We propose efficient, post-quantum threshold ring signatures constructed from one-wayness of AES encryption and the VOLE-in-the-Head zero-knowledge proof system. Our scheme scales efficiently to large rings and extends the linkable ring signatures paradigm. We define and construct key-binding deterministic tags to achieve linkability. We then extend our threshold ring signatures to realize post-quantum anonymous ledger transactions in the spirit of Monero. Finally, our deterministic tags also enable succinct aggregation using approximate lower bound arguments of knowledge; this allows us to achieve succinct (approximate) multi-signatures without SNARKs. Our constructions assume symmetric key primitives only.

Recent years have seen the emergence of practical advanced cryptographic tools that not only protect data privacy and authenticity, but also allow for jointly processing data from different institutions without sacrificing privacy. The ability to do so has enabled implementations of a number of traditional and decentralized financial applications that would have required sacrificing privacy or trusting a third party. The main catalyst of this revolution was the advent of decentralized cryptocurrencies that use public ledgers to register financial transactions, which must be verifiable by any third party, while keeping sensitive data private. Zero Knowledge (ZK) proofs rose to prominence as a solution to this challenge, allowing for the owner of sensitive data (e.g. the identities of users involved in an operation) to convince a third party verifier that a certain operation has been correctly executed without revealing said data. It quickly became clear that performing arbitrary computation on private data from multiple sources by means of secure Multiparty Computation (MPC) and related techniques allows for more powerful financial applications, also in traditional finance. In this SoK, we categorize the main traditional and decentralized financial applications that can benefit from state-of-the-art Privacy-Enhancing Technologies (PETs) and identify design patterns commonly used when applying PETs in the context of these applications. In particular, we consider the following classes of applications: 1. Identity Management, KYC & AML; 2. Markets & Settlement; 3. Legal; and 4. Digital Asset Custody. We examine how ZK proofs, MPC and related PETs have been used to tackle the main security challenges in each of these applications. Moreover, we provide an assessment of the technological readiness of each PET in the context of different financial applications according to the availability of: theoretical feasibility results, preliminary benchmarks (in scientific papers) or benchmarks achieving real-world performance (in commercially deployed solutions). Finally, we propose future applications of PETs as Fintech solutions to currently unsolved issues. While we systematize financial applications of PETs at large, we focus mainly on those applications that require privacy preserving computation on data from multiple parties.

Automated Market Makers (AMMs) are decentralized applications that allow users to exchange crypto-tokens without the need for a matching exchange order. AMMs are one of the most successful DeFi use cases: indeed, major AMM platforms process a daily volume of transactions worth USD billions. Despite their popularity, AMMs are well-known to suffer from transaction-ordering issues: adversaries can influence the ordering of user transactions, and possibly front-run them with their own, to extract value from AMMs, to the detriment of users. We devise an effective procedure to construct a strategy through which an adversary can maximize the value extracted from user transactions.

In the classical setting of differential privacy, a privacy-preserving query is performed on a private database, after which the query result is released to the analyst; a differentially private query ensures that the presence of a single database entry is protected from the analyst’s view. In this work, we contribute the first definitional framework for differential privacy in the trusted curator setting (Fig. 1); clients submit private inputs to the trusted curator, which then computes individual outputs privately returned to each client. The adversary is more powerful than the standard setting; it can corrupt up to n-1 clients and subsequently decide inputs and learn outputs of corrupted parties. In this setting, the adversary also obtains leakage from the honest output that is correlated with a corrupted output. Standard differentially private mechanisms protect client inputs but do not mitigate output correlation leaking arbitrary client information, which can forfeit client privacy completely. We initiate the investigation of a novel notion of correlated-output differential privacy to bound the leakage from output correlation in the trusted curator setting. We define the satisfaction of both standard and correlated-output differential privacy as round differential privacy and highlight the relevance of this novel privacy notion to all application domains in the trusted curator model. We explore round differential privacy in traditional "dark pool" market venues, which promise privacy-preserving trade execution to mitigate front-running; privately submitted trade orders and trade execution are kept private by the trusted venue operator. We observe that dark pools satisfy neither classic nor correlated-output differential privacy; in markets with low trade activity, the adversary may trivially observe recurring, honest trading patterns, and anticipate and front-run future trades. In response, we present the first round differentially private market mechanisms that formally mitigate information leakage from all trading activity of a user. This is achieved with fuzzy order matching, inspired by the standard randomized response mechanism; however, this also introduces a liquidity mismatch as buy and sell orders are not guaranteed to execute pairwise, thereby weakening output correlation; this mismatch is compensated for by a round differentially private liquidity provider mechanism, which freezes a noisy amount of assets from the liquidity provider for the duration of a privacy epoch, but leaves trader balances unaffected. We propose oblivious algorithms for realizing our proposed market mechanisms with secure multi-party computation (MPC) and implement these in the Scale-Mamba Framework using Shamir Secret Sharing based MPC. We demonstrate practical, round differentially private trading with comparable throughput as prior work implementing (traditional) dark pool algorithms in MPC; our experiments demonstrate practicality for both traditional finance and decentralized finance settings.

Automated market makers (AMMs) are one of the most prominent decentralized finance (DeFi) applications. AMMs allow users to trade different types of crypto-tokens, without the need to find a counter-party. There are several implementations and models for AMMs, featuring a variety of sophisticated economic mechanisms. We present a theory of AMMs. The core of our theory is an abstract operational model of the interactions between users and AMMs, which can be concretised by instantiating the economic mechanisms. We exploit our theory to formally prove a set of fundamental properties of AMMs, characterizing both structural and economic aspects. We do this by abstracting from the actual economic mechanisms used in implementations, and identifying sufficient conditions which ensure the relevant properties. Notably, we devise a general solution to the arbitrage problem, the main game-theoretic foundation behind the economic mechanisms of AMMs.