further shows that the EU protocol is unnecessarily complex and can be significantly simplified while maintaining the same (weak) level of security. Finally, we propose a new construction for privacy-preserving certificate validation that provably satisfies all desired goals.

Fair exchange (also referred to as atomic swap) is a fundamental operation in any cryptocurrency that allows users to atomically exchange coins. While a large body of work has been devoted to this problem, most solutions lack on-chain privacy. Thus, coins retain a public transaction history which is known to degrade the fungibility of a currency. This has led to a flourishing line of related research on fair exchange with privacy guarantees. Existing protocols either rely on heavy scripting (which also degrades fungibility and leads to high transaction fees), do not support atomic swaps across a wide range of currencies, or come with incomplete security proofs. To overcome these limitations, we introduce Sweep-UC (Read as Sweep Ur Coins.), the first fair exchange protocol that simultaneously is efficient, minimizes scripting, and is compatible with a wide range of currencies (more than the state of the art). We build Sweep-UC from modular sub-protocols and give a rigorous security analysis in the UC framework. Many of our tools and security definitions can be used in standalone fashion and may serve as useful components for future constructions of fair exchange.

Correlated secret randomness is a useful resource for secure computation protocols, often enabling dramatic speedups compared to protocols in the plain model. This has motivated a line of work on identifying and securely generating useful correlations. Different kinds of correlations can vary greatly in terms of usefulness and ease of generation. While there has been major progress on efficiently generating oblivious transfer (OT) correlations, other useful kinds of correlations are much more costly to generate. Thus, it is highly desirable to develop efficient techniques for securely converting copies of a given source correlation into copies of a given target correlation, especially when the former are cheaper to generate than the latter. In this work, we initiate a systematic study of such conversions that only involve a single uni-directional message. We refer to such a conversion as a one-message secure reduction (OMSR). Recent works (Agarwal et al, Eurocrypt 2022; Khorasgani et al, Eurocrypt 2022) studied a similar problem when no communication is allowed; this setting is quite restrictive, however, with few non-trivial conversions being feasible. The OMSR setting substantially expands the scope of feasible results, allowing for direct applications to existing MPC protocols. We obtain the following positive and negative results. - OMSR constructions. We present a general rejection-sampling based technique for OMSR with OT source correlations. We apply it to substantially improve in the communication complexity of optimized protocols for distributed symmetric cryptography (Dinur et al., Crypto 2021). - OMSR lower bounds. We develop general techniques for proving lower bounds on the communication complexity of OMSR, matching our positive results up to small constant factors.

Quantum key distribution (QKD) constitutes the most widespread family of information preservation techniques in the context of Quantum Cryptography. However, these techniques must deal with a series of technological challenges that prevent their efficient implementation, in space, as well as in exclusively terrestrial configurations. Moreover, the current smallsat constellations of Low Earth Orbit (LEO with an altitude of approx. 500 km) added to other satellites in Medium Earth Orbit (MEO), and geostationary orbits (GEO), plus a large amount of space debris present around the planet, have become a serious obstacle for Astronomy. In this work, a classic alternative to QKD is presented, also based on a symmetric key, but with low cost, and high efficiency, which dispenses with all the implementation problems present in the QKD protocols and does not require the use of satellites, and which we will call non-distributable key sharing (NDKS). Due to its low cost, simplicity of implementation, and high efficiency, NDKS is presented as an ideal solution to the problem of cybersecurity on the Internet of Things (IoT), in general, and IoT-fog-clouds, in particular.

We propose SublonK - a new zero-knowledge succinct non-interactive argument of knowledge (zkSNARK). SublonK builds on PlonK [EPRINT'19], a popular state-of-the-art practical zkSNARK. Our new construction preserves all the great features of PlonK, i.e., it supports constant size proofs, constant time proof verification, a circuit-independent universal setup, as well as support for custom gates and lookup gates. Moreover, SublonK achieves improved prover running time over PlonK. In PlonK, the prover runtime grows with circuit size. Instead, in Sublonk, the prover runtime grows with the size of the "active part" of the circuit. For instance, consider circuits encoding conditional execution, where only a fraction of the circuit is exercised by the input. For such circuits, the prover runtime in SublonK grows only with the exercised execution path. As an example, consider the zkRollup circuit. This circuit involves executing one of n code segments k times. For this case, using PlonK involves proving a circuit of size n.k code segments. In SublonK, the prover costs are close to proving a PlonK proof for a circuit of size roughly k code segments. Concretely, based on our implementation, for parameter choices derived from rollup contracts on Ethereum, n = 8, k = {2^{10},...,2^{16}}, the SublonK prover is approximately 4.6 times faster than the PlonK prover. Proofs in SublonK are 2.4KB, and can be verified in under 50ms.

We construct a falsifiable set (non-)membership NIZK $\Pi^*$ that is considerably more efficient than known falsifiable set (non-)membership NIZKs. It also has a universal CRS. $\Pi^*$ is based on the novel concept of determinantal accumulators. Determinantal primitives have a similar relation to recent pairing-based (non-succinct) NIZKs of Couteau and Hartmann (Crypto 2020) and Couteau et al. (CLPØ, Asiacrypt 2021) that structure-preserving primitives have to the Groth-Sahai NIZK. We also extend CLPØ by proposing efficient (non-succinct) set non-membership arguments for a large class of languages.

Zero-knowledge Succinct Non-interactive Arguments of Knowledge (zk-SNARKs) are the most efficient proof systems in terms of proof size and verification. Currently, Groth's scheme from EUROCRYPT 2016, $\textsf{Groth16}$, is the state-of-the-art and is widely deployed in practice. $\mathsf{Groth16}$ is originally proven to achieve knowledge soundness, which does not guarantee the non-malleability of proofs. There has been considerable progress in presenting new zk-SNARKs or modifying $\mathsf{Groth16}$ to efficiently achieve $\textit{strong}$ Simulation Extractability (SE), which is shown to be a necessary requirement in some applications. In this paper, we revise the Random Oracle (RO) based variant of $\mathsf{Groth16}$ proposed by Bowe and Gabizon, BG18, the most efficient one in terms of prover efficiency and CRS size among the candidates, and present a more efficient variant that saves $2$ pairings in the verification and $1$ group element in the proof. This supersedes our preliminary construction, presented in CANS 2020 [BPR20], which saved 1 pairing in the verification, and was proven in the Generic Group Model (GGM). Our new construction also improves on BG18 in that our proofs are in the Algebraic Group Model (AGM) with Random Oracles and reduces security to standard computational assumptions in bilinear groups (as opposed to using the full power of the GGM). We implement our proposed SE zk-SNARK along with BG18 in the $\textsf{Arkworks}$ library and compare the efficiency of our scheme with some related works. Our empirical experiences confirm that our SE zk-SNARK is more efficient than all previous SE schemes in most dimensions and it has very close efficiency to the original $\mathsf{Groth16}$.

Succinct Non-interactive Arguments of Knowledge (SNARKs) allow an untrusted prover to establish that it correctly ran some "witness-checking procedure" on a witness. A zkVM (short for zero-knowledge Virtual Machine) is a SNARK that allows the witness-checking procedure to be specified as a computer program written in the assembly language of a specific instruction set architecture (ISA). A $\textit{front-end}$ converts computer programs into a lower-level representation such as an arithmetic circuit or generalization thereof. A SNARK for circuit-satisfiability can then be applied to the resulting circuit. We describe a new front-end technique called Jolt that applies to a variety of ISAs. Jolt arguably realizes a vision called the $\textit{lookup singularity}$, which seeks to produce circuits that only perform lookups into pre-determined lookup tables. The circuits output by Jolt primarily perform lookups into a gigantic lookup table, of size more than $2^{128}$, that depends only on the ISA. The validity of the lookups are proved via a new $\textit{lookup argument}$ called Lasso described in a companion work (Setty, Thaler, and Wahby, e-print 2023). Although size-$2^{128}$ tables are vastly too large to materialize in full, the tables arising in Jolt are structured, avoiding costs that grow linearly with the table size. We describe performance and auditability benefits of Jolt compared to prior zkVMs, focusing on the popular RISC-V ISA as a concrete example. The dominant cost for the Jolt prover applied to this ISA (on $64$-bit data types) is cryptographically committing to about six $256$-bit field elements per step of the RISC-V CPU. This compares favorably to prior zkVM provers, even those focused on far simpler VMs.

Common verification steps in cryptographic protocols, such as signature or message authentication code checks or the validation of elliptic curve points, are crucial for the overall security of the protocol. Yet implementation errors omitting these steps easily remain unnoticed, as often the protocol will function perfectly anyways. One of the most prominent examples is Apple's goto fail bug where the erroneous certificate verification skipped over several of the required steps, marking invalid certificates as correctly verified. This vulnerability went undetected for at least 17 months. We propose here a mechanism which supports the detection of such errors on a cryptographic level. Instead of merely returning the binary acceptance decision, we let the verification return more fine-grained information in form of what we call a confirmation code. The reader may think of the confirmation code as disposable information produced as part of the relevant verification steps. In case of an implementation error like the goto fail bug, the confirmation code would then miss essential elements. The question arises now how to verify the confirmation code itself. We show how to use confirmation codes to tie security to basic functionality at the overall protocol level, making erroneous implementations be detected through the protocol not functioning properly. More concretely, we discuss the usage of confirmation codes in secure connections, established via a key exchange protocol and secured through the derived keys. If some verification steps in a key exchange protocol execution are faulty, then so will be the confirmation codes, and because we can let the confirmation codes enter key derivation, the connection of the two parties will eventually fail. In consequence, an implementation error like goto fail would now be detectable through a simple connection test.

A mutator set is a cryptographic data structure for authenticating operations on a changing set of data elements called items. Informally: - There is a short commitment to the set. - There are succinct membership proofs for elements of the set. - It is possible to update the commitment as well as the membership proofs with minimal effort as new items are added to the set or as existing items are removed from it. - Items cannot be removed before they were added. - It is difficult to link an item's addition to the set to its removal from the set, except when using information available only to the party that generated it. This paper formally defines the notion, motivates its existence with an application to scalable privacy in the context of cryptocurrencies, and proposes an instantiation inspired by Merkle mountain ranges and Bloom filters.

Private set union (PSU) allows two parties to compute the union of their sets without revealing anything else. It has been widely used in various applications. While several computationally efficient PSU protocols have been developed for the balanced case, they have a potential limitation in their communication complexity, which grows (super)-linearly with the size of the larger set. This poses a challenge when performing PSU in the unbalanced setting, where one party is a constrained device holding a small set, and another is a service provider holding a large set. In this work, we propose a generic construction of unbalanced PSU from leveled fully homomorphic encryption and a newly introduced protocol called permuted matrix private equality test. By instantiating the generic construction, we obtain two unbalanced PSU protocols whose communication complexity is linear in the size of the smaller set, and logarithmic in the larger set. We implement our protocols. Experiments demonstrate that our protocols outperform all previous protocols in the unbalanced setting. The larger difference between the sizes of two sets, the better our protocols perform. For input sets of sizes $2^{10}$ and $2^{20}$ with items of length $128$ bits, our PSU requires only $2.767$ MB of communication. Compared with the state-of-the-art PSU proposed by Zhang et al. (USENIX Security 2023), there are $37 \times$ shrink in communication and roughly $10 - 35 \times$ speedup in the running time depending on the network environments.

Secure aggregation enables a server to learn the sum of client-held vectors in a privacy-preserving way, and has been successfully applied to distributed statistical analysis and machine learning. In this paper, we both introduce a more efficient secure aggregation construction and extend secure aggregation by enabling input validation, in which the server can check that clients' inputs satisfy required constraints such as $L_0$, $L_2$, and $L_\infty$ bounds. This prevents malicious clients from gaining disproportionate influence on the computed aggregated statistics or machine learning model. Our new secure aggregation protocol improves the computational efficiency of the state-of-the-art protocol of Bell et al. (CCS 2020) both asymptotically and concretely: we show via experimental evaluation that it results in $2$-$8$X speedups in client computation in practical scenarios. Likewise, our extended protocol with input validation improves on prior work by more than $30$X in terms of client communiation (with comparable computation costs). Compared to the base protocols without input validation, the extended protocols incur only $0.1$X additional communication, and can process binary indicator vectors of length $1$M, or 16-bit dense vectors of length $250$K, in under $80$s of computation per client.

