This paper is about a new way to make public blockchains more private while still allowing for regulatory compliance. Public blockchains are transparent by design, which means that anyone can see every transaction that happens on the blockchain. While this is good for transparency, it can be problematic for privacy. The new protocol, called Privacy Pools, aims to create a balance between privacy and transparency.

The core idea of Privacy Pools is to allow users to publish zero-knowledge proofs to demonstrate that their funds do not come from known unlawful sources without revealing their entire transaction history. Zero-knowledge proofs are a way to prove that something is true without revealing any other information. For example, if you want to prove that you know a secret password, you can use a zero-knowledge proof to prove that you know the password without revealing what the password is.

In the case of Privacy Pools, users can use zero-knowledge proofs to prove that their funds are not coming from known unlawful sources without revealing their entire transaction history. This is done by grouping transactions together into association sets. These association sets are constructed in a way that satisfies certain properties required by regulation or social consensus. Users can then prove membership in these association sets using zero-knowledge proofs.

The proposal could support arbitrary denominations and discuss special cases like re-proofing, bilateral direct proofs, and sequential proofs. This means that the protocol could work with any amount of cryptocurrency and could handle more complex transactions.

The paper also discusses the potential benefits and drawbacks of using zero-knowledge proofs to prove regulatory compliance. On the one hand, zero-knowledge proofs can enable regulatory compliance without revealing entire transaction histories, which could be beneficial for industries such as finance and self-sovereign identities. On the other hand, there are concerns about the scalability and complexity of using zero-knowledge proofs.

Privacy Pools could be a first step towards a future where people could prove regulatory compliance without having to reveal their entire transaction history. This could be beneficial for industries such as finance and self-sovereign identities, where privacy and regulatory compliance are both important.

The paper provides a technical background on zero-knowledge proofs and Privacy Pools. It elaborates on further technical details and special cases of Privacy Pools. The paper concludes with practical considerations and potential future applications of Privacy Pools-like protocols beyond finance and self-sovereign identities.