Layla Zulfa
The Ethereum Foundation Formal Verification team, in a collaborative effort with leading entities Yukon and zkSecurity, has officially launched better.codes, an innovative open autoresearch challenge designed to advance the foundational security of modern succinct non-interactive proof systems (SNARKs). This pioneering initiative seeks to bridge the critical gap between conjectured and mathematically proven security benchmarks for crucial cryptographic primitives, particularly those underpinning the robustness of decentralized technologies.
Unpacking the Challenge: koalaIRS12 and the Proximity Prize Legacy
At its core, better.codes presents a highly specific, self-contained problem derived from the extensive research conducted under the Ethereum Foundation’s earlier "Proximity Prize" initiative. This problem, formally identified as koalaIRS12, is meticulously formalized within Lean, a state-of-the-art interactive theorem prover. Participants in the better.codes challenge are tasked with pushing the machine-checked "soundness bound" of koalaIRS12, which is a complex Reed-Solomon proximity problem. The progress made by solvers is then reflected on a public leaderboard, fostering a dynamic and competitive environment for cryptographic advancement.
The challenge is not merely an academic exercise; it directly addresses a fundamental vulnerability in the deployment of SNARKs. SNARKs are cryptographic proofs that allow one party to prove to another that a statement is true, without revealing any information beyond the veracity of the statement itself, and crucially, without requiring significant computational effort from the verifier. They are vital components in a wide array of emerging technologies, from scaling solutions like zk-rollups and zkVMs to critical elements of Ethereum’s long-term post-quantum roadmap. The security of these systems often hinges on the reliability of underlying mathematical conjectures, specifically concerning proximity gaps and correlated agreement for Reed-Solomon codes. While researchers have strong intuitions about the security benchmarks of these primitives, formal, machine-checked proofs are often lacking or fall short of the desired levels, typically targeting 128-bit security. better.codes aims to close this theoretical-to-practical gap by establishing rigorously proven security guarantees.
The Proximity Prize, launched earlier this year by the Ethereum Foundation, set the stage for this challenge by explicitly calling for research to prove, or disprove, these Reed-Solomon proximity gaps conjectures. The intellectual framework for this grand challenge was laid out in the seminal paper "Open Problems in List Decoding and Correlated Agreement" by renowned cryptographers Gal Arnon, Dan Boneh, and Giacomo Fenzi. The koalaIRS12 problem within better.codes is a direct outgrowth of this academic endeavor, designed to translate these theoretical grand challenges into a verifiable, incremental research problem. Its formalization is meticulously handled end-to-end in ArkLib, the Lean 4 library specifically developed for formally verified arguments of knowledge, ensuring the highest degree of mathematical rigor and proof integrity.
The Critical Need for Provable Security in a Decentralized World
The reliance on proximity gaps and correlated agreement for Reed-Solomon codes is pervasive across nearly all production hash-based SNARKs. These include the sophisticated proof systems that secure high-throughput zk-rollups, enable private computations on zkVMs, and form integral components of Ethereum’s strategic preparations for a post-quantum cryptographic landscape. The prevailing security assumption for these deployed systems targets a 128-bit security level, a guarantee that holds unequivocally only if the underlying mathematical conjectures are demonstrably true. However, current provable results often fall short of what researchers intuitively believe these benchmarks to be, creating a subtle yet significant security deficit.
This disparity between conjectured and formally proven security is a crucial concern in the realm of cryptography, particularly for systems that secure billions of dollars in digital assets and underpin future global financial infrastructure. A lack of formal proof, even when strong empirical evidence exists, can leave systems vulnerable to unforeseen attacks or theoretical breakthroughs that exploit unproven assumptions. The better.codes autoresearch challenge directly confronts this issue, fostering an open, incremental, verifiable, and public research environment to systematically elevate the proven security benchmarks to match or exceed their conjectured counterparts. By enhancing the mathematical certainty of these cryptographic foundations, the initiative aims to fortify the trust and resilience of the entire Web3 ecosystem.
