Clean is a new domain-specific language (DSL) built in Lean 4 for formally verifying zero-knowledge circuits. It aims to bridge the gap between circuit development and formal verification by offering a high-level, functional programming style for defining circuits, along with automated proofs of correctness within Lean's powerful theorem prover. Clean compiles to the intermediate representation used by the Circom zk-SNARK toolkit, enabling practical deployment of verified circuits. This approach allows developers to write circuits in a clear, maintainable way, and rigorously prove that these circuits correctly implement the desired logic, enhancing security and trust in zero-knowledge applications. The DSL includes features like higher-order functions and algebraic data types, enabling more expressive and composable circuit design than existing tools.
This blog post explores the fascinating world of zero-knowledge proofs (ZKPs), focusing on how they can verify computational integrity without revealing any underlying information. The author uses the examples of Sudoku solutions and Super Mario speedruns to illustrate this concept. A ZKP allows someone to prove they know a valid Sudoku solution or a specific sequence of controller inputs for a speedrun without disclosing the actual solution or inputs. The post explains that this is achieved through clever cryptographic techniques that encode the "knowledge" as mathematical relationships, enabling verification of adherence to rules (Sudoku) or game mechanics (Mario) without revealing the strategy or execution. This demonstrates how ZKPs offer a powerful mechanism for trust and verification in various applications, ensuring validity while preserving privacy.
Hacker News users generally praised the clarity and accessibility of the blog post explaining zero-knowledge proofs. Several commenters highlighted the effective use of Sudoku and Mario speedruns as relatable examples, making the complex topic easier to grasp. Some pointed out the post's concise explanation of the underlying cryptographic principles and appreciated the lack of overly technical jargon. One commenter noted the clever use of visually interactive elements within the Sudoku example. There was a brief discussion about different types of zero-knowledge proofs and their applications, with some users mentioning specific use cases like verifiable computation and blockchain technology. A few commenters also offered additional resources for readers interested in delving deeper into the subject.
This blog post explores methods for proving false statements within formal systems like logic and mathematics. It focuses on proof by contradiction, where you assume the statement is true and then demonstrate that this assumption leads to a logical inconsistency, thereby proving the original statement false. The post uses the example of proving the irrationality of √2, illustrating how assuming its rationality (expressibility as a fraction) ultimately contradicts the fundamental theorem of arithmetic. It highlights the importance of clearly defining the terms and axioms of the system within which the proof operates.
Hacker News users discuss the potential misuse of zero-knowledge proofs (ZKPs), expressing concern that they could be used to convincingly lie or create fraudulent attestations. Some commenters highlight the importance of distinguishing between a ZKP verifying a computation versus verifying a real-world fact. They argue that while ZKPs can prove the correct execution of a program on given inputs, they cannot inherently prove the veracity of those inputs. Others discuss the "garbage in, garbage out" principle in this context, suggesting the need for robust, real-world verification methods alongside ZKPs to prevent their misuse. The trustworthiness of the prover remains crucial, and ZKPs alone cannot bridge the gap between computation and reality. A few comments also touch upon the complexity of understanding and implementing ZKPs correctly, potentially leading to vulnerabilities.
Summary of Comments ( 2 )
https://news.ycombinator.com/item?id=43496577
Several Hacker News commenters praise Clean's innovative approach to verifying zero-knowledge circuits, appreciating its use of Lean4 for formal proofs and its potential to improve the security and reliability of ZK systems. Some express excitement about Lean4's dependent types and metaprogramming capabilities, and how they might benefit the project. Others raise practical concerns, questioning the performance implications of using a theorem prover for this purpose, and the potential difficulty of debugging generated circuits. One commenter questions the comparison to other frameworks like Noir and Arkworks, requesting clarification on the specific advantages of Clean. Another points out the relative nascency of formal verification in the ZK space, emphasizing the need for further development and exploration. A few users also inquire about the tooling and developer experience, wondering about the availability of IDE support and debugging tools for Clean.
The Hacker News post titled "Clean, a formal verification DSL for ZK circuits in Lean4" (https://news.ycombinator.com/item?id=43496577) has a moderate number of comments discussing various aspects of the project and its implications.
Several commenters express enthusiasm for the use of Lean4, highlighting its potential for rigorous formal verification in the zero-knowledge proof space. They see the project as a positive step toward improving the security and reliability of ZK circuits. One commenter specifically praises the choice of Lean4 over other theorem provers, mentioning its speed and the active development community. This sentiment is echoed by another commenter who appreciates the metaprogramming capabilities of Lean4, suggesting it's a good fit for this kind of DSL development.
There's a discussion around the practicality and usability of formal verification for ZK circuits. One commenter questions the scalability of this approach for larger, real-world circuits, wondering if the proof development overhead becomes too significant. Another commenter points out the inherent complexity of formally verifying cryptographic primitives and protocols, acknowledging the challenge but emphasizing the importance of this work for ensuring security.
The conversation also touches upon the trade-offs between different formal verification approaches. One commenter contrasts the Lean4-based approach with other methods like Coq, highlighting potential benefits and drawbacks of each. They discuss the potential for integrating with existing tools and frameworks within the ZK ecosystem.
Some commenters delve into more technical details, discussing the specific features of Lean4 that make it well-suited for this task, such as dependent types and its metaprogramming system. They also discuss the challenges of representing ZK circuits within a formal system and the potential for automated proof generation.
Finally, there's a thread discussing the broader implications of formal verification in the context of blockchain technology and smart contracts. Commenters acknowledge the growing need for robust security guarantees in these systems and see projects like Clean as important contributions towards achieving this goal. One commenter expresses excitement about the potential for formally verified ZK circuits to enable more complex and secure smart contract applications.