zkPoH: Zero-Knowledge Proof-of-Hodl

The email provides an in-depth technical comparison and explanation of different cryptographic constructions used within blockchain technologies, namely AUT-CT (Authenticated Curve Trees) and zkPoH (Zero-Knowledge Proof of Hash). AUT-CT leverages a highly optimized Taproot and Curve Trees construction. This optimization is significant in scenarios where proving ownership of certain assets or conditions without revealing all underlying data is essential. For example, AUT-CT can be utilized to prove that a user holds a specific amount of currency (sats) utilizing a bulletproofs circuit. This method was highlighted in a blog post, which details the process of proof of ownership for a range of utxos from a snapshot using bulletproofs, a general-purpose proving system known for its compact proofs at the cost of less efficient verification performance.

On the other hand, zkPoH involves a more general-purpose circuit that can handle various application-specific conditions but may suffer from poor verification performance when dealing with hashed outputs. The original bulletproofs paper is cited as a fundamental resource that outlines the capability of bulletproofs in these kinds of applications. Despite bulletproofs not being a SNARK (Succinct Non-interactive ARgument of Knowledge), its utility in certain scenarios, such as when working with a utxo snapshot of taproot utxos, is evident. In such cases, the circuit only needs to demonstrate ownership of a number of curve-tree-leaves and the attached sums within specific limits, which does not expose the drawbacks of bulletproofs due to the simplicity of the required proof.

In summary, both AUT-CT and zkPoH provide valuable tools for blockchain applications, though their effectiveness can vary based on the specific requirements of the verification process and the nature of the outputs involved. The detailed discussion underscores the importance of choosing the right cryptographic tools based on the balance between proof compactness and verification scalability.