Fully secure multiparty computation (or guaranteed output delivery) among $n$ parties can be achieved with perfect security if the number of corruptions $t$ is less than $n/3$, or with statistical security with the help of a broadcast channel if $t<n/2$. In the case of $t<n/3$, it is known that it is possible to achieve linear communication complexity, but at a cost of having a round count of $\Omega(\mathsf{depth}(C) + n)$ in the worst case. The number of rounds can be reduced to $O(\mathsf{depth}(C))$ by either increasing communication, or assuming some correlated randomness (a setting also known as the preprocesing model). For $t<n/2$ it is also known that linear communication complexity is achievable, but at the cost of $\Omega(\mathsf{depth}(C) + n^2)$ rounds, due to the use of a technique called dispute control. However, in contrast to the $t<n/3$ setting, it is not known how to reduce this round count for $t<n/2$ to $O(\mathsf{depth}(C))$, neither allowing for larger communication, or by using correlated randomness. In this work we make progress in this direction by taking the second route above: we present a fully secure protocol for $t<n/2$ in the preprocessing model, that achieves linear communication complexity, and whose round complexity is only $O(\mathsf{depth}(C))$, without the additive $n^2$ term that appears from the use of dispute control. While on the $t<n/3$ such result requires circuits of width $\Omega(n)$, in our case circuits must be of width $\Omega(n^2)$, leaving it as an interesting future problem to reduce this gap. Our $O(\mathsf{depth}(C))$ round count is achieved by avoiding the use of dispute control entirely, relying on a different tool for guaranteeing output. In the $t<n/3$ setting when correlated randomness is available, this is done by using error correction to reconstruct secret-shared values, but in the $t<n/2$ case the equivalent is robust secret-sharing, which guarantees the reconstruction of a secret in spite of errors. However, we note that a direct use of such tool would lead to \emph{quadratic} communication, stemming from the fact that each party needs to authenticate their share towards each other party. At the crux of our techniques lies a novel method for reconstructing a batch of robustly secret-shared values while involving only a linear amount of communication per secret, which may also be of independent interest.

Many real-world group messaging systems delegate group administration to the application level, failing to provide formal guarantees related to group membership. Taking a cryptographic approach to group administration can prevent both implementation and protocol design pitfalls that result in a loss of confidentiality and consistency for group members. In this work, we introduce a cryptographic framework for the design of group messaging protocols that offer strong security guarantees for group membership. To this end, we extend the continuous group key agreement (CGKA) paradigm used in the ongoing IETF MLS group messaging standardisation process and introduce the administrated CGKA (A-CGKA) primitive. Our primitive natively enables a subset of group members, the group admins, to control the addition and removal of parties and to update their own keying material in a secure manner. We embed A-CGKA with a novel correctness notion which provides guarantees for group evolution and consistency, and a security model that prevents even corrupted (non-admin) members from forging messages that add new users to a group. Moreover, we present two efficient and modular constructions of group administrators that are correct and secure with respect to our definitions. Finally, we propose, implement, and benchmark an efficient extension of MLS that integrates cryptographic administrators. Our constructions admit little overhead over running a CGKA and can be extended to support advanced admin functionalities.

We give the first construction of a fully black-box round-optimal secure multiparty computation (MPC) protocol in the plain model. Our protocol makes black-box use of a sub-exponentially secure two-message statistical sender private oblivious transfer (SSP-OT), which in turn can be based on (sub-exponential variants of) almost all of the standard cryptographic assumptions known to imply public-key cryptography.

In this paper, we take inspiration from an invited talk presented at CBCrypto'23 to design identification protocols and signature schemes from group actions using the MPC-in-the-head paradigm. We prove the security of the given identification schemes and rely on the Fiat-Shamir transformation to turn them into signatures. We also establish a parallel with the technique used for the MPC-in-the-head approach and the seed tree method that has been recently used in some signature and ring signatures algorithms based on group action problems.

In this paper, we present a new quantum-resistant weak Verifiable Delay Function based on a purely algebraic construction. Its delay depends on computing a large-degree isogeny between elliptic curves, whereas its verification relies on the computation of isogenies between products of two elliptic curves. One of its major advantages is its expected fast verification time. However, it is important to note that the practical implementation of our theoretical framework poses significant challenges. We examine the strengths and weaknesses of our construction, analyze its security and provide a proof-of-concept implementation.

Witness Encryption is a holy grail of cryptography that remains elusive. It asks that a secret is only revealed when a particular computational problem is solved. Modern smart contracts and blockchains make assumptions of “honest majority”, which allow for a social implementation of Witness Encryption. The core idea is to make use of a partially trusted committee to carry out the responsibilities mandated by these functionalities – such as keeping the secret private, and then releasing it publicly after a solution to the computational puzzle is presented. We implement Witness Encryption (with public witness security) in the form of an open source smart contract that can be utilized as an oracle by others within the broader DeFi ecosystem. We devise a cryptoeconomic scheme to incentivize honest participation, and analyze its security under the honest majority and rational majority settings. We conclude by measuring and optimizing gas costs and illustrating the practicality of our scheme.

The accelerated advances in information communication technologies have made it possible for enterprises to deploy large scale applications in a multi-server architecture (also known as cloud computing environment). In this architecture, a mobile user can remotely obtain desired services over the Internet from multiple servers by initially executing a single registration on a trusted registration server (RS). Due to the hazardous nature of the Internet, to protect user privacy and online communication, a lot of multi-server authenticated-key-agreement (MSAKA) schemes have been furnished. However, all such designs lack in two very vital aspects, i.e., 1) no security under the partially trusted RS and 2) RS cannot control a user to access only a wanted combination of service-providing servers. To address these shortcomings, we present a new MSAKA protocol using self-certified public-key cryptography (SCPKC). We confirm the security of the proposed scheme by utilizing the well-known automated verification tool AVISPA and also provide a formal security proof in the random oracle model. Moreover, the software implementation of the proposed scheme, and a performance and security metrics comparison shows that it portrays a better security performance trade-off, and hence is more appropriate for real-life applications having resource constraint devices.

We put forth new protocols for oblivious transfer extension and vector OLE, called \emph{Silver}, for SILent Vole and oblivious transfER. Silver offers extremely high performances: generating 10 million random OTs on one core of a standard laptop requires only 300ms of computation and 122KB of communication. This represents 37% less computation and ~1300x less communication than the standard IKNP protocol, as well as ~4x less computation and ~4x less communication than the recent protocol of Yang et al. (CCS 2020). Silver is \emph{silent}: after a one-time cheap interaction, two parties can store small seeds, from which they can later \emph{locally} generate a large number of OTs \emph{while remaining offline}. Neither IKNP nor Yang et al. enjoys this feature; compared to the best known silent OT extension protocol of Boyle et al. (CCS 2019), upon which we build up, Silver has 19x less computation, and the same communication. Due to its attractive efficiency features, Silver yields major efficiency improvements in numerous MPC protocols. Our approach is a radical departure from the standard paradigm for building MPC protocols, in that we do \emph{not} attempt to base our constructions on a well-studied assumption. Rather, we follow an approach closer in spirit to the standard paradigm in the design of symmetric primitives: we identify a set of fundamental structural properties that allow us to withstand all known attacks, and put forth a candidate design, guided by our analysis. We also rely on extensive experimentations to analyze our candidate and experimentally validate their properties. In essence, our approach boils down to constructing new families of linear codes with (plausibly) high minimum distance and extremely low encoding time. While further analysis is of course warranted to confidently assess the security of Silver, we hope and believe that initiating this approach to the design of MPC primitives will pave the way to new secure primitives with extremely attractive efficiency features.

The task of achieving full security (with guaranteed output delivery) in secure multiparty computation (MPC) is a long-studied problem. Known impossibility results (Cleve, STOC 86) rule out general solutions in the dishonest majority setting. In this work, we consider solutions that use an external trusted party (TP) to bypass the impossibility results, and study the minimal requirements needed from this trusted party. In particular, we restrict ourselves to the extreme setting where the size of the TP is independent of the size of the functionality to be computed (called “small” TP) and this TP is invoked only once during the protocol execution. We present several positive and negative results for fully-secure MPC in this setting. -- For a natural class of protocols, specifically, those with a universal output decoder, we show that the size of the TP must necessarily be exponential in the number of parties. This result holds irrespective of the computational assumptions used in the protocol. The class of protocols to which our lower bound applies is broad enough to capture prior results in the area, implying that the prior techniques necessitate the use of an exponential-sized TP. We additionally rule out the possibility of achieving information-theoretic full security (without the restriction of using a universal output decoder) using a “small” TP in the plain model (i.e., without any setup). -- In order to get around the above negative result, we consider protocols without a universal output decoder. The main positive result in our work is a construction of such a fully-secure MPC protocol assuming the existence of a succinct Functional Encryption scheme. We also give evidence that such an assumption is likely to be necessary for fully-secure MPC in certain restricted settings. -- Finally, we explore the possibility of achieving full-security with a semi-honest TP that could collude with other malicious parties (which form a dishonest majority). In this setting, we show that even fairness is impossible to achieve regardless of the “small TP” requirement.

In this paper we continue the study of two-round broadcast-optimal MPC, where broadcast is used in one of the two rounds, but not in both. We consider the realistic scenario where the round that does not use broadcast is asynchronous. Since a first asynchronous round (even when followed by a round of broadcast) does not admit any secure computation, we introduce a new notion of asynchrony which we call $(t_d, t_m)$-asynchrony. In this new notion of asynchrony, an adversary can delay or drop up to $t_d$ of a given party's incoming messages; we refer to $t_d$ as the deafness threshold. Similarly, the adversary can delay or drop up to $t_m$ of a given party's outgoing messages; we refer to $t_m$ as the muteness threshold. We determine which notions of secure two-round computation are achievable when the first round is $(t_d, t_m)$-asynchronous, and the second round is over broadcast. Similarly, we determine which notions of secure two-round computation are achievable when the first round is over broadcast, and the second round is (fully) asynchronous. We consider the cases where a PKI is available, when only a CRS is available but private communication in the first round is possible, and the case when only a CRS is available and no private communication is possible before the parties have had a chance to exchange public keys.

An attribute-based credential system enables users to prove possession of a credential and statements over certified attributes to verifiers in zero-knowledge while maintaining anonymity and unlinkability. In a relational anonymous credential system, users can further prove their relationship to other entities in their social graph, such as position in an organizational hierarchy or friends-of-friends status in an online social network graph, while protecting their own privacy and that of other users involved in the social graph. While traditional anonymous credential schemes make no provisions for privacy-preserving relationship predicates, a relational credential system is more usable, because it can facilitate relationship-based access control with a wide range of predicates and offers strong privacy guarantees for relationship proofs. We propose the first relational credential scheme, based on a new $q$-SDH graph signature scheme and an efficient zero-knowledge proof system for graph predicates. We rigorously prove the security for the proposed scheme and provide a benchmark using Facebook social graphs.

Byzantine fault-tolerant state machine replication (BFT-SMR) replicates a state machine across a set of replicas, and processes requests as a single machine even in the presence of Byzantine faults. Recently, synchronous BFT-SMRs have received tremendous attention due to their simple design and high fault-tolerance threshold. In this paper, we propose Arena, the first multi-leader synchronous BFT-SMR. Thanks to the synchrony assumption, Arena gains the performance benefit from multi-leader with a much simpler design (compared to other partially synchronous multi-leader designs). Furthermore, it is more robust: ``no progress'' of a leader will not trigger a view-change. Our experimental results show that Arena achieves a peak throughput of up to 7.7$\times$ higher than the state-of-the-art.

Zero-Knowledge protocols have increasingly become both popular and practical in recent years due to their applicability in many areas such as blockchain systems. Unfortunately, public verifiability and small proof sizes of zero-knowledge protocols currently come at the price of strong assumptions, large prover time, or both, when considering statements with millions of gates. In this regime, the most prover-efficient protocols are in the designated verifier setting, where proofs are only valid to a single party that must keep a secret state. In this work, we bridge this gap between designated-verifier proofs and public verifiability by distributing the verifier. Here, a set of verifiers can then verify a proof and, if a given threshold $t$ of the $n$ verifiers is honest and trusted, can act as guarantors for the validity of a statement. We achieve this while keeping the concrete efficiency of current designated-verifier proofs, and present constructions that have small concrete computation and communication cost. We present practical protocols in the setting of threshold verifiers with $t<n/4$ and $t<n/3$, for which we give performance figures, showcasing the efficiency of our approach.

A secret-sharing scheme enables a dealer, holding a secret string, to distribute shares to parties such that only pre-defined authorized subsets of parties can reconstruct the secret. The collection of authorized sets is called an access structure. There is a huge gap between the best known upper bounds on the share size of a secret-sharing scheme realizing an arbitrary access structure and the best known lower bounds on the size of these shares. For an arbitrary $n$-party access structure, the best known upper bound on the share size is $2^{O(n)}$. On the other hand, the best known lower bound on the total share size is much smaller, i.e., $\Omega(n^2/\log (n))$ [Csirmaz, \emph{Studia Sci. Math. Hungar.}]. This lower bound was proved more than 25 years ago and no major progress has been made since. In this paper, we study secret-sharing schemes for $k$-hypergraphs, i.e., for access structures where all minimal authorized sets are of size exactly $k$ (however, unauthorized sets can be larger). We consider the case where $k$ is small, i.e., constant or at most $\log (n)$. The trivial upper bound for these access structures is $O(n\cdot \binom{n-1}{k-1})$ and this can be slightly improved. If there were efficient secret-sharing schemes for such $k$-hypergraphs (e.g., $2$-hypergraphs or $3$-hypergraphs), then we would be able to construct secret-sharing schemes for arbitrary access structures that are better than the best known schemes. Thus, understanding the share size required for $k$-hypergraphs is important. Prior to our work, the best known lower bound for these access structures was $\Omega(n \log (n))$, which holds already for graphs (i.e., $2$-hypergraphs). We improve this lower bound, proving a lower bound of $\Omega(n^{2-1/(k-1)}/k)$ on the total share size for some explicit $k$-hypergraphs, where $3 \leq k \leq \log (n)$. For example, for $3$-hypergraphs we prove a lower bound of $\Omega(n^{3/2})$. For $\log (n)$-hypergraphs, we prove a lower bound of $\Omega(n^{2}/\log (n))$, i.e., we show that the lower bound of Csirmaz holds already when all minimal authorized sets are of size $\log (n)$. Our proof is simple and shows that the lower bound of Csirmaz holds for a simple variant of the access structure considered by Csirmaz. Using our results, we prove a near quadratic separation between the required share size for realizing an explicit access structure and the monotone circuit size describing the access structure,i.e., the share size in $\Omega(n^2/\log(n))$ and the monotone circuit size is $O(n\log(n))$ (where the circuit has depth $3$).

We present a new framework for building round-optimal (two-round) $adaptively$ secure MPC. We show that a relatively weak notion of OT that we call $indistinguishability \ OT \ with \ receiver \ oblivious \ sampleability$ (r-iOT) is enough to build two-round, adaptively secure MPC against $malicious$ adversaries in the CRS model. We then show how to construct r-iOT from CDH, LPN, or isogeny-based assumptions that can be viewed as group actions (such as CSIDH and CSI-FiSh). This yields the first constructions of two-round adaptively secure MPC against malicious adversaries from CDH, LPN, or isogeny-based assumptions. We further extend our non-isogeny results to the plain model, achieving (to our knowledge) the first construction of two-round adaptively secure MPC against semi-honest adversaries in the plain model from LPN. Our results allow us to build a two-round adaptively secure MPC against malicious adversaries from essentially all of the well-studied assumptions in cryptography. In addition, our constructions from isogenies or LPN provide the first post-quantum alternatives to LWE-based constructions for round-optimal adaptively secure MPC. Along the way, we show that r-iOT also implies non-committing encryption(NCE), thereby yielding the first constructions of NCE from isogenies or LPN.

Structure-Aware private set intersection (sa-PSI) is a variant of PSI where Alice's input set $A$ has some publicly known structure, Bob's input $B$ is an unstructured set of points, and Alice learns the intersection $A \cap B$. sa-PSI was recently introduced by Garimella et al. (Crypto 2022), who described a semi-honest protocol with communication that scales with the description size of Alice's set, instead of its cardinality. In this paper, we present the first sa-PSI protocol secure against malicious adversaries. sa-PSI protocols are built from function secret sharing (FSS) schemes, and the main challenge in our work is ensuring that multiple FSS sharings encode the same structured set. We do so using a cut-and-choose approach. In order to make FSS compatible with cut-and-choose, we introduce a new variant of function secret sharing, called derandomizable FSS (dFSS). We show how to construct dFSS for union of geometric balls, leading to a malicious-secure sa-PSI protocol where Alice's input is a union of balls. We also improve prior FSS constructions, giving asymptotic improvements to semi-honest sa-PSI.

This technical paper explores two solutions for arithmetization of computational integrity statements in STARKs, namely the algebraic intermediate representation, AIR, and is preprocessed variant, PAIR. The work then focuses on their soundness implications for Reed-Solomon proximity testing. It proceeds by presenting a comparative study of these methods, providing their theoretical foundations and deriving the degree bounds for low-degree proximity testing. The study shows that using PAIR increases the degree bound for Reed-Solomon proximity testing, which affects its soundness and complexity. However, the possibility of reducing the degree bound with multiple selector columns is also explored, namely by following an approach based on the decomposition of the selector values. Focusing on performance optimization, the work proceeds by qualitatively comparing computational demands of the components of both arithmetization methods, particularly their impact on the low-degree extensions. The paper concludes that, while PAIR might simplify constraint enforcement, it can be easily translated to AIR, and system testing with benchmarks is necessary to determine the application-specific superiority of either method. This work should provide insight into the strengths and limitations of each method, helping researchers and practitioners in the field of STARKs make informed design choices.

Subversion-resistant zk-SNARKs allow the provers to verify the Structured Reference String (SRS), via an SRS Verification (SV) algorithm and bypass the need for a Trusted Third Party (TTP). Pairing-based zk-SNARKs with \(updatable\) and \(universal\) SRS are an extension of subversion-resistant ones which additionally allow the verifiers to update the SRS, via an SRS Updating (SU) algorithm, and similarly bypass the need for a TTP. In this paper, we examine the setup of these zk-SNARKs by benchmarking the efficiency of the SV and SU algorithms within the \(\textsf{Arkworks}\) library. The benchmarking covers a range of updatable zk-SNARKs, including Sonic, Plonk, Marlin, Lunar, and Basilisk. Our analysis reveals that relying solely on the standard Algebraic Group Model (AGM) may not be sufficient in practice, and we may need a model with weaker assumptions. Specifically, we find that while Marlin is secure in the AGM, additional elements need to be added to its SRS to formally prove certain security properties in the updatable CRS model. We demonstrate that the SV algorithms become inefficient for mid-sized circuits with over 20,000 multiplication gates and 100 updates. To address this, we introduce Batched SV algorithms (BSV) that leverage standard batching techniques and offer significantly improved performance. As a tool, we propose an efficient verification approach that allows the parties to identify a malicious SRS updater with logarithmic verification in the number of updates. In the case of Basilisk, for a circuit with \(2^{20}\) multiplication gates, a \(1000\)-time updated SRS can be verified in less than 30 sec, a malicious updater can be identified in less than 4 min (improvable by pre-computation), and each update takes less than 6 min.

The efficiency of blockchain systems is often compared to popular credit card networks with respect to the transactions per second rate. This seems to be an unfair comparison since these networks do not complete a transaction from beginning to end. Rather they buy the risk and settle it much later. Typically transactions have only two players, the payer and the payee, and the settlement of this transaction requires time since it depends on basic properties of the consensus protocol. In practice, the payee, very often, needs to wait for confirmation in order to ship the traded goods. Alternatively, the payee, or merchant, can ship it in faith that the transaction will be confirmed. Our contribution, the Maravedí Protocol, introduces a third player to minimize the risk of the payee to be left without the payment even without the consensus layer confirmation. The main idea is that the third player can work similarly to a credit card company. That is, it buys the risk from the merchant, by a small discount, and allows the third player to pay it instantaneously via a payment-channel like protocol. In parallel, the third player receives the regular payment transaction from the payer that can be settled on the chain, thus, after waiting the consensus/blockchain required time. Moreover, the on-chain transaction pays the full amount, allowing the third player to cash in the discount. Hence, on the side of the merchant, our protocol puts forth instantaneous finality in a novel way to the best of our knowledge.

Blockchain protocols have revolutionized the way individuals and devices can interact and transact over the internet. More recently, a trend has emerged to harness blockchain technology as a catalyst to enable advanced security features in distributed applications, in particular fairness. However, the tools employed to achieve these security features are either resource wasteful (e.g., time-lock primitives) or only efficient in theory (e.g., witness encryption). We present McFly, a protocol that allows one to efficiently ``encrypt a message to the future'' such that the receiver can decrypt the message almost effortlessly. Towards this goal, we design and implement a novel primitive we call signature-based witness encryption and combine it with a BFT blockchain (or a blockchain finality layer) in such a way that the decryption of the message can be piggybacked on the tasks already performed by the blockchain committee, resulting in almost-for-free decryption. To demonstrate the practicality of the McFly protocol, we implemented our signature-based witness encryption scheme and evaluated it on a standard laptop with Intel i7 @2,3 GHz. For the popular BLS12-381 curve, a $381$-bit message and a committee of size $500$ the encryption time is $9.8s$ and decryption is $14.8 s$. The scheme remains practical for a committee of size $2000$ with an encryption time of $58 s$ and decryption time of $218 s$.

The Internet of Things (IoT)-enabled ride sharing is one of the most transforming and innovative technologies in the transportation industry. It has myriads of advantages, but with increasing demands there are security concerns as well. Traditionally, cryptographic methods are used to address the security and privacy concerns in a ride sharing system. Unfortunately, due to the emergence of quantum algorithms, these cryptographic protocols may not remain secure. Hence, there is a necessity for privacy-preserving ride sharing protocols which can resist various attacks against quantum computers. In the domain of privacy preserving ride sharing, a threshold private set intersection (TPSI) can be adopted as a viable solution because it enables the users to determine the intersection of private data sets if the set intersection cardinality is greater than or equal to a threshold value. Although TPSI can help to alleviate privacy concerns, none of the existing TPSI is quantum secure. Furthermore, the existing TPSI faces the issue of long-term security. In contrast to classical and post quantum cryptography, quantum cryptography (QC) provides a more robust solution, where QC is based on the postulates of quantum physics (e.g., Heisenberg uncertainty principle, no cloning theorem, etc.) and it can handle the prevailing issues of quantum threat and long-term security. Herein, we propose the first QC based TPSI protocol which has a direct application in privacy preserving ride sharing. Due to the use of QC, our IoT-enabled ride sharing scheme remains quantum secure and achieves long-term security as well.

Over the last few years, Internet of Medical Things (IoMT) has completely transformed the healthcare industry. It is bringing out the most notable, and unprecedented impacts on human health, and has totally changed the way we look at the healthcare industry. The healthcare sector all around the globe are leapfrogging, and adopting the technology, helping in transforming drastically in a very short span of time. However, as more and more number of medical devices are being connected to IoMT, security issues like ensuring authenticity and integrity of the transmitted data are also on the rise. In view of the context, there is a need of an efficient cryptographic primitive that can address these issues in a viable manner. A signature scheme seems to be the natural choice to mitigate the security concerns. But, traditional signature schemes, both PKI-based and Identity-based have their own disadvantages which makes them unsuitable for IoMT networks. Thus, to address the security issues and problems like certificate management and key escrow, herein, we put forward the {\em first} multivariate based certificateless signature scheme, namely {\sf Mul-CLS}, which is built on top of the intractability of multivariate-quadratic (MQ) problem. The fact that multivariate public key cryptosystem (MPKC) provides fast, post-quantum safe, and efficient primitives, makes it a front runner candidate among the other post-quantum cryptography candidates. Our scheme {\sf Mul-CLS} provides existential unforgeability against chosen message and chosen identity Super Type I and Super Type II adversary if solving the MQ problem is NP-hard. In addition to that, our proposed {\sf Mul-CLS} presents itself as a robust and cost-friendly cryptographic building block for building IoMT networks.

