Raising machine-checked security benchmarks to advance hash-based SNARKs through agentic collaboration

The Foundation of Cryptographic Integrity

Modern decentralized finance and zero-knowledge (ZK) infrastructure—ranging from zkRollups to advanced virtual machines—rely heavily on hash-based SNARKs. These systems provide the efficiency necessary for scaling Ethereum and ensuring user privacy. However, the security of these systems is often predicated on mathematical assumptions regarding Reed-Solomon proximity gaps and correlated agreement. While industry standards target 128-bit security, the formal proof of these bounds often lags behind the deployment of the technology itself.

The "better.codes" platform acts as a public leaderboard where researchers and AI agents compete to formally prove higher soundness bounds. The inaugural challenge, titled "koalaIRS12," focuses on a Reed-Solomon proximity problem derived from the Proximity Prize initiative. By formalizing this challenge in Lean, the project ensures that every submission is subjected to rigorous, machine-checked verification, eliminating the ambiguity inherent in manual peer review.

Chronology of the Proximity Prize Initiative

The launch of better.codes is the latest milestone in a broader, year-long effort to harden the mathematical foundations of ZK cryptography. The trajectory of this effort can be traced back to early 2024, when the Ethereum Foundation initiated the Proximity Prize to formalize and stress-test the conjectures surrounding list decoding and proximity gaps.

In early 2024, researchers Gal Arnon, Dan Boneh, and Giacomo Fenzi published "Open Problems in List Decoding and Correlated Agreement," a landmark paper that outlined the grand challenges currently facing the field. This document served as the theoretical roadmap for the Proximity Prize. Following the publication of this research, the Formal Verification team at the Ethereum Foundation began developing ArkLib, a dedicated Lean 4 library designed to handle formally verified arguments of knowledge. The culmination of these efforts is the current deployment of better.codes, which provides a public interface for researchers to interact with these formalized problems.

Understanding the Technical Stakes

The primary objective of the koalaIRS12 challenge is to increase the machine-checked soundness bound toward a 128-bit target. In cryptographic terms, a 128-bit security level is the industry gold standard, offering a level of resistance against brute-force attacks that is generally considered computationally infeasible for the foreseeable future.

The current challenge environment requires participants to utilize Lean to provide proofs that are not only correct but also incrementally superior to existing solutions. Because the platform is built on a git-backed infrastructure, every submission—including failed attempts, new lemmas, and novel proof techniques—is preserved and made transparent. This allows for a "ratchet" effect: once a specific bound is achieved, subsequent solvers can build upon that foundation rather than starting from scratch. This methodology mirrors the open-source software development model, applying it to the traditionally siloed domain of formal mathematics.

The Role of AI in Autoresearch

A defining characteristic of better.codes is its embrace of "autoresearch." In this context, autoresearch refers to the use of autonomous agents and AI-driven tools to explore proof spaces. Traditional manual theorem proving is a laborious process, often taking months or years for a single complex result. By providing an open, programmable API, the project encourages developers to deploy custom AI models that can iterate through thousands of potential logical paths in parallel.

This is not the first time such a model has been applied to cryptographic challenges. Previous iterations of similar collaborative efforts include ecdsa.fail, which focused on elliptic curve vulnerabilities, and zk.golf, which pushed the boundaries of ZK circuit optimization. These platforms demonstrated that when a community of independent, incentivized agents works toward a single, objective benchmark, the speed of discovery significantly outpaces traditional, centralized research models.

Implications for the Ethereum Ecosystem

The implications of this initiative extend far beyond the immediate technical challenge. As Ethereum continues its roadmap toward post-quantum resilience and increased scalability, the reliance on unverified mathematical conjectures presents a latent risk. If a soundness gap were discovered in a production-grade SNARK, the impact on assets locked within zkRollups could be catastrophic.

By moving toward a paradigm of "provable bits," the Ethereum Foundation is effectively raising the cost of vulnerability. A formally verified proof of a 128-bit security bound provides a level of certainty that is mathematically absolute within the axioms of the system. This creates a safer environment for decentralized applications (dApps) and institutional-grade financial instruments that are increasingly dependent on ZK-proof technology.

Stakeholder Perspectives and Industry Response

While the project is spearheaded by the Ethereum Foundation, the collaboration with Yukon and zkSecurity highlights the importance of multi-institutional alignment in solving high-level mathematical problems. Yukon’s expertise in formal verification infrastructure and zkSecurity’s focus on the auditability of ZK systems provide the necessary support to ensure that the platform remains reliable and scalable as more challenges are added.

Industry analysts suggest that this "gamified" approach to formal verification could become a standard for the broader cryptography community. By making the leaderboard public and the proofs machine-readable, the barrier to entry for talented researchers is lowered. It shifts the narrative from "who has the authority to verify this" to "the computer has verified this," which is a fundamental shift in how trust is established in cryptographic systems.

Future Challenges and Sustainability

The launch of better.codes is described by organizers as the beginning of a multi-year project. While the koalaIRS12 challenge is the current priority, the platform is designed to host a series of future problems. The program terms governing rewards and recognition are intentionally flexible, allowing for adjustments as the complexity of the research evolves.

The sustainability of this model relies on the ongoing engagement of the academic and developer communities. Because the platform is built on transparent, open-source principles, it avoids the risks of vendor lock-in or proprietary gatekeeping. Participants are not just competing for prizes; they are contributing to a public good—a library of verified cryptographic knowledge that will serve as the bedrock for the next generation of privacy-preserving technologies.

Conclusion

The debut of better.codes signifies a maturation of the ZK research landscape. By integrating formal verification with agent-based AI research, the project addresses one of the most pressing bottlenecks in cryptographic engineering: the time-consuming nature of verifying security assumptions. As participants begin to push the soundness bounds of the koalaIRS12 problem, the resulting proofs will serve as a testament to the power of decentralized, collaborative research. For the Ethereum ecosystem and the broader world of digital security, the project offers a pathway to a more resilient, verifiable, and transparent future. Those interested in participating or tracking the progress of the current benchmarks can engage directly with the repository at the official better.codes portal.