Anamorphic signatures allow covert communication through signatures in environments where encryption is restricted. They enable trusted recipients with a double-key to extract hidden messages while the signature remains indistinguishable from a regular one. However, the traditional notion of anamorphic signatures suffers from vulnerabilities, particularly when a single recipient or sender is compromised, exposing all hidden messages and providing undeniable proof that citizens are part of the anamorphic exchange. To address these limitations, we explore a threshold-based approach to distribute trust among multiple recipients, preventing adversaries from decrypting anamorphic messages even if some recipients are compromised. Our first contribution is the formalization of the notion of threshold-recipient anamorphic signatures, where decryption is possible only through collaboration among a subset of recipients. We then explore a stronger model in which the dictator controls the key-generation process through which it learns all secret keys, as well as how citizens store cryptographic keys. A particular example of this model in the real world is a dictator providing citizens with electronic identity documents (eIDs) and blocking all other usage of cryptography. We demonstrate that anamorphic communication is still possible even in such a scenario. Our construction is secure against quantum adversaries and does not rely on any computational assumptions beyond the random-oracle model. Finally, we present an impossibility result for encoding anamorphic messages with a threshold-sender model when using many existing threshold signature schemes, even when the adversary is part of the signing group. Our work outlines both the possibilities and limitations of extending anamorphic signatures with threshold cryptography, offering new insights into improving the security and privacy of individuals under authoritarian regimes.

Web3 applications, such as on-chain games, NFT minting, and leader elections necessitate access to unbiased, unpredictable, and publicly verifiable randomness. Despite its broad use cases and huge demand, there is a notable absence of comprehensive treatments of on-chain verifiable randomness services. To bridge this, we offer an extensive formal analysis of on-chain verifiable randomness services. We present the first formalization of on-chain verifiable randomness in the blockchain setting by introducing the notion of Verifiable Randomness as a Service (VRaaS). We formally define VRaaS using an ideal functionality$\mathcal{F}\text{VRaaS}$in the Universal Composability model. Our definition not only captures the core features of randomness services, such as unbiasability, unpredictability, and public verifiability, but also accounts for many other crucial nuances pertaining to different entities involved, such as smart contracts. Within our framework we study a generic design of Verifiable Random Function (VRF)-based randomness service - where the randomness requester provides an input on which the randomness is evaluated as VRF output. We show that it does satisfy our formal VRaaS definition. Furthermore, we show that the generic protocol captures many real-world randomness services like Chainlink VRF and Supra dVRF. Moreover, we investigate the minimalism of the frame-work. Towards that, first we show that, the two transactions in-built in our framework are actually necessary for any randomness service to support the essential qualities. We also discover practical vulnerabilities in other designs such as Algorand beacon, Pyth VRF and Band VRF, captured within our framework.

Blockchain service offerings have seen a rapid rise in recent times. Many of these services realize a decentralized architecture with a threshold adversary to avoid a single point of failure and to mitigate key escrow issues. Although payments to such services are straightforward in systems that support smart contracts, achieving fairness poses challenges in systems like Bitcoin, which use the UTXO model with limited scripting capabilities. This is especially challenging without smart contracts, as we wish to pay only the required threshold of$t$+ 1 out of the$n$servers offering the service, without any server claiming payment twice. In this paper, we introduce Vitārit11.A Sanskrit word for ‘distributed’, a novel payment solution tailored for threshold cryptographic services in UTXO systems like Bitcoin. Our approach guarantees robust, provable security while facilitating practical deployment. We focus on the t-out-of-n distributed threshold verifiable random function (VRF) service with certain properties, such as threshold BLS signatures, a recently highlighted area of interest. Our protocol enables clients to request verifiable random function (VRF) values from the threshold service, triggering payments to up to$t$+ 1 servers of the distributed threshold VRF. Our efficient design relies on simple transactions using signature verification scripts, making it immediately applicable in Bitcoin-like systems. We also introduce new tools and techniques at both the cryptographic and transaction layers, including a novel signature-VRF exchange protocol for standard constructions, which may be of independent interest. Additionally, our transaction flow design prevents malicious servers from claiming payments twice, offering broader implications for decentralized payment systems. Our prototype implementation shows that in the two-party interaction, the client takes 126.4 msec, and the server takes 204 msec, demonstrating practicality and deployability of the system.

We put forward a non-interactive verifiable secret sharing (NI-VSS) scheme using class groups - we call it cgVSS. Our construction follows the standard framework of encrypting the shares to a set of recipients and generating a non-interactive proof of correct sharing. However, as opposed to prior works, such as Groth's [Eprint 2021], or Gentry et al.'s [Eurocrypt 2022], we do not require any range proof - this is possible due to the unique structure of class groups, that enables efficient encryption/decryption of large field elements in the exponent of an ElGamal-style encryption scheme. Importantly, this is possible without destroying the additive homomorphic structure, which is required to make the proof-of-correctness highly efficient. This approach not only substantially simplifies the NI-VSS process, but also outperforms the state-of-art schemes significantly. For example, our implementation shows that for a 150 node system cgVSS outperforms (a simplified implementation of) Groth's protocol in overall communication complexity by 5.6x, about 9.3 -- 9.7x in the dealer time and 2.4 - 2.7x in the receiver time per node.

In scenarios where a seller holds sensitive data x, like employee / patient records or ecological data, and a buyer seeks to obtain an evaluation of specific function f on this data, solutions in trustless digital environments like blockchain-based Web3 systems typically fall into two categories: (1) Smart contract-powered solutions and (2) cryptographic solutions leveraging tools such as adaptor signatures. The former approach offers atomic transactions where the buyer learns the function evaluation f(x) (and not x entirely) upon payment. However, this approach is often inefficient, costly, lacks privacy for the seller's data, and is incompatible with systems that do not support smart contracts with required functionalities. In contrast, the adaptor signature-based approach addresses all of the above issues but comes with an "all-or-nothing" guarantee, where the buyer fully extracts x and does not support functional extraction of the sensitive data. In this work, we aim to bridge the gap between these approaches, developing a solution that enables fair functional sales of information while offering improved efficiency, privacy, and compatibility similar to adaptor signatures.

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-UC1, 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 SweepUC 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.

Private payments in blockchain-based cryptocurrencies have been a topic of research, both academic and industrial, ever since the advent of Bitcoin. Stealth address payments were proposed as a solution to improve payment privacy for users and are, in fact, deployed in several major cryptocurrencies today. The mechanism lets users receive payments so that none of these payments are linkable to each other or the recipient. Currently known stealth address mechanisms either (1) are insecure in certain reasonable adversarial models, (2) are inefficient in practice or (3) are incompatible with many existing currencies.

Payment channels (PC) are a promising solution to the scalability issue of cryptocurrencies, allowing users to perform the bulk of the transactions off-chain without needing to post everything on the blockchain. Many PC proposals however, suffer from a severe limitation: Both parties need to constantly monitor the blockchain to ensure that the other party did not post an outdated transaction. If this event happens, the honest party needs to react promptly and engage in a punishment procedure. This means that prolonged absence periods (e.g., a power outage) may be exploited by malicious users. As a mitigation, the community has introduced watchtowers, a third-party monitoring the blockchain on behalf of off-line users. Unfortunately, watchtowers are either trusted, which is critical from a security perspective, or they have to lock a certain amount of coins, called collateral, for each monitored PC in order to be held accountable, which is financially infeasible for a large network. We present Sleepy Channels, the first bi-directional PC protocol without watchtowers (or any other third party) that supports an unbounded number of payments and does not require parties to be persistently online. The key idea is to confine the period in which PC updates can be validated on-chain to a short, pre-determined time window, which is when the PC parties have to be online. This behavior is incentivized by letting the parties lock a collateral in the PC, which can be adjusted depending on their mutual trust and which they get back much sooner if they are online during this time window. Our protocol is compatible with any blockchain that is capable of verifying digital signatures (e.g., Bitcoin), as shown by our proof of concept. Moreover, our experimental results show that Sleepy Channels impose a communication and computation overhead similar to state-of-the-art PC protocols while removing watchtower's collateral and fees for the monitoring service.

Coin mixing services allow users to mix their cryptocurrency coins and thus enable unlinkable payments in a way that prevents tracking of honest users' coins by both the service provider and the users themselves. The easy bootstrapping of new users and backwards compatibility with cryptocurrencies (such as Bitcoin) with limited support for scripts are attractive features of this architecture, which has recently gained considerable attention in both academia and industry.

Trading goods lies at the backbone of the modern economy and the recent advent of cryptocurrencies has opened the door for trading decentralized (digital) assets: A large fraction of the value of cryptocurrencies comes from the inter-currency exchange and trading, which has been arguably the most successful application of decentralized money. The security issues observed with centralized, custodial cryptocurrency exchanges have motivated the design of atomic swaps, a protocol for coin exchanges between any two users. Yet, somewhat surprisingly, no atomic swap protocol exists that simultaneously satisfies the following simple but desired properties: (i) non-custodial, departing from a third party trusted holding the coins from users during the exchange; (ii) universal that is, compatible with all (current and future) cryptocurrencies; (iii) multi-asset, supporting the exchange of multiple coins in a single atomic swap.From a theoretical standpoint, in this work we show a generic protocol to securely swap n coins from any (possible multiple) currencies for $\tilde{n}$ coins of any other currencies, for any n and $\tilde{n}$. We do not require any custom scripting language supported by the corresponding blockchains, besides the bare minimum ability to verify signatures on transactions. For the special case when the blockchains use ECDSA or Schnorr signatures, we design a practically efficient protocol based on adaptor signatures and time-lock puzzles. As a byproduct of our approach, atomic swaps transactions no longer include custom scripts and are identical to standard one-to-one transactions. We also show that our protocol naturally generalizes to any cycle of users, i.e., atomic swaps with more than two participants. To demonstrate the practicality of our approach, we have evaluated a prototypical implementation of our protocol for Schnorr/ECDSA signatures and observed that an atomic swap requires below one second on commodity machines. Even on blockchains with expressive smart contract support (e.g., Ethereum), our approach reduces the on-chain cost both in terms of transaction size and gas cost.

Timed commitments [Boneh and Naor, CRYPTO 2000] are the timed analogue of standard commitments, where the commitment can be non-interactively opened after a pre-specified amount of time passes. Timed commitments have a large spectrum of applications, such as sealed bid auctions, fair contract signing, fair multi-party computation, and cryptocurrency payments. Unfortunately, all practical constructions rely on a (private-coin) trusted setup and do not scale well with the number of participants. These are two severe limiting factors that have hindered the widespread adoption of this primitive.

Repeated Modular Squaring is a versatile computational operation that has led to practical constructions of timed-cryptographic primitives like time-lock puzzles (TLP) and verifiable delay functions (VDF) that have a fast growing list of applications. While there is a huge interest for timed-cryptographic primitives in the blockchains area, we find two real-world concerns that need immediate attention towards their large-scale practical adoption: Firstly, the requirement to constantly perform computations seems unrealistic for most of the users. Secondly, choosing the parameters for the bound (T) seems complicated due to the lack of heuristics and experience. We present OpenSquare, a decentralized repeated modular squaring service, that overcomes the above concerns. OpenSquare lets clients outsource their repeated modular squaring computation via smart contracts to any computationally powerful servers that offer computational services for rewards in an unlinkable manner.

Payment Channel Networks (PCNs) have given a huge boost to the scalability of blockchain-based cryptocurrencies: Beyond improving the transaction rate, PCNs enabled cheap cross-currency payments and atomic swaps. However, current PCNs proposals either heavily rely on special scripting features of the underlying blockchain (e.g. Hash Time Lock Contracts) or are tailored to a handful of digital signature schemes, such as Schnorr or ECDSA signatures. This leaves us in an unsatisfactory situation where many currencies that are being actively developed and use different signature schemes cannot enjoy the benefits of a PCN.In this work, we investigate whether we can construct PCNs assuming the minimal ability of a blockchain to verify a digital signature, for any signature scheme. In answering this question in the affirmative, we introduce the notion of lockable signatures, which constitutes the cornerstone of our PCN protocols. Our approach is generic and the PCN protocol is compatible with any digital signature scheme, thus inheriting all favorable properties of the underlying scheme that are not offered by Schnorr/ECDSA (e.g. aggregatable signatures or post-quantum security).While the usage of generic cryptographic machinery makes our generic protocol impractical, we view it as an important feasibility result as it may serve as the basis for constructing optimized protocols for specific signature schemes. To substantiate this claim, we design a highly efficient PCN protocol for the special case of Boneh-Lynn-Shacham (BLS) signatures. BLS signatures enjoy many unique features that make it a viable candidate for a blockchain, e.g. short, unique, and aggregatable signatures. Yet, prior to our work, no PCN was known to be compatible with it (without requiring an advanced scripting language). The cost of our PCN is dominated by a handful of calls to the BLS algorithms. Our concrete evaluation of these basic operations shows that users with commodity hardware can process payments with minimal overhead.

A verifiable timed signature (VTS) scheme allows one to time-lock a signature on a known message for a given amount of time T such that after performing a sequential computation for time T anyone can extract the signature from the time-lock. Verifiability ensures that anyone can publicly check if a time-lock contains a valid signature on the message without solving it first, and that the signature can be obtained by solving the same for time T.

Monero is the largest cryptocurrency with built-in cryptographic privacy features. The transactions are authenticated using zero-knowledge spend proofs, which provide a certain level of anonymity by hiding the source accounts from which the funds are sent among a set of other accounts. Due to its similarities to ring signatures, this core cryptographic component is called Ring Confidential Transactions (RingCT). Because of its practical relevance, several works attempt to analyze the security of RingCT. Since RingCT is rather complex, most of them are either informal, miss fundamental functionalities, or introduce undesirable trusted setup assumptions. Regarding efficiency, Monero currently deploys a scheme in which the size of the spend proof is linear in the ring size. This limits the ring size to only a few accounts, which in turn limits the acquired anonymity significantly and facilitates de-anonymization attacks. As a solution to these problems, we present the first rigorous formalization of RingCT as a cryptographic primitive. We then propose a generic construction of RingCT and prove it secure in our formal security model. By instantiating our generic construction with new efficient zero-knowledge proofs, we obtain Omniring, a fully-fledged RingCT scheme in the discrete logarithm setting that provides the highest concrete and asymptotic efficiency as of today. Omniring is the first RingCT scheme which 1) does not require a trusted setup or pairing-friendly elliptic curves, 2) has a proof size logarithmic in the size of the ring, and 3) allows to share the same ring between all source accounts in a transaction, thereby enabling significantly improved privacy level without sacrificing performance. Our zero-knowledge proofs rely on novel enhancements to the Bulletproofs framework (S&P 2018), which we believe are of independent interest.

Bitcoin is an immutable permissionless blockchain system that has been extensively used as a public bulletin board by many different applications that heavily relies on its immutability. However, Bitcoin's immutability is not without its fair share of demerits. Interpol exposed the existence of harmful and potentially illegal documents, images and links in the Bitcoin blockchain, and since then there have been several qualitative and quantitative analysis on the types of data currently residing in the Bitcoin blockchain. Although there is a lot of attention on blockchains, surprisingly the previous solutions proposed for data redaction in the permissionless setting are far from feasible, and require additional trust assumptions. Hence, the problem of harmful data still poses a huge challenge for law enforcement agencies like Interpol (Tziakouris, IEEE S&P'18). We propose the first efficient redactable blockchain for the permissionless setting that is easily integrable into Bitcoin, and that does not rely on heavy cryptographic tools or trust assumptions. Our protocol uses a consensus-based voting and is parameterised by a policy that dictates the requirements and constraints for the redactions; if a redaction gathers enough votes the operation is performed on the chain. As an extra feature, our protocol offers public verifiability and accountability for the redacted chain. Moreover, we provide formal security definitions and proofs showing that our protocol is secure against redactions that were not agreed by consensus. Additionally, we show the viability of our approach with a proof-of-concept implementation that shows only a tiny overhead in the chain validation of our protocol when compared to an immutable one.

Abstract An individual’s genetic information is possibly the most valuable personal information. While knowledge of a person’s DNA sequence can facilitate the diagnosis of several heritable diseases and allow personalized treatment, its exposure comes with significant threats to the patient’s privacy. Currently known solutions for privacy-respecting computation require the owner of the DNA to either be heavily involved in the execution of a cryptographic protocol or to completely outsource the access control to a third party. This motivates the demand for cryptographic protocols which enable computation over encrypted genomic data while keeping the owner of the genome in full control. We envision a scenario where data owners can exercise arbitrary and dynamic access policies, depending on the intended use of the analysis results and on the credentials of who is conducting the analysis. At the same time, data owners are not required to maintain a local copy of their entire genetic data and do not need to exhaust their computational resources in an expensive cryptographic protocol. In this work, we present METIS, a system that assists the computation over encrypted data stored in the cloud while leaving the decision on admissible computations to the data owner. It is based on garbled circuits and supports any polynomially-computable function. A critical feature of our system is that the data owner is free from computational overload and her communication complexity is independent of the size of the input data and only linear in the size of the circuit’s output. We demonstrate the practicality of our approach with an implementation and an evaluation of several functions over real datasets.