Decentralized finance based on blockchain has experienced rapid development. To safeguard the privacy of participants, decentralized anonymous payment (DAP) systems such as ZCash and Zether have emerged. These systems employ cryptographic techniques to conceal the trader addresses and payment amounts. However, this anonymity presents challenges in terms of regulation. To address this issue, we propose the Walsh-DAP (WDAP) scheme, an efficient and generic regulation scheme for decentralized anonymous payments that strikes a balance between regulation and privacy preservation. Our scheme introduces two regulation policies: first, users who have exceeded their spending limits within a certain period will be identified during the regulation process; second, the supervisor possesses the capability to trace any anonymous transaction. To implement regulation effectively, we have designed an innovative commitment scheme, Walsh commitment, which leverages the orthogonal properties of Walsh codes to achieve the features of aggregation and extraction. The supervisor in WDAP only needs to deal with the aggregation result of the Walsh commitments instead of the huge amount of raw transactions information, which greatly increases the efficiency. In a DAP system with 256 users, 10 transaction per second and 30 days as a regulation period, we reduced the communication cost for regulation from 14 GB to 94.20 KB, and the computing cost from $\text{1.6}\times \text{10}^{\text{5}}$ s to 2.17 s. Both improvement is of over five orders of magnitude. We formally discussed the security of the whole system, and verified its feasibility and practicability in the ZCash system.

This paper introduces arithmetic sketching, an abstraction of a primitive that several previous works use to achieve lightweight, low-communication zero-knowledge verification of secret-shared vectors. An arithmetic sketching scheme for a language $\mathcal{L} \in \mathbb{F}^n$ consists of (1) a randomized linear function compressing a long input x to a short “sketch,” and (2) a small arithmetic circuit that accepts the sketch if and only if $x \in \mathcal{L}$, up to some small error. If the language $\mathcal{L}$ has an arithmetic sketching scheme with short sketches, then it is possible to test membership in $\mathcal{L}$ using an arithmetic circuit with few multiplication gates. Since multiplications are the dominant cost in protocols for computation on secret-shared, encrypted, and committed data, arithmetic sketching schemes give rise to lightweight protocols in each of these settings. Beyond the formalization of arithmetic sketching, our contributions are: – A general framework for constructing arithmetic sketching schemes from algebraic varieties. This framework unifies schemes from prior work and gives rise to schemes for useful new languages and with improved soundness error. – The first arithmetic sketching schemes for languages of sparse vectors: vectors with bounded Hamming weight, bounded $L_1$ norm, and vectors whose few non-zero values satisfy a given predicate. – A method for “compiling” any arithmetic sketching scheme for a language $\mathcal{L}$ into a low-communication malicious-secure multi-server protocol for securely testing that a client-provided secret-shared vector is in $\mathcal{L}$. We also prove the first nontrivial lower bounds showing limits on the sketch size for certain languages (e.g., vectors of Hamming-weight one) and proving the non-existence of arithmetic sketching schemes for others (e.g., the language of all vectors that contain a specific value).

YOSO-style MPC protocols (Gentry et al., Crypto'21), are a promising framework where the overall computation is partitioned into small, short-lived pieces, delegated to subsets of one-time stateless parties. Such protocols enable gaining from the security benefits provided by using a large community of participants where "mass corruption" of a large fraction of participants is considered unlikely, while keeping the computational and communication costs manageable. However, fully realizing and analyzing YOSO-style protocols has proven to be challenging: While different components have been defined and realized in various works, there is a dearth of protocols that have reasonable efficiency and enjoy full end to end security against adaptive adversaries. The YOSO model separates the protocol design, specifying the short-lived responsibilities, from the mechanisms assigning these responsibilities to machines participating in the computation. These protocol designs must then be translated to run directly on the machines, while preserving security guarantees. We provide a versatile and modular framework for analyzing the security of YOSO-style protocols, and show how to use it to compile any protocol design that is secure against static corruptions of $t$ out of $c$ parties, into protocols that withstand adaptive corruption of $T$ out of $N$ machines (where $T/N$ is closely related to $t/c$, specifically when $t/c<0.5$, we tolerate $T/N \leq 0.29$) at overall communication cost that is comparable to that of the traditional protocol even when $c << N$. Furthermore, we demonstrate how to minimize the use of costly non-committing encryption, thereby keeping the computational and communication overhead manageable even in practical terms, while still providing end to end security analysis. Combined with existing approaches for transforming stateful protocols into stateless ones while preserving static security (e.g. Gentry et al. 21, Kolby et al. 22), we obtain end to end security.

The Elliptic Curve Digital Signature Algorithm (ECDSA) is one of the most widely used schemes in deployed cryptography. Through its applications in code and binary authentication, web security, and cryptocurrency, it is likely one of the few cryptographic algorithms encountered on a daily basis by the average person. However, its design is such that executing multi-party or threshold signatures in a secure manner is challenging: unlike other, less widespread signature schemes, secure multi-party ECDSA requires custom protocols, which has heretofore implied reliance upon additional cryptographic assumptions and primitives such as the Paillier cryptosystem. We propose new protocols for multi-party ECDSA key-generation and signing with a threshold of two, which we prove secure against malicious adversaries in the Random Oracle Model using only the Computational Diffie-Hellman Assumption and the assumptions already relied upon by ECDSA itself. Our scheme requires only two messages, and via implementation we find that it outperforms the best prior results in practice by a factor of 56 for key generation and 11 for signing, coming to within a factor of 18 of local signatures. Concretely, two parties can jointly sign a message in just over three milliseconds. This document is an updated version. A new preface includes errata and notes relevant to the original work, and a brief description of a revised protocol with a revised proof. The original paper appears in unedited form at the end. The authors consider this work to be fully subsumed by the more recent three-round protocol of Doerner, Kondi, Lee, and shelat (2023), and direct new readers to that work.

Messaging platforms like Signal are widely deployed and provide strong security in an asynchronous setting. It is a challenging problem to construct a protocol with similar security guarantees that can \emph{efficiently} scale to large groups. A major bottleneck are the frequent key rotations users need to perform to achieve post compromise forward security. In current proposals -- most notably in TreeKEM (which is part of the IETF's Messaging Layer Security (MLS) protocol draft) -- for users in a group of size $n$ to rotate their keys, they must each craft a message of size $\log(n)$ to be broadcast to the group using an (untrusted) delivery server. In larger groups, having users sequentially rotate their keys requires too much bandwidth (or takes too long), so variants allowing any $T \leq n$ users to simultaneously rotate their keys in just $2$ communication rounds have been suggested (e.g. "Propose and Commit" by MLS). Unfortunately, $2$-round concurrent updates are either damaging or expensive (or both); i.e. they either result in future operations being more costly (e.g. via "blanking'' or "tainting'') or are costly themselves requiring $\Omega(T)$ communication for each user [Bienstock et al., TCC'20]. In this paper we propose CoCoA; a scheme that allows for $T$ concurrent updates that are neither damaging nor costly. That is, they add no cost to future operations yet they only require $\Omega(\log^2(n))$ communication per user. To circumvent the [Bienstock et al.] lower bound, CoCoA increases the number of rounds needed to complete all updates from $2$ up to (at most) $\log(n)$; though typically fewer rounds are needed. The key insight of the protocol is the following: in the (non-concurrent version of) TreeKEM, a delivery server which gets $T$ concurrent update requests will approve one and reject the remaining $T-1$. In contrast, our server attempts to apply all of them. If more than one user requests to rotate the same key during a round, the server arbitrarily picks a winner. Surprisingly, we prove that regardless of how the server chooses the winners, all previously compromised users will recover after at most $\log(n)$ such update rounds. To keep the communication complexity low, CoCoA is a server-aided CGKA. That is, the delivery server no longer blindly forwards packets, but instead actively computes individualized packets tailored to each user. As the server is untrusted, this change requires us to develop new mechanisms ensuring robustness of the protocol.

Zero-knowledge proofs are a cryptographic cornerstone of privacy-preserving technologies such as "Confidential Transactions" (CT), which aims at hiding monetary amounts in cryptocurrency transactions. Due to its asymptotically logarithmic proof size and transparent setup, most state-of-the-art CT protocols use the Bulletproofs (BP) zero-knowledge proof system for set membership proofs such as range proofs. However, even taking into account recent efficiency improvements, BP comes with a serious overhead in terms of concrete proof size as well as verifier running time and thus puts a large burden on practical deployments of CT and its extensions. In this work, we introduce Bulletproofs++ (BP++), a drop-in replacement for BP that improves its concrete efficiency and compactness significantly. As for BP, the security of BP++ relies only on the hardness of the discrete logarithm problem in the random oracle model, and BP++ retains all features of Bulletproofs including transparent setup and support for proof aggregation, multi-party proving and batch verification. Asymptotically, BP++ range proofs require only $O(n / \log n)$ group scalar multiplications compared to $O(n)$ for BP and BP+. At the heart of our construction are novel techniques for permutation and set membership, which enable us to prove statements encoded as arithmetic circuits very efficiently. Concretely, a single BP++ range proof to establish that a committed value is in a 64-bit range (as commonly required by CT) is just 416 bytes over a 256-bit elliptic curve, 38\% smaller than an equivalent BP and 27\% smaller than BP+. When instantiated using the secp256k1 curve as used in Bitcoin, our benchmarks show that proving is about 5 times faster than BP and verification is about 3 times faster than BP. When aggregating 32 range proofs, proving and verification are about 9.5 times and 5.5 times faster, respectively.

Verifiable timed commitments serve as cryptographic tools that enable the binding of information to specific time intervals. By integrating these commitments into signature schemes, secure and tamper-evident digital signatures can be generated, ensuring the integrity of time-sensitive mechanisms. This article delves into the concept of verifiable timed commitments and explores their efficient applications in digital signature constructions. Specifically, it focuses on two important signature schemes: proxy signatures and multi-signatures. The idea of the timed proxy signature is to enable the delegation of signing rights for a specified period, allowing designated entities to sign messages on behalf of the original signer. On the other hand, multi-signatures allow multiple parties to collectively generate a single signature, ensuring enhanced security and accountability. The article presents an in-depth analysis of the underlying mechanisms, discussing their properties, strengths, and computational complexity. Through this exploration, the article aims to shed light on the potential of verifiable timed commitments and inspire further research in this evolving field of cryptography.

Commodity encrypted storage platforms (e.g., IceDrive, pCloud) permit data store and sharing across multiple users while preserving data confidentiality. However, end-to-end encryption may not be sufficient since it only offers confidentiality when the data is at rest or in transit. Meanwhile, sensitive information can be leaked from metadata representing activities during data operations (e.g., query, processing). Recent encrypted search platforms such as DORY (OSDI’20) or DURASIFT (WPES’19) permit multi-user data query functionalities, while protecting metadata privacy. However, they either incur a high processing overhead or offer limited secu- rity/functionality, and require strong trust assumptions. We propose MAPLE, a new metadata-hiding encrypted search platform that offers query functionalities (search, update) on the shared data across multiple users with complex policy controls. MAPLE protects metadata privacy all the time during query processing, while achieving significantly (asymptotically) lower processing overhead than state-of-the-art platforms. The core technique of MAPLE is the design of oblivious data structures for search index and access control coupled with secure computation techniques to enable efficient query processing with a minimal trust. We fully implemented MAPLE and evaluated its performance on commodity cloud (Amazon EC2) under real settings. Experimental results showed that MAPLE achieved a concrete performance comparable with its counterparts, while offering provably stronger security guarantees and more diverse functionalities.

Data security and secrecy from unwanted applications are the subjects of the science known as cryptography. The advanced encryption standard algorithm is the most used and secure algorithm to encrypt data. The AES algorithm is based on the symmetric algorithm and uses a single key to encrypt and decrypt data. The AES algorithm uses 128 bits length of plain text with 128 bits, 192 bits, or 256 bits key size to encrypt data. Latin script uses ASCII codes, and a single byte represents each alphabet. Therefore, in 128 bits AES encryption, 16 characters can be encrypted each time. The other language script used the Unicode standard to represent their alphabets. In Unicode, at least 2 bytes are required to represent a character. Therefore, eight characters can be encrypted at a time. Also, there is no available S-box for Unicode characters. Therefore, a modified algorithm is proposed for Unicode to encrypt data. To use the AES algorithm in Unicode data, we need to convert the Unicode into character encoding, such as UTF-16. Nevertheless, In UTF-16, some Unicode characters have similar recurrent values. This paper demonstrates a modified AES algorithm to encrypt the Unicode script to reduce time complexity.

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 Agreement using Cryptography'' [Cachin, Kursawe, and Shoup, PODC 2000] has influenced the design of practical total-order broadcast through its use of threshold cryptography. However, it needs a setup protocol to be efficient. In a proof-of-stake setting with dynamic stake this setup would have to be continually recomputed, making the protocol impractical. The work ``Asynchronous Byzantine Agreement with Subquadratic Communication'' [Blum, Katz, Liu-Zhang, and Loss, TCC 2020] showed how to use an initial setup for broadcast to asymptotically efficiently generate sub-sequent setups. The protocol, however, resorted to fully homomorphic encryption and was therefore not practically efficient. We adopt their approach to the proof-of-stake setting with dynamic stake, apply it to the Constantinople paper, and remove the need for fully homomorphic encryption. This results in simple and practical proof-of-stake protocols. We discuss how to use the new coin-flip protocols together with DAG rider [Keidar et al., PODC 2021] and create a variant which works for dynamic proof of stake. Our method can be employed together with many further asynchronous total-order broadcast protocols.

Bulletproofs are general-purpose Zero Knowledge Proof protocols that allow a Prover to demonstrate to a Verifier knowledge of a solution to a set of equations, represented as a Rank 1 Constraint System. We present a protocol extending the standard Bulletproof protocol, which introduces a second layer of interactivity to the protocol, by allowing the Verifier to choose the set of equations after the Prover has already committed to portions of the solution. We show that such Verifier-chosen (or stochastically-chosen) equation sets can be used to design smaller equation sets with less variables that have the same proving-power as their larger, deterministic counterparts but are, in practice, orders of magnitude faster both in proof generation and in proof verification, and even reduce the size of the resulting proofs. We demonstrate this with an example from a real-world application. Our method maintains all the classical benefits of the Bulletproof approach: efficient proof generation, efficient proof checking, extremely short proofs, and the ability to use Fiat-Shamir challenges in order to turn an interactive proof into a non-interactive proof.

We study encrypted storage schemes where a client outsources data to an untrusted third-party server (such as a cloud storage provider) while maintaining the ability to privately query and dynamically update the data. We focus on encrypted multi-maps (EMMs), a structured encryption (STE) scheme that stores pairs of label and value tuples. EMMs allow queries on labels and return the associated value tuple. As responses are variable-length, EMMs are subject to volume leakage attacks introduced by Kellaris et al. [CCS’16]. To prevent these attacks, volume-hiding EMMs were introduced by Kamara and Moataz [Eurocrypt’19] that hide the label volumes (i.e., the value tuple lengths). As our main contribution, we present the first fully dynamic volume-hiding EMMs that are both asymptotically and concretely efficient. Furthermore, they are simultaneously forward and backward private which are the de-facto standard security notions for dynamic STE schemes. Additionally, we implement our schemes to showcase their concrete efficiency. Our experimental evaluations show that our constructions are able to add dynamicity with minimal to no additional cost compared to the prior best static volume-hiding schemes of Patel et al. [CCS’19].

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 meaningful security guarantees in the standard model. In particular, our notion implies that the hardness of a wide range of security games is preserved when the CRS is replaced with a distributed sampler. We also show how to realize our notion of distributed samplers. A core technical tool enabling our construction is a new notion of single-message zero knowledge.

Distributed key generation (DKG) allows bootstrapping threshold cryptosystems without relying on a trusted party, nowadays enabling fully decentralized applications in blockchains and multiparty computation (MPC). While we have recently seen new advancements for asynchronous DKG (ADKG) protocols, their performance remains the bottleneck for many applications, with only one protocol being implemented (DYX+ ADKG, IEEE S&P 2022). DYX+ ADKG relies on the Decisional Composite Residuosity assumption (being expensive to instantiate) and the Decisional Diffie-Hellman assumption, incurring a high latency (more than 100s with a failure threshold of 16). Moreover, the security of DYX+ ADKG is based on the random oracle model (ROM) which takes hash function as an ideal function; assuming the existence of random oracle is a strong assumption, and up to now, we cannot find any theoretically-sound implementation. Furthermore, the ADKG protocol needs public key infrastructure (PKI) to support the trustworthiness of public keys. The strong models (ROM and PKI) further limit the applicability of DYX+ ADKG, as they would add extra and strong assumptions to underlying threshold cryptosystems. For instance, if the original threshold cryptosystem works in the standard model, then the system using DYX+ ADKG would need to use ROM and PKI. In this paper, we design and implement a modular ADKG protocol that offers improved efficiency and stronger security guarantees. We explore a novel and much more direct reduction from ADKG to the underlying blocks, reducing the computational overhead and communication rounds of ADKG in the normal case. Our protocol works for both the low-threshold and high-threshold scenarios, being secure under the standard assumption (the well-established discrete logarithm assumption only) in the standard model (no trusted setup, ROM, or PKI).

We offer two very transparent digital signature schemes: one using non-square matrices and the other using scrap automorphisms. The former can be easily converted to a public key encryption scheme.

Adaptor signatures are a new cryptographic primitive that binds the authentication of a message to the revelation of a secret value. In recent years, this primitive has gained increasing popularity both in academia and practice due to its versatile use-cases in different Blockchain applications such as atomic swaps and payment channels. The security of these applications, however, crucially relies on users storing and maintaining the secret values used by adaptor signatures in a secure way. For standard digital signature schemes, cryptographic wallets have been introduced to guarantee secure storage of keys and execution of the signing procedure. However, no prior work has considered cryptographic wallets for adaptor signatures. In this work, we introduce the notion of adaptor wallets. Adaptor wallets allow parties to securely use and maintain adaptor signatures in the Blockchain setting. Our adaptor wallets are both deterministic and operate in the hot/cold paradigm, which was first formalized by Das et al. (CCS 2019) for standard signature schemes. We introduce a new cryptographic primitive called adaptor signatures with rerandomizable keys, and use it to generically construct adaptor wallets. We further show how to instantiate adaptor signatures with rerandomizable keys from the ECDSA signature scheme and discuss that they can likely be built for Schnorr and Katz-Wang schemes as well. Finally, we discuss the limitations of the existing ECDSA- and Schnorr-based adaptor signatures w.r.t. deterministic wallets in the hot/cold setting and prove that it is impossible to overcome these drawbacks given the current state-of-the-art design of adaptor signatures.

In this paper, we provide a systematic treatment for the batch arithmetic circuit satisfiability and evaluation problem. Building on the core idea which treats circuit inputs/outputs as a low-degree polynomials, we explore various interactive argument and proof schemes that can produce succinct proofs with short verification time. In particular, for the batch satisfiability problem, we provide a construction of succinct interactive argument of knowledge for generic log-space uniform circuits based on the bilinear pairing and common reference string assumption. Our argument has size in $O(poly(\lambda) \cdot (|\mathbf{w}| + d \log |C|))$, where $\lambda$ is the security parameter, $|\mathbf{w}|$ is the size of the witness, and $d$ and $|C|$ are the depth and size of the circuit, respectively. Note that the argument size is independent of the batch size. To the best of our knowledge, asymptotically it is the smallest among all known batch argument schemes that allow public verification. The batch satisfiablity problem simplifies to a batch evaluation problem when the circuit only takes in public inputs (i.e., no witness). For the evaluation problem, we construct statistically sound interactive proofs for various special yet highly important types of circuits, including linear circuits, and circuits representing sum of polynomials. Our proposed protocols are able to achieve proof sizes independent of the batch size. We also describe protocols optimized specifically for batch FFT and batch matrix multiplication which achieve desirable properties, including lower prover time and better composability. We believe these protocols are of interest in their own right and can be used as primitives in more complex applications.

Proof-of-useful-work (PoUW), an alternative to the widely used proof-of-work (PoW), aims to re-purpose the network's computing power. Namely, users evaluate meaningful computational problems, e.g., solving optimization problems, instead of computing numerous hash function values as in PoW. A recent approach utilizes the training process of deep learning as ``useful work''. However, these works lack security analysis when deploying them with blockchain-based protocols, let alone the informal and over-complicated system design. This work proposes a distributed proof-of-deep-learning (D-PoDL) scheme concerning PoUW's requirements. With a novel hash-traininßg-hash structure and model-referencing mechanism, our scheme is the first deep learning-based PoUW scheme that enables achieving better accuracy distributively. Next, we introduce a transformation from the D-PoDL scheme to a generic D-PoDL blockchain protocol which can be instantiated with two chain selection rules, i.e., the longest-chain rule and the weight-based blockchain framework (LatinCrypt' 21). This work is the first to provide formal proofs for deep learning-involved blockchain protocols concerning the robust ledger properties, i.e., chain growth, chain quality, and common prefix. Finally, we implement the D-PoDL scheme to discuss the effectiveness of our design.

Garbled circuits are a fundamental cryptographic primitive that allows two or more parties to securely evaluate an arbitrary Boolean circuit without revealing any information beyond the output using a constant number of communication rounds. Garbled circuits have been introduced by Yao (FOCS’86) and generalized to the multi-party setting by Beaver, Micali and Rogaway (STOC’90). Since then, several works have improved their efficiency by providing different garbling schemes and several implementations exist. Starting with the seminal Fairplay compiler (USENIX Security’04), several implementation frameworks decoupled the task of compiling the function to be evaluated into a Boolean circuit from the engine that securely evaluates that circuit, e.g., using a secure two-party computation protocol based on garbled circuits. In this paper, we show that this decoupling of circuit generation and evaluation allows a subtle attack on several prominent garbling schemes. It occurs when violating the implicit assumption on the circuit that gates have different input wires which is most often not explicitly specified in the respective papers. The affected garbling schemes use separate calls to a deterministic encryption function for the left and right input wire of a gate to derive pseudo-random encryption pads that are XORed together. When a circuit contains a gate where the left and right input wire are the same, these two per-wire encryption pads cancel out and we demonstrate that this can result in a complete break of privacy. We show how the vulnerable garbling schemes can be fixed easily.

Public data can be authenticated by obtaining from a trustworthy website with TLS. Private data, such as user profile, are usually restricted from public access. If a user wants to authenticate his private data (e.g., address) provided by a restricted website (e.g., user profile page of a utility company website) to a verifier, he cannot simply give his username and password to the verifier. DECO (CCS 2020) provides a solution for liberating these data without introducing undesirable trust assumption, nor requiring server-side modification. Their implementation is mainly based on TLS 1.2. In this paper, we propose an optimized solution for TLS 1.3 websites. We tackle a number of open problems, including the support of X25519 key exchange in TLS 1.3, the design of round-optimal three-party key exchange, the architecture of two-party computation of TLS 1.3 key scheduling, and circuit design optimized for two-party computation. We test our implementation with real world website and show that our optimization is necessary to avoid timeout in TLS handshake.

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 Challenge-Response variant of our assumption. Unlike standard GapCDH, CorrCRGapCDH implies the security of the popular AKE protocol HMQV in the eCK model, tightly and without rewinding. Again, we prove hardness of CorrCRGapCDH in the generic group model, with (almost) optimal bounds. Our new results allow implementations of NAXOS, X3DH, and HMQV without having to adapt the group sizes to account for the tightness loss of previous reductions. As a side result of independent interest, we also obtain modular and simple security proofs from standard GapCDH with tightness loss, improving previously known bounds.

The area of practical computational integrity proof systems, like SNARKs, STARKs, Bulletproofs, is seeing a very dynamic development with several constructions having appeared recently with improved properties and relaxed setup requirements. Many use cases of such systems involve, often as their most expensive part, proving the knowledge of a preimage under a certain cryptographic hash function, which is expressed as a circuit over a large prime field. A notable example is a zero-knowledge proof of coin ownership in the Zcash cryptocurrency, where the inadequacy of the SHA-256 hash function for such a circuit caused a huge computational penalty. In this paper, we present a modular framework and concrete instances of cryptographic hash functions which work natively with GF(p) objects. Our hash function Poseidon uses up to 8x fewer constraints per message bit than Pedersen Hash. Our construction is not only expressed compactly as a circuit, but can also be tailored for various proof systems using specially crafted polynomials, thus bringing another boost in performance. We demonstrate this by implementing a 1-out-of-a-billion membership proof with Merkle trees in less than a second by using Bulletproofs.

We construct the first tight verifiable delay function (VDF) where the evaluation algorithm only evaluates sequentially the function and hence outputs and empty proof, verification is independent of time parameter $T$ and setup has constant size parameters. Our VDF is based on repeated squaring in hidden order groups, but it requires that coins used to sample a random instance must be kept secret in order to guarantee sequentiality. We denote such a VDF as a private coin verifiable delay function and show that it can be used to obtain multiplicatively homomorphic non-interactive timed commitment with efficient publicly verifiable force decommitment algorithm.

Private set intersection (PSI) is a cryptographic primitive that allows two or more parties to learn the intersection of their input sets and nothing else. In this paper, we present a private set intersection protocol based on a new secure multi-party quantum protocol for greatest common divisor (GCD). The protocol is mainly inspired by the recent quantum private set union protocol based on least common multiple by Liu, Yang, and Li. Performance analysis guarantees the correctness and it also shows that the proposed protocols are completely secure in semi-honest model. Moreover, the complexity is proven to be efficient (poly logarithmic) in the size of the input sets.

The problem of designing authenticated key establishment protocols has a rich history. Since 1976 more than a hundred different protocols have been proposed. But the task of comparing and classifying existing protocols is usually complicated by the fact that they are described in different terms and with different levels of detail. This paper contains intermediate results on enumeration and uniform description of AKE protocols. We publish it in order to get feedback on the description principles used. Here we describe 100 AKE protocols (there are much more such protocols, but we found these earlier) in identical terms and the same level of detail. The proposed descriptions are not structured (chronologically only) but classifying of these protocols is future work direction.

YOSO MPC (Gentry et al., Crypto 2021) is a new MPC framework where each participant can speak at most once. This models an adaptive adversary’s ability to watch the network and corrupt or destroy parties it deems significant based on their communication. By using private channels to anonymous receivers (e.g. by encrypting to a public key whose owner is unknown), the communication complexity of YOSO MPC can scale sublinearly with the total number N of available parties, even when the adversary’s corruption threshold is linear in N (e.g. just under N/2). It was previously an open problem whether YOSO MPC can achieve guaranteed output delivery in a constant number of rounds without relying on trusted setup. In this work, we show that this can indeed be accomplished. We demonstrate three different approaches: the first two (which we call YaOSO and YOSO-GLS) use two and three rounds of communication, respectively. Our third approach (which we call YOSO-LHSS) uses O(d) rounds, where d is the multiplicative depth of the circuit being evaluated; however, it can be used to bootstrap any constant-round YOSO protocol that requires setup, by generating that setup within YOSO-LHSS. Though YOSO-LHSS requires more rounds than our first two approaches, it may be more practical, since the zero knowledge proofs it employs are more efficient to instantiate. As a contribution of independent interest, we introduce a verifiable state propagation UC functionality, which allows parties to send private message which are verifiably derived in the “correct” way (according to the protocol in question) to anonymous receivers. This is a natural functionality to build YOSO protocols on top of.

We introduce a new candidate post-quantum digital signature scheme from the regular syndrome decoding (RSD) assumption, an established variant of the syndrome decoding assumption which asserts that it is hard to find $w$-regular solutions to systems of linear equations over $\mathbb{F}_2$ (a vector is regular if it is a concatenation of $w$ unit vectors). Our signature is obtained by introducing and compiling a new 5-round zero-knowledge proof system constructed using the MPC-in-the-head paradigm. At the heart of our result is an efficient MPC protocol in the preprocessing model that checks the correctness of a regular syndrome decoding instance by using a share ring-conversion mechanism. The analysis of our construction is non-trivial and forms a core technical contribution of our work. It requires careful combinatorial analysis and combines several new ideas, such as analyzing soundness in a relaxed setting where a cheating prover is allowed to use any witness sufficiently close to a regular vector. We complement our analysis with an in-depth overview of existing attacks against RSD. Our signatures are competitive with the best-known code-based signatures, ranging from $12.52$ KB (fast setting, with a signing time of the order of a few milliseconds on a single core of a standard laptop) to about $9$ KB (short setting, with estimated signing time of the order of 15ms).

Data, when coupled with state-of-the-art machine learning models, can enable remarkable applications. But, there exists an underlying tension: users wish to keep their data private, and model providers wish to protect their intellectual property. Homomorphic encryption (HE) and multi-party computation (MPC) techniques have been proposed as solutions to this problem; however, both techniques require model providers to fully trust the server performing the machine learning computation. This limits the scale of inference applications, since it prevents model providers from leveraging shared public cloud infrastructures. In this work, we present CHEX-MIX, a solution to the problem of privacy-preserving machine learning between two mutually distrustful parties in an untrusted cloud setting. CHEX-MIX relies on a combination of HE and trusted execution environments (TEEs), using HE to provide clients with confidentiality guarantees, and TEEs to provide model providers with confidentiality guarantees and protect the integrity of computation from malicious cloud adversaries. Unlike prior solutions to this problem, such as multi-key HE, single-key HE, MPC, or TEE-only techniques, our solution assumes that both the client and the cloud can be malicious, makes no collusion assumptions, and frees model providers from needing to maintain private online infrastructures. Our results show that CHEX-MIX can execute at high efficiency, with low communication cost, while providing security guarantees unaddressed by prior work. Compared to a recent multi-key HE work that allows partial cloud offload, for example, CHEX-MIX achieves a 3× lower communication cost and a 3× faster computation time.

This paper's primary purpose is to provide a source of introductory information into building a zero knowledge proof system for general computation. We review how to build such a system with a polynomial commitment scheme, and how to implement a fully functional command set in terms of zero knowledge primitives.

With the ever greater adaptation of blockchain systems, smart contract based ecosystems have formed to provide financial services and other utility. This results in an ever increasing demand for transactions on blockchains, however, the amount of transactions per second on a given ledger is limited. Layer-2 systems attempt to improve scalability by taking transactions off-chain, with building blocks that are two party channels which are concatenated to form networks. Interaction between two parties requires (1) routing such a network, (2) interaction with and collateral from all intermediaries on the routed path and (3) interactions are often more limited compared to what can be done on the ledger. In contrast to that design, recent constructions such as Hydra Heads (FC’21) are both multi-party and isomorphic, allowing interactions to have the same expressiveness as on the ledger making it akin to a ledger located on Layer-2. The follow up Interhead Construction (MARBLE’22) further extends the protocol to connect Hydra Heads into networks by means of a “virtual” Hydra Head construction. This work puts forth an even greater generalization of the Interhead Protocol, allowing for inter- action across different Layer-2 ledgers with a multitude of improvements. As concrete example, our design is modular and lightweight, which makes it viable for both full virtual ledger constructions as well as straightfor- ward one-time interactions and payments systems.

Succinct Non-interactive Arguments of Knowledge (SNARKs) enable a party to cryptographically prove a statement regarding a computation to another party that has constrained resources. Practical use of SNARKs often involves a Zero-Knowledge Virtual Machine (zkVM) that receives an input program and input data, then generates a SNARK proof of the correct execution of the input program. Most zkVMs emulate the von Neumann architecture and must prove relations between a program's execution and its use of Random Access Memory. However, there are conceptually simpler models of computation that are naturally modeled in a SNARK yet are still practical for use. Nock is a minimal, homoiconic combinator function, a Turing-complete instruction set that is practical for general computation, and is notable for its use in Urbit. We introduce Eden, an Efficient Dyck Encoding of Nock that serves as a practical, SNARK-friendly combinator function and instruction set architecture. We describe arithmetization techniques and polynomial equations used to represent the Eden ISA in an Interactive Oracle Proof. Eden provides the ability to prove statements regarding the execution of any program that compiles down to the Eden ISA. We present the Eden zkVM, a particular instantiation of Eden as a zk-STARK.

Anonymous credentials (AC) have emerged as a promising privacy-preserving solu- tion for user-centric identity management. They allow users to authenticate in an anonymous and unlinkable way such that only required information (i.e., attributes) from their credentials are re- vealed. With the increasing push towards decentralized systems and identity, e.g., self-sovereign identity (SSI) and the concept of verifiable credentials, this also necessitates the need for suit- able AC systems. For instance, when relying on existing AC systems, obtaining credentials from different issuers requires the presentation of independent credentials, which can become cum- bersome. Consequently, it is desirable for AC systems to support the so-called multi-authority (MA) feature. It allows a compact and efficient showing of multiple credentials from different is- suers. Another important property is called issuer hiding (IH). This means that showing a set of credentials is not revealed which issuer has issued which credentials but only whether a verifier- defined policy on the acceptable set of issuers is satisfied. This issue becomes particularly acute in the context of MA, where a user could be uniquely identified by the combination of issuers in their showing. Unfortunately, there are no AC schemes that satisfy both these properties simul- taneously. To close this gap, we introduce the concept of Issuer-Hiding Multi-Authority Anonymous Cre- dentials (IhMA). Our proposed solution involves the development of two new signature primi- tives with versatile randomization features which are independent of interest: 1) Aggregate Sig- natures with Randomizable Tags and Public Keys (AtoSa) and 2) Aggregate Mercurial Signatures (ATMS), which extend the functionality of AtoSa to additionally support the randomization of messages and yield the first instance of an aggregate (equivalence-class) structure-preserving sig- nature. These primitives can be elegantly used to obtain IhMA with different trade-offs but have applications beyond. We formalize all notations and provide rigorous security definitions for our proposed primi- tives. We present provably secure and efficient instantiations of the two primitives as well as corresponding IhMA systems. Finally, we provide benchmarks based on an implementation to demonstrate the practical efficiency of our constructions

We introduce a new data-independent priority queue which supports amortized polylogarithmic-time insertions and constant-time deletions, and crucially, (non-amortized) constant-time \textit{read-front} operations, in contrast with a prior construction of Toft (PODC'11). Moreover, we reduce the number of required comparisons. Data-independent data structures - first identified explicitly by Toft, and further elaborated by Mitchell and Zimmerman (STACS'14) - facilitate computation on encrypted data without branching, which is prohibitively expensive in secure computation. Using our efficient data-independent priority queue, we introduce a new privacy-preserving dark pool application, which significantly improves upon prior constructions which were based on costly sorting operations. Dark pools are securities-trading venues which attain ad-hoc order privacy, by matching orders outside of publicly visible exchanges. In this paper, we describe an efficient and secure dark pool (implementing a full continuous double auction), building upon our priority queue construction. Our dark pool's security guarantees are cryptographic - based on secure multiparty computation (MPC) - and do not require that the dark pool operators be trusted. Our approach improves upon the asymptotic and concrete efficiency attained by previous efforts. Existing cryptographic dark pools process new orders in time which grows linearly in the size of the standing order book; ours does so in polylogarithmic time. We describe a concrete implementation of our protocol, with malicious security in the honest majority setting. We also report benchmarks of our implementation, and compare these to prior works. Our protocol reduces the total running time by several orders of magnitude, compared to prior secure dark pool solutions.

Despite the great potential and flexibility of smart contract-enabled blockchains, building privacy-preserving applications using these platforms remains an open question. Existing solutions fall short since they ask end users to coordinate and perform the computation off-chain themselves. While such an approach reduces the burden of the miners of the system, it largely limits the ability of lightweight users to enjoy privacy since performing the actual computation on their own and attesting to its correctness is expensive even with state-of-the-art proof systems. To address this limitation, we propose smartFHE, a framework to support private smart contracts using fully homomorphic encryption (FHE). To the best of our knowledge, smartFHE is the first to use FHE in the blockchain model; moreover, it is the first to support arbitrary privacy-preserving applications for lightweight users under the same computation-on-demand model pioneered by Ethereum. smartFHE does not overload the user since miners are instead responsible for performing the private computation. This is achieved by employing FHE so miners can compute over encrypted data and account balances. Users are only responsible for proving well-formedness of their private inputs using efficient zero-knowledge proof systems (ZKPs). We formulate a notion for a privacy-preserving smart contract (PPSC) scheme and show a concrete instantiation of our smartFHE framework. We address challenges resulting from using FHE in the blockchain setting---including concurrency and dealing with leveled schemes. We also show how to choose suitable FHE and ZKP schemes to instantiate our framework, since naively choosing these will lead to poor performance in practice. We formally prove correctness and security of our construction. Finally, we conduct experiments to evaluate its efficiency, including comparisons with a state-of-the-art scheme and testing several private smart contract applications. We have open-sourced our (highly optimized) ZKP library, which could be of independent interest.

Statistical sender privacy (SSP) is the strongest achievable security notion for two-message oblivious transfer (OT) in the standard model, providing statistical security against malicious receivers and computational security against semi-honest senders. In this work we provide a novel construction of SSP OT from the Decisional Diffie-Hellman (DDH) and the Learning Parity with Noise (LPN) assumptions achieving (asymptotically) optimal amortized communication complexity, i.e. it achieves rate 1. Concretely, the total communication complexity for $k$ OT instances is $2k(1+o(1))$, which (asymptotically) approaches the information-theoretic lower bound. Previously, it was only known how to realize this primitive using heavy rate-1 FHE techniques [Brakerski et al., Gentry and Halevi TCC'19]. At the heart of our construction is a primitive called statistical co-PIR, essentially a a public key encryption scheme which statistically erases bits of the message in a few hidden locations. Our scheme achieves nearly optimal ciphertext size and provides statistical security against malicious receivers. Computational security against semi-honest senders holds under the DDH assumption.

Circuit-based Private Set Intersection (circuit-PSI) refers to cryptographic protocols that let two parties with input set $X$ and $Y$ compute a function $f$ over the intersection set $X \cap Y$, without revealing any other information. The research efforts for circuit-PSI mainly focus on the case where input set sizes $|X|$ and $|Y|$ are similar so far, and they scale poorly for extremely unbalanced set sizes $|X| \gg |Y|$. Recently, Lepoint \textit{et al.} (ASIACRYPT'21) proposed the first dedicated solutions for this problem, which has online cost only linear in the small set size $|Y|$. However, it requires an expensive setup phase that requires huge storage of about $O(|X|)$ on the small set holder side, which can be problematic in applications where the small set holder is assumed to have restricted equipment. In this work, we suggest new efficient proposals for circuit-PSI tailored for unbalanced inputs, which feature {\emph{zero}} small set holder side storage, and comparable online phase performance to the previous work. At the technical core, we use homomorphic encryption (HE) based {\emph{plain}} PSI protocols of Cong \textit{et al.} (CCS'21), with several technically non-trivial arguments on algorithm and security. We demonstrate the superiority of our proposals in several input set sizes by an implementation. As a representative example, for input sets of size $2^{24}$ and $2^{12}$, our proposals require {\emph{zero}} storage on the small set holder whereas Lepoint \textit{et al.} requires over $7$GB. The online phase remains similar; over LAN network setting, ours takes $7.5$ (or $20.9$s) seconds with $45$MB (or $11.7$MB) communication, while Lepoint \textit{et al.} requires $4.2$ seconds with $117$MB communication.

The relationship between oblivious transfer (OT) and public-key encryption (PKE) has been studied by Gertner et al. (FOCS 2000). They showed that OT can be constructed from special types of PKE, i.e., PKE with oblivious sampleability of public keys or ciphertexts. In this work, we give new black-box constructions of OT from PKE without any oblivious sampleability. Instead, we require that the PKE scheme is rerandomizable, meaning that one can use the public key to rerandomize a ciphertext into a fresh ciphertext. We give two different OT protocols with different efficiency features based on rerandomizable PKE. For $1$-out-of-$n$ OT, in our first OT protocol, the sender has sublinear (in $n$) cost, and in our second OT protocol, the cost of the receiver is independent of $n$. As a comparison, in the PKE-based OT protocols of Gertner et al., both the sender and receiver have linear cost.

A cryptographic accumulator is a succinct set commitment scheme with efficient (non-)membership proofs that typically supports updates (additions and deletions) on the accumulated set. When elements are added to or deleted from the set, an update message is issued. The collection of all the update messages essentially leaks the underlying accumulated set which in certain applications is not desirable. In this work, we define oblivious accumulators, a set commitment with concise membership proofs that hides the elements and the set size from every entity: an outsider, a verifier or other element holders. We formalize this notion of privacy via two properties: element hiding and add-delete indistinguishability. We also define almost-oblivious accumulators, that only achieve a weaker notion of privacy called add-delete unlinkability. Such accumulators hide the elements but not the set size. We consider the trapdoorless, decentralized setting where different users can add and delete elements from the accumulator and compute membership proofs. We then give a generic construction of an oblivious accumulator based on key-value commitments (KVC). We also show a generic way to construct KVCs from an accumulator and a vector commitment scheme. Finally, we give lower bounds on the communication (size of update messages) required for oblivious accumulators and almost-oblivious accumulators.

In this paper, we present a new diverse class of post-quantum group-based Digital Signature Schemes (DSS). The approach is significantly different from previous examples of group-based digital signatures and adopts the framework of group action-based cryptography: we show that each finite group defines a group action relative to the semidirect product of the group by its automorphism group, and give security bounds on the resulting signature scheme in terms of the group-theoretic computational problem known as the Semidirect Discrete Logarithm Problem (SDLP). Crucially, we make progress towards being able to efficiently compute the novel group action, and give an example of a parameterised family of groups for which the group action can be computed for any parameters, thereby negating the need for expensive offline computation or inclusion of redundancy required in other schemes of this type.

We present a new method for transforming zero-knowledge protocols in the designated verifier setting into public-coin protocols, which can be made non-interactive and publicly verifiable. Our transformation applies to a large class of ZK protocols based on oblivious transfer. In particular, we show that it can be applied to recent, fast protocols based on vector oblivious linear evaluation (VOLE), with a technique we call VOLE-in-the-head, upgrading these protocols to support public verifiability. Our resulting ZK protocols have linear proof size, and are simpler, smaller and faster than related approaches based on MPC-in-the-head. To build VOLE-in-the-head while supporting both binary circuits and large finite fields, we develop several new technical tools. One of these is a new proof of security for the SoftSpokenOT protocol (Crypto 2022), which generalizes it to produce certain types of VOLE correlations over large fields. Secondly, we present a new ZK protocol that is tailored to take advantage of this form of VOLE, which leads to a publicly verifiable VOLE-in-the-head protocol with only 2x more communication than the best, designated-verifier VOLE-based protocols. We analyze the soundness of our approach when made non-interactive using the Fiat-Shamir transform, using round-by-round soundness. As an application of the resulting NIZK, we present FAEST, a post-quantum signature scheme based on AES. FAEST is the first AES-based signature scheme to be smaller than SPHINCS+, with signature sizes between 5.6 and 6.6kB at the 128-bit security level. Compared with the smallest version of SPHINCS+ (7.9kB), FAEST verification is slower, but the signing times are between 8x and 40x faster.

Cross-chain communication is instrumental in unleashing the full potential of blockchain technologies, as it allows users and developers to exploit the unique design features and the profit opportunities of different existing blockchains. The majority of interoperability solutions are provided by centralized exchanges and bridge protocols based on a trusted majority, both introducing undesirable trust assumptions compared to native blockchain assets. Hence, increasing attention has been given to decentralized solutions: Light and super-light clients paved the way for chain relays, which allow verifying on a blockchain the state of another blockchain by respectively verifying and storing a linear and logarithmic amount of data. Unfortunately, relays turn out to be inefficient in terms of computational costs, storage, or compatibility. We introduce Glimpse, an on-demand bridge that leverages a novel on-demand light client construction with only constant on-chain storage, cost, and computational overhead. Glimpse is expressive, enabling a plethora of DeFi and off-chain applications such as lending, pegs, proofs of oracle attestations, and betting hubs. Glimpse also remains compatible with blockchains featuring a limited scripting language such as the Liquid Network (a pegged sidechain of Bitcoin), for which we present a concrete instantiation. We prove Glimpse security in the Universal Composability (UC) framework and further conduct an economic analysis. We evaluate the cost of Glimpse for Bitcoin-like chains: verifying a simple transaction has at most 700 bytes of on-chain overhead, resulting in a one-time fee of $3, only twice as much as a standard Bitcoin transaction.

Private set intersection (PSI) enables two parties, each holding a private set to compute their intersection without revealing other information in the process. We introduce a variant of conventional PSI termed as third-party PSI, whereby the intersection output of the two parties is only known to an inputless third party. In this setting, the two parties who participate in the protocol have no knowledge of the intersection result or any information of the set content of the other party. In general, third-party PSI settings arise where there is a need for an external party to obtain the intersection outcome without leakage of additional information to any other party. This setting is motivated by an increasing importance in several real-world applications. We describe protocols which achieve this functionality with minimal communication overhead. To the best of knowledge, our work is the first of its kind to explore this variant of PSI.

Healthcare providers cannot share their patients' encrypted data among themselves because of interoperability issues. Many blockchain- based solutions have been proposed to allow for sharing medical data in a privacy-preserving manner, but interoperability problems persist. In this paper, we present a protocol called Blockchain-Format Preserving Encryption (B-FPE) to preserve patients' data privacy. Each patient is provided with an FPE key at the time of registration. All medical records are encrypted with the FPE key and stored in the blockchain. All the blockchain transactions are signed using group signatures. We use group signatures for signing the transactions to maintain the anonymity of healthcare providers. The new encrypted data block is concatenated to the blockchain. We present two cases: The regular phase, in which a patient is in a conscious state to share their FPE key with the healthcare provider, and the Emergency phase, in which a patient is not in a conscious state to share their key with the healthcare provider. In the latter case, the healthcare provider reconstructs the FPE key and decrypts the ciphertext. We assume this decryption happens in an oblivious manner.

Considering password-based authentication technique, password memorability is a real challenge on users. Hence, password reuse across different web applications is a common trend among users which makes websites vulnerable to credential stuffing attack. A solution as password manager helps the users to create random passwords for different websites on the user machine. However, it has practical challenges. Password database breach detection is another related and challenging task. Among recent developments for breach detection, honeyword-based approach is much appreciated by the research community. However, honeyword generation itself is a challenging part of the solution. In this work, we propose i) Password Reuse Detection (PRD) protocol for detecting password reuse using a secure two party private set intersection; ii) Breach Detection (BD) protocol that detects credential stuffing attacks using two party private set inclusion protocol based on random oblivious transfer. Both the proposals are designed for the authentication servers of the respective applications and need communication between multiple websites following the work by wang et al. Through analysis we show that our PRD protocol is around 2.8 times faster, and space efficient than existing works for 5000 honeywords. Our near to real-time BD protcol is around 2 times faster than existing works.

We propose a novel approach that utilizes fuzzification theory to perform feature selection on website content for encryption purposes. Our objective is to identify and select the most relevant features from the website by harnessing the principles of fuzzy logic. Fuzzification allows us to transform the crisp website content into fuzzy representations, enabling a more nuanced analysis of their characteristics. By considering the degree of membership of each feature in different fuzzy categories, we can evaluate their importance and relevance for encryption. This approach enables us to prioritize and focus on the features that exhibit higher membership degrees, indicating their significance in the encryption process. By employing fuzzification-based feature selection, we aim to enhance the effectiveness and efficiency of website content encryption, ultimately improving the overall internet security

Private-ID (PID) protocol enables two parties, each holding a private set of items, to privately compute a set of random universal identifiers (UID) corresponding to the records in the union of their sets, where each party additionally learns which UIDs correspond to which items in its set but not if they belong to the intersection or not. PID is very useful in the privacy computation of databases query, e.g. inner join and join for compute. Known PID protocols all assume the input of both parties is a set. In the case of join, a more common scenario is that one party's primary key (unique) needs to join the other party's foreign key (duplicate). How to construct an efficient Private Multiset ID (PMID) protocol to support the above \emph{key-foreign key join} remains open. We resolve this problem by constructing efficient PMID protocols from Oblivious PRF, Private Set Union, and a newly introduced primitive called Deterministic-Value Oblivious Programmable PRF (dv-OPPRF). We also propose some PMID applications, including Private Inner Join, Private Full Join, and Private Join for Compute. We implement our PMID protocols and state-of-the-art PID protocols as performance baselines. The experiments show that the performances of our PMID are almost the same as the state-of-the-art PIDs when we set the multiplicity $U_x = U_y = 1$. Our PMID protocols scale well when either $U_x > 1$ or $U_y > 1$. The performances also correctly reflect excessive data expansion when both $U_x, U_y > 1$ for the more general \emph{cross join} case.

Secure multiparty computation (MPC) on incomplete communication networks has been studied within two primary models: (1) Where a partial network is fixed a priori, and thus corruptions can occur dependent on its structure, and (2) Where edges in the communication graph are determined dynamically as part of the protocol. Whereas a rich literature has succeeded in mapping out the feasibility and limitations of graph structures supporting secure computation in the fixed-graph model (including strong classical lower bounds), these bounds do not apply in the latter dynamic-graph setting, which has recently seen exciting new results, but remains relatively unexplored. In this work, we initiate a similar foundational study of MPC within the dynamic-graph model. As a first step, we investigate the property of graph expansion. All existing protocols (implicitly or explicitly) yield communication graphs which are expanders, but it is not clear whether this is inherent. Our results consist of two types (for constant fraction of corruptions): * Upper bounds: We demonstrate secure protocols whose induced communication graphs are not expander graphs, within a wide range of settings (computational, information theoretic, with low locality, even with low locality and adaptive security) each assuming some form of input-independent setup. * Lower bounds: In the setting without setup and adaptive corruptions, we demonstrate that for certain functionalities, no protocol can maintain a non-expanding communication graph against all adversarial strategies. Our lower bound relies only on protocol correctness (not privacy), and requires a surprisingly delicate argument. More generally, we provide a formal framework for analyzing the evolving communication graph of MPC protocols, giving a starting point for studying the relation between secure computation and further, more general graph properties.

Nova is an efficient recursive proof system built from an elegant folding scheme for (relaxed) R1CS statements. The original Nova paper (CRYPTO'22) presented Nova using a single elliptic curve group of order $p$. However, for improved efficiency, the implementation of Nova alters the scheme to use a 2-cycle of elliptic curves. This altered scheme is only described in the code and has not been proven secure. In this work, we point out a soundness vulnerability in the original implementation of the 2-cycle Nova system. To demonstrate this vulnerability, we construct a convincing Nova proof for the correct evaluation of $2^{75}$ rounds of the Minroot VDF in only 1.46 seconds. We then present a modification of the 2-cycle Nova system and formally prove its security. The modified system also happens to be more efficient than the original implementation. In particular, the modification eliminates an R1CS instance-witness pair from the recursive proof. The implementation of Nova has now been updated to use our optimized and secure system. We also show that Nova's IVC proofs are malleable and discuss several mitigations.

Restricting access to certified users is not only desirable for many blockchain applications, it is also legally mandated for decentralized finance (DeFi) applications to counter malicious actors. Existing solutions, however, are either (i) non-private, i.e., they reveal the link between users and their wallets to the authority granting credentials, or (ii) they introduce additional trust assumptions by relying on a decentralized oracle to verify anonymous credentials (ACs). To remove additional trust in the latter approach, we propose verifying credentials on-chain in this work. We find that this approach has impractical costs with prior AC schemes, and propose a new AC scheme ZEBRA that crucially relies on zkSNARKs to provide efficient on-chain verification for the first time. In addition to the standard unlinkability property that provides privacy for users, ZEBRA also supports auditability, revocation, traceability, and theft detection, which adds accountability for malicious users and convenience for honest users to our access control solution. Even with these properties, ZEBRA reduces the gas cost incurred on the Ethereum Virtual Machine (EVM) by 14.3x when compared to Coconut [NDSS 2019], the state-of-the-art AC scheme for blockchains that only provides unlinkability. This improvement translates to a reduction in transaction fees from 176 USD to 12 USD on Ethereum in May 2023. Since 12 USD is still high for most applications, ZEBRA further drives down credential verification costs through batched verification. For a batch of 512 layer-1 and layer-2 wallets, the transaction fee on Ethereum is reduced to just 0.44 USD and 0.02 USD, respectively, which is comparable to the minimum transaction costs on Ethereum.

In permissionless consensus, the ordering of transactions or inputs in each block is freely determined by an anonymously elected block leader. A rational block leader will choose an ordering of inputs that maximizes financial gain; the emergence of automatic market makers in decentralized finance enables the block leader to front-run honest trade orders by injecting its own inputs prior to and after honest trades. Front-running is rampant in decentralized finance and reduces the utility of the system by extracting financial value from honest trades and increasing demand for block-space. Current proposals to prevent input order attacks by encrypting user inputs are not permissionless, as they rely on small static committees to perform distributed key generation and threshold decryption. Such committees require party authentication, knowledge of the number of participating parties or do not permit player replaceability and are therefore not permissionless. Moreover, alternative solutions based on sequencing inputs in order of their arrival cannot prevent front-running in an unauthenticated peer-2-peer network where message arrival is adversarially controlled. We present FairPoS, the first consensus protocol to achieve input fairness in the permissionless setting with security against adaptive adversaries in semi-synchronous networks. In FairPoS, the adversary cannot learn the plaintext of any client input before it is included in a block in the chain's common-prefix. Thus, input ordering attacks that depend on observing pending client inputs in the clear are no longer possible. In FairPoS, this is achieved via Delay Encryption (DeFeo et al., EUROCRYPT 2021), a recent cryptographic primitive related to time-lock puzzles, allowing all client inputs in a given round to be encrypted under a key that can only be extracted after enough time has elapsed. In contrast to alternative approaches, the key extraction task in delay encryption can, in principle, be performed by any party in the permissionless setting and requires no distribution of secret key material amongst authenticated parties. However, key extraction requires highly specialized hardware in practice. Thus, FairPoS requires resource-rich staking parties to insert extracted keys into blocks, enabling light-clients to decrypt past inputs and relieving parties who join the execution from decrypting all inputs in the entire chain history. Realizing this in proof-of-stake is non-trivial; naive application of key extraction to proof-of-stake can result in chain stalls lasting the entire key extraction period. We overcome this challenge with a novel key extraction protocol, which tolerates adversarial delays in block delivery intended to prevent key extraction from completing on schedule. Critically, this also enables the adoption of a new longest-extendable-chain rule which allows FairPoS to achieve the same guarantees as Ouroborous Praos against an adaptive adversary.

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 arguments that exploit lattice-based commitments. The eventual goal is smaller proof sizes than those achieved via the Merkle-tree paradigm. Alas, known constructions lack succinct verification. In this paper, we construct the first interactive argument system for NP with succinct verification that, departing from the Merkle-tree paradigm, exploits the homomorphic properties of lattice-based commitments. For an arithmetic circuit with N gates, our construction achieves verification time polylog(N) based on the hardness of the Ring Short-Integer-Solution (RSIS) problem. The core technique in our construction is a delegation protocol built from commitment schemes based on leveled bilinear modules, a new notion that we deem of independent interest. We show that leveled bilinear modules can be realized from pre-quantum and from post-quantum cryptographic assumptions.

This paper presents the first protocols for Proactive Secret Sharing (PSS) that only require constant (in the number of parties, $n$) communication per party per epoch. By harnessing the power of expander graphs, we are able to obtain strong guarantees about the security of the system. We present the following PSS protocols: – A PSS protocol that provides privacy (but no robustness) against an adversary controlling $O(n)$ parties per epoch. – A PSS protocol that provides robustness (but no privacy) against an adversary controlling $O(n)$ parties per epoch. – A PSS protocol that provides privacy against an adversary controlling $O(n^{a})$ parties per epoch and provides robustness against an adversary controlling $O(n^{1−a})$ parties per epoch, for any constant $0 \leq a \leq 1$. Instantiating this with $a = \frac{1}{2}$ gives a PSS protocol that is proactively secure (private and robust) against an adversary controlling $O(\sqrt{n})$ parties per epoch. Additionally, we discuss how secure channels, whose existence is usually assumed by PSS protocols, are challenging to create in the mobile adversary setting, and we present a method to instantiate them from a weaker assumption.

We propose a new inner product argument (IPA), called TENET, which features sublogarithmic proof size and sublinear verifier without a trusted setup. IPA is a core primitive for various advanced proof systems including range proofs, circuit satisfiability, and polynomial commitment, particularly where a trusted setup is hard to apply. At ASIACRYPT 2022, Kim, Lee, and Seo showed that pairings can be utilized to exceed the complexity barrier of the previous discrete logarithm-based IPA without a trusted setup. More precisely, they proposed two pairing-based IPAs, one with sublogarithmic proof size and the other one with sublinear verifier cost, but they left achieving both complexities simultaneously as an open problem. We investigate the obstacles for this open problem and then provide our solution TENET, which achieves both sublogarithmic proof size and sublinear verifier. We prove the soundness of TENET under the discrete logarithm assumption and double pairing assumption.

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. While this is certainly not a viable solution for all ABC use-cases, there are relevant and timely use-cases, such as vaccination credentials as widely deployed during the COVID-19 pandemic. In such settings, ABCs that are tied to biometrics, which we call Biometric-Bound Attribute-Based Credentials (bb-ABC), allow to implement scalable and privacy-friendly systems to control physical access to (critical) infrastructure and facilities. While there are some previous works on bb-ABC in the literature, the state of affairs is not satisfactory. Firstly, in existing work the problem is treated in a very abstract way when it comes to the actual type of biometrics. Thus, it does not provide concrete solutions which allow for assessing their practicality when deployed in a real-world setting. Secondly, there is no formal model which rigorously captures bb-ABC systems and their security requirements, making it hard to assess their security guarantees. With this work we overcome these limitations and provide a rigorous formalization of bb-ABC systems. Moreover, we introduce two generic constructions which offer different trade-offs between efficiency and trust assumptions, and provide benchmarks from a concrete instantiation of such a system using facial biometrics. The latter represents a contact-less biometric feature that provides acceptable accuracy and seems particularly suitable to the above use-case.

In this paper, we introduce $\mathsf{SparsePIR}$, a single-server keyword private information retrieval (PIR) construction that enables querying over sparse databases. At its core, $\mathsf{SparsePIR}$ is based on a novel encoding algorithm that encodes sparse database entries as linear combinations while being compatible with important PIR optimizations including recursion. $\mathsf{SparsePIR}$ achieves response overhead that is half of state-of-the art keyword PIR schemes without requiring long term client storage of linear sized mappings. We also introduce two variants, $\mathsf{SparsePIR}^g$ and $\mathsf{SparsePIR}^c$, that further reduces the size of the serving database at the cost of increased encoding time and small additional client storage, respectively. Our frameworks enable performing keyword PIR with, essentially, the same costs as standard PIR. Finally, we also show that $\mathsf{SparsePIR}$ may be used to build batch keyword PIR with halved response overhead without any client mappings.

On the one hand, the web needs to be secured from malicious activities such as bots or DoS attacks; on the other hand, such needs ideally should not justify services tracking people's activities on the web. Anonymous tokens provide a nice tradeoff between allowing an issuer to ensure that a user has been vetted and protecting the users' privacy. However, in some cases, whether or not a token is issued reveals a lot of information to an adversary about the strategies used to distinguish honest users from bots or attackers. In this work, we focus on designing an anonymous token protocol between a client and an issuer (also a verifier) that enables the issuer to support its fraud detection mechanisms while preserving users' privacy. This is done by allowing the issuer to embed a hidden (from the client) metadata bit into the tokens. We first study an existing protocol from CRYPTO 2020 which is an extension of Privacy Pass from PoPETs 2018; that protocol aimed to provide support for a hidden metadata bit, but provided a somewhat restricted security notion. We demonstrate a new attack, showing that this is a weakness of the protocol, not just the definition. In particular, the metadata bit hiding is weak in the setting where the attacker can redeem some tokens and get feedback on whether the bit extraction succeeded. We then revisit the formalism of anonymous tokens with private metadata bit, consider the more natural notion, and design a scheme which achieves it. In order to design this new secure protocol, we base our construction on algebraic MACs instead of PRFs. Our security definitions capture a realistic threat model where adversaries could, through direct feedback or side channels, learn the embedded bit when the token is redeemed. Finally, we compare our protocol with one of the CRYPTO 2020 protocols. We obtain 20% more efficient performance.

Comparison of integers, a traditional topic in secure multiparty computation since Yao's pioneering work on "Millionaires' Problem" (FOCS 1982), is also well studied in card-based cryptography. For the problem, Miyahara et al. (Theoretical Computer Science, 2020) proposed a protocol using binary cards (i.e., cards with two kinds of symbols) that is highly efficient in terms of numbers of cards and shuffles, and its extension to number cards (i.e., cards with distinct symbols). In this paper, with a different design strategy which we name "Tug-of-War technique", we propose new protocols based on binary cards and on number cards. For binary cards, our protocol improves the previous protocol asymptotically (in bit lengths of input integers) in terms of numbers of cards and shuffles when adopting ternary encoding of input integers. For number cards, at the cost of increasing the number of cards, our protocol improves the number of shuffles of the previous protocol even with binary encoding, and more with $q$-ary encoding where $q > 2$.