Post Quantum Fuzzy Stealth Signatures and Applications

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. In this work, we formalize the underlying cryptographic abstraction of this mechanism, namely, stealth signatures with formal game-based definitions. We show a surprising application of our notions to passwordless authentication defined in the Fast IDentity Online (FIDO) standard. We then present SPIRIT, the first efficient post-quantum secure stealth signature construction based on the NIST standardized signature and key-encapsulation schemes, Dilithium and Kyber. The basic form of SPIRIT is only secure in a weak security model, but we provide an efficiency-preserving and generic transform, which boosts the security of SPIRIT to guarantee the strongest security notion defined in this work. Compared to state-of-the-art, there is an approximately 800x improvement in the signature size while keeping signing and verification as efficient as 0.2 ms. We extend SPIRIT with a fuzzy tracking functionality where recipients can outsource the tracking of incoming transactions to a tracking server, satisfying an anonymity notion similar to that of fuzzy message detection (FMD) recently introduced in [CCS 2021]. We also extend SPIRIT with a new fuzzy tracking framework called scalable fuzzy tracking that we introduce in this work. This new framework can be considered as a dual of FMD, in that it reduces the tracking server\u27s computational workload to sublinear in the number of users, as opposed to linear in FMD. Experimental results show that, for millions of users, the server only needs 3.4 ms to filter each incoming message which is a significant improvement upon the state-of-the-art

MatRiCT: Efficient, Scalable and Post-Quantum Blockchain Confidential Transactions Protocol

We introduce MatRiCT, an efficient RingCT protocol for blockchain confidential transactions, whose security is based on ``post-quantum\u27\u27 (module) lattice assumptions. The proof length of the protocol is around two orders of magnitude shorter than the existing post-quantum proposal, and scales efficiently to large anonymity sets, unlike the existing proposal. Further, we provide the first full implementation of a post-quantum RingCT, demonstrating the practicality of our scheme. In particular, a typical transaction can be generated in a fraction of a second and verified in about 23 ms on a standard PC. Moreover, we show how our scheme can be extended to provide auditability, where a user can select a particular authority from a set of authorities to reveal her identity. The user also has the ability to select no auditing and all these auditing options may co-exist in the same environment. The key ingredients, introduced in this work, of MatRiCT are 1) the shortest to date scalable ring signature from standard lattice assumptions with no Gaussian sampling required, 2) a novel balance zero-knowledge proof and 3) a novel extractable commitment scheme from (module) lattices. We believe these ingredients to be of independent interest for other privacy-preserving applications such as secure e-voting. Despite allowing 64-bit precision for transaction amounts, our new balance proof, and thus our protocol, does not require a range proof on a wide range (such as 32- or 64-bit ranges), which has been a major obstacle against efficient lattice-based solutions. Further, we provide new formal definitions for RingCT-like protocols, where the real-world blockchain setting is captured more closely. The definitions are applicable in a generic setting, and thus are believed to contribute to the development of future confidential transaction protocols in general (not only in the lattice setting)

SoK: Privacy-Preserving Signatures

Modern security systems depend fundamentally on the ability of users to authenticate their communications to other parties in a network. Unfortunately, cryptographic authentication can substantially undermine the privacy of users. One possible solution to this problem is to use privacy-preserving cryptographic authentication. These protocols allow users to authenticate their communications without revealing their identity to the verifier. In the non-interactive setting, the most common protocols include blind, ring, and group signatures, each of which has been the subject of enormous research in the security and cryptography literature. These primitives are now being deployed at scale in major applications, including Intel\u27s SGX software attestation framework. The depth of the research literature and the prospect of large-scale deployment motivate us to systematize our understanding of the research in this area. This work provides an overview of these techniques, focusing on applications and efficiency

Lattice-Based Linkable Ring Signature in the Standard Model

Ring signatures enable a user to sign messages on behalf of an arbitrary set of users, called the ring. The anonymity property guarantees that the signature does not reveal which member of the ring signed the message. The notion of linkable ring signatures (LRS) is an extension of the concept of ring signatures such that there is a public way of determining whether two signatures have been produced by the same signer. Lattice-based LRS is an important and active research line since lattice-based cryptography has attracted more attention due to its distinctive features, especially the quantum-resistant. However, all the existing lattice-based LRS relied on random oracle heuristics, i.e., no lattice-based LRS in the standard model has been introduced so far. In this paper, we present a lattice-based LRS scheme in the standard model. Toward our goal, we present a lattice basis extending algorithm which is the key ingredient in our construction, that may be of indepen- dent interes

PayMo: Payment Channels For Monero

Decentralized cryptocurrencies still suffer from three interrelated weaknesses: Low transaction rates, high transaction fees, and long confirmation times. Payment Channels promise to be a solution to these issues, and many constructions for real-life cryptocurrencies, such as Bitcoin, are known. Somewhat surprisingly, no such solution is known for Monero, the largest privacy-preserving cryptocurrency, without requiring system-wide changes like a hard-fork of its blockchain. In this work, we close this gap by presenting \textsc{PayMo}, the first payment channel protocol that is fully compatible with Monero. \textsc{PayMo} does not require any modification of Monero and can be readily used to perform off-chain payments. Notably, transactions in \textsc{PayMo} are identical to standard transactions in Monero, therefore not hampering the coins\u27 fungibility. Using \textsc{PayMo}, we also construct the first fully compatible secure atomic-swap protocol for Monero: One can now securely swap a token of Monero with a token of several major cryptocurrencies such as Bitcoin, Ethereum, Ripple, Cardano, etc. Before our work, it was not known how to implement secure atomic swaps protocols for Monero without forcing a hard fork. Our main technical contribution is a new construction of an efficient verifiable timed linkable ring signature, where signatures can be hidden for a pre-determined amount of time, in a verifiable way. Our scheme is fully compatible with the transaction scheme of Monero and it might be of independent interest. We implemented \textsc{PayMo} and our results show that, even with high network latency and with a single CPU core, two regular users can perform up to 93500 payments over a span of 2 minutes (the block production rate of Monero). This is approximately five orders of magnitude improvement over the current payment rate of Monero

Asynchronous Remote Key Generation for Post-Quantum Cryptosystems from Lattices

Asynchronous Remote Key Generation (ARKG), introduced by Frymann et al. at CCS 2020, allows for the generation of unlinkable public keys by third parties, for which corresponding private keys may be later learned only by the key pair\u27s legitimate owner. These key pairs can then be used in common public-key cryptosystems, including signatures, PKE, KEMs, and schemes supporting delegation, such as proxy signatures. The only known instance of ARKG generates discrete-log-based keys. In this paper, we introduce new ARKG constructions for lattice-based cryptosystems. The key pairs generated using our ARKG scheme can be applied to lattice-based signatures and KEMs, which have recently been selected for standardisation in the NIST PQ process, or as alternative candidates. In particular, we address challenges associated with the noisiness of lattice hardness assumptions, which requires a new generalised definition of ARKG correctness, whilst preserving the security and privacy properties of the former instantiation. Our ARKG construction uses key encapsulation techniques by Brendel et al. (SAC 2020) coined Split KEMs. As an additional contribution, we also show that Kyber (Bos et al., EuroS&P 2018) can be used to construct a Split KEM. The security of our protocol is based on standard LWE assumptions. We also discuss its use with selected candidates from the NIST process and provide an implementation and benchmarks

Towards compact bandwidth and efficient privacy-preserving computation

In traditional cryptographic applications, cryptographic mechanisms are employed to ensure the security and integrity of communication or storage. In these scenarios, the primary threat is usually an external adversary trying to intercept or tamper with the communication between two parties. On the other hand, in the context of privacy-preserving computation or secure computation, the cryptographic techniques are developed with a different goal in mind: to protect the privacy of the participants involved in a computation from each other. Specifically, privacy-preserving computation allows multiple parties to jointly compute a function without revealing their inputs and it has numerous applications in various fields, including finance, healthcare, and data analysis. It allows for collaboration and data sharing without compromising the privacy of sensitive data, which is becoming increasingly important in today's digital age. While privacy-preserving computation has gained significant attention in recent times due to its strong security and numerous potential applications, its efficiency remains its Achilles' heel. Privacy-preserving protocols require significantly higher computational overhead and bandwidth when compared to baseline (i.e., insecure) protocols. Therefore, finding ways to minimize the overhead, whether it be in terms of computation or communication, asymptotically or concretely, while maintaining security in a reasonable manner remains an exciting problem to work on. This thesis is centred around enhancing efficiency and reducing the costs of communication and computation for commonly used privacy-preserving primitives, including private set intersection, oblivious transfer, and stealth signatures. Our primary focus is on optimizing the performance of these primitives.Im Gegensatz zu traditionellen kryptografischen Aufgaben, bei denen Kryptografie verwendet wird, um die Sicherheit und Integrität von Kommunikation oder Speicherung zu gewährleisten und der Gegner typischerweise ein Außenstehender ist, der versucht, die Kommunikation zwischen Sender und Empfänger abzuhören, ist die Kryptografie, die in der datenschutzbewahrenden Berechnung (oder sicheren Berechnung) verwendet wird, darauf ausgelegt, die Privatsphäre der Teilnehmer voreinander zu schützen. Insbesondere ermöglicht die datenschutzbewahrende Berechnung es mehreren Parteien, gemeinsam eine Funktion zu berechnen, ohne ihre Eingaben zu offenbaren. Sie findet zahlreiche Anwendungen in verschiedenen Bereichen, einschließlich Finanzen, Gesundheitswesen und Datenanalyse. Sie ermöglicht eine Zusammenarbeit und Datenaustausch, ohne die Privatsphäre sensibler Daten zu kompromittieren, was in der heutigen digitalen Ära immer wichtiger wird. Obwohl datenschutzbewahrende Berechnung aufgrund ihrer starken Sicherheit und zahlreichen potenziellen Anwendungen in jüngster Zeit erhebliche Aufmerksamkeit erregt hat, bleibt ihre Effizienz ihre Achillesferse. Datenschutzbewahrende Protokolle erfordern deutlich höhere Rechenkosten und Kommunikationsbandbreite im Vergleich zu Baseline-Protokollen (d.h. unsicheren Protokollen). Daher bleibt es eine spannende Aufgabe, Möglichkeiten zu finden, um den Overhead zu minimieren (sei es in Bezug auf Rechen- oder Kommunikationsleistung, asymptotisch oder konkret), während die Sicherheit auf eine angemessene Weise gewährleistet bleibt. Diese Arbeit konzentriert sich auf die Verbesserung der Effizienz und Reduzierung der Kosten für Kommunikation und Berechnung für gängige datenschutzbewahrende Primitiven, einschließlich private Schnittmenge, vergesslicher Transfer und Stealth-Signaturen. Unser Hauptaugenmerk liegt auf der Optimierung der Leistung dieser Primitiven

Extendable Threshold Ring Signatures with Enhanced Anonymity

Threshold ring signatures are digital signatures that allow $t$ parties to sign a message while hiding their identity in a larger set of $n$ users called \u27\u27ring\u27\u27. Recently, Aranha et al. [PKC 2022] introduced the notion of \emph{extendable} threshold ring signatures (ETRS). ETRS allow one to update, in a non-interactive manner, a threshold ring signature on a certain message so that the updated signature has a greater threshold, and/or an augmented set of potential signers. An application of this primitive is anonymous count me in. A first signer creates a ring signature with a sufficiently large ring announcing a proposition in the signed message. After such cause becomes \emph{public}, other parties can anonymously decide to support that proposal by producing an updated signature. Crucially, such applications rely on partial signatures being posted on a \emph{publicly accessible} bulletin board since users may not know/trust each other. In this paper, we first point out that even if anonymous count me in was suggested as an application of ETRS, the anonymity notion proposed in the previous work is insufficient in many application scenarios. Indeed, the existing notion guarantees anonymity only against adversaries who just see the last signature, and are not allowed to access the \u27\u27full evolution of an ETRS. This is in stark contrast with applications where partial signatures are posted in a public bulletin board. We therefore propose stronger anonymity definitions and construct a new ETRS that satisfies such definitions. Interestingly, while satisfying stronger anonymity properties, our ETRS asymptotically improves on the two ETRS presented in prior work [PKC 2022] in terms of both time complexity and signature size. Our ETRS relies on extendable non-interactive witness-indistinguishable proof of knowledge (ENIWI PoK), a novel technical tool that we formalize and construct, and that may be of independent interest. We build our constructions from pairing groups under the SXDH assumption

Cryptography for Bitcoin and friends

Numerous cryptographic extensions to Bitcoin have been proposed since Satoshi Nakamoto introduced the revolutionary design in 2008. However, only few proposals have been adopted in Bitcoin and other prevalent cryptocurrencies, whose resistance to fundamental changes has proven to grow with their success. In this dissertation, we introduce four cryptographic techniques that advance the functionality and privacy provided by Bitcoin and similar cryptocurrencies without requiring fundamental changes in their design: First, we realize smart contracts that disincentivize parties in distributed systems from making contradicting statements by penalizing such behavior by the loss of funds in a cryptocurrency. Second, we propose CoinShuffle++, a coin mixing protocol which improves the anonymity of cryptocurrency users by combining their transactions and thereby making it harder for observers to trace those transactions. The core of CoinShuffle++ is DiceMix, a novel and efficient protocol for broadcasting messages anonymously without the help of any trusted third-party anonymity proxies and in the presence of malicious participants. Third, we combine coin mixing with the existing idea to hide payment values in homomorphic commitments to obtain the ValueShuffle protocol, which enables us to overcome major obstacles to the practical deployment of coin mixing protocols. Fourth, we show how to prepare the aforementioned homomorphic commitments for a safe transition to post-quantum cryptography.Seit seiner revolutionären Erfindung durch Satoshi Nakamoto im Jahr 2008 wurden zahlreiche kryptographische Erweiterungen für Bitcoin vorgeschlagen. Gleichwohl wurden nur wenige Vorschläge in Bitcoin und andere weit verbreitete Kryptowährungen integriert, deren Resistenz gegen tiefgreifende Veränderungen augenscheinlich mit ihrer Verbreitung wächst. In dieser Dissertation schlagen wir vier kryptographische Verfahren vor, die die Funktionalität und die Datenschutzeigenschaften von Bitcoin und ähnlichen Kryptowährungen verbessern ohne deren Funktionsweise tiefgreifend verändern zu müssen. Erstens realisieren wir Smart Contracts, die es erlauben widersprüchliche Aussagen einer Vertragspartei mit dem Verlust von Kryptogeld zu bestrafen. Zweitens schlagen wir CoinShuffle++ vor, ein Mix-Protokoll, das die Anonymität von Benutzern verbessert, indem es ihre Transaktionen kombiniert und so deren Rückverfolgung erschwert. Sein Herzstück ist DiceMix, ein neues und effizientes Protokoll zur anonymen Veröffentlichung von Nachrichten ohne vertrauenswürdige Dritte und in der Präsenz von bösartigen Teilnehmern. Drittens kombinieren wir dieses Protokoll mit der existierenden Idee, Geldbeträge in Commitments zu verbergen, und erhalten so das ValueShuffle-Protokoll, das uns ermöglicht, große Hindernisse für den praktischen Einsatz von Mix-Protokollen zu überwinden. Viertens zeigen wir, wie die dabei benutzten Commitments für einen sicheren Übergang zu Post-Quanten-Kryptographie vorbereitet werden können