Autoresearch: A Paradigm Shift in Collaborative Scientific Discovery
better.codes embodies a novel model for open collaboration known as "autoresearch." This paradigm empowers participants to deploy their own AI models, specialized computational harnesses, and sophisticated tools to collectively tackle a common, machine-verified benchmark. The defining characteristic of this approach is that every successfully promoted submission — meaning, every validated proof that raises the soundness bound — effectively establishes a new baseline, or "raises the floor," for all subsequent progress. This creates a cumulative and accelerating effect on research.
The rationale behind autoresearch is rooted in the understanding that no single agentic setup or research team possesses an optimal approach to solving complex, open mathematical problems. By enabling numerous independent setups to work concurrently on the same benchmark, the collective frontier of knowledge can be advanced significantly faster than through isolated efforts. This distributed intelligence model leverages the diversity of algorithmic strategies, heuristic approaches, and computational resources that individual solvers and AI agents bring to the table.
The effectiveness of this autoresearch model has already been demonstrated in several high-profile initiatives within the cryptographic and computational research communities. Projects like ecdsa.fail have pushed the boundaries of quantum circuit design, identifying vulnerabilities and optimizing quantum algorithms for elliptic curve digital signature algorithms. Similarly, zk.golf has driven innovation in verified zero-knowledge circuits, leading to more efficient and secure implementations. Furthermore, snark.fast has accelerated research into post-quantum proving speeds, a critical area for ensuring the long-term security of cryptographic systems against future quantum threats. These precedents underscore the potential of autoresearch to rapidly accelerate progress in highly specialized and computationally intensive fields, transforming the landscape of scientific discovery.
Participating in better.codes: A Transparent and Collaborative Workflow
Engaging with the better.codes challenge is designed to be accessible and transparent, leveraging familiar open-source collaboration tools. Prospective solvers begin by signing in with their GitHub accounts at the better.codes platform. This grants them access to clone the challenge repository, which contains the immutable theorem statement, the specific parameter point for the koalaIRS12 problem, and the robust verification harness.
Participants then operate within a designated "submission surface" where they develop and refine their proofs, aiming to establish a larger soundness lower bound. This bound is quantified and scored in "bits," providing a clear metric for progress. A crucial aspect of the challenge’s integrity is the rigorous verification process: a specialized comparator tool first ensures that each submitted theorem statement precisely matches the pinned, original statement. Following this, the Lean kernel, an exceptionally powerful and trustworthy proof assistant, meticulously checks the proof itself for mathematical correctness and logical soundness.
Only accepted results, those that pass the stringent verification checks, are then promoted to the public repository. Each successful submission is not only credited to the individual solver but also transparently attributes the AI model or tools utilized in its creation. This level of transparency is foundational to the autoresearch model. All submissions are git-backed, meaning a complete, auditable history of every change, every new lemma, every novel proof technique, and every impossibility result is openly available. This enables the entire community of solvers and AI agents to examine past "diffs" (changes between submissions), learn from previously successful approaches, and, critically, identify and avoid "dead ends" in their research. This iterative, open-source approach ensures that progress is truly cumulative, incrementally advancing the collective understanding and pushing the frontier of provable security for all participants.
The Ethereum Foundation’s Broader Vision for Formal Verification and Security
The launch of better.codes is not an isolated event but rather a strategic component of the Ethereum Foundation’s overarching commitment to formal verification and cryptographic security. As the Ethereum network continues its evolution, particularly with the transition to Ethereum 2.0 and the increasing reliance on advanced cryptographic primitives for scaling and privacy, the importance of absolute mathematical certainty cannot be overstated. SNARKs, for instance, are central to the development of zk-rollups, which bundle thousands of transactions off-chain into a single, succinct proof, dramatically increasing transaction throughput and reducing costs on the mainnet. Similarly, zkVMs (zero-knowledge Virtual Machines) promise to enