Zero Knowledge Proofs and Applications to Financial Regulation

Abstract

We consider zero-knowledge proofs, a class of cryptographic protocols by which an agent (a Prover) can prove to another agent (a Verifier) that a statement is true without revealing any additional information. For example, a zero-knowledge proof allows one to prove knowledge of a password to somebody at the other end of the communication without actually revealing the password. We present an introduction to and survey literature on zero-knowledge proofs, covering the history, formal definition, and classical applications of zero-knowledge proofs. In addition, we consider connections to complexity, demonstrating that all problems in the complexity class NP have zero-knowledge proofs, and also discuss more exotic applications of zero-knowledge, namely in electronic voting and nuclear disarmament. We then consider applications of zero-knowledge to financial regulation, specifically in balancing transparency and confidentiality in financial reporting. Namely, we polled professionals in the financial industry to identify three major classes of regulatory problems. We then utilize zero-knowledge proofs to develop and present cryptographic protocols/mechanisms and solutions to these regulatory problems: (1) An employer verifying an employee has no financial holdings on a blacklist without revealing the other (allowed) holdings of the employee, (2) A fund convincing its investors that its holdings subscribe to particular risk constraints, without disclosing the actual holdings, (3) A collection of investors of a fund verifying aggregate information provided by the fund, while preserving pairwise anonymity. Applications (1) and (3) are novel applications developed in this paper, while (2) is drawn from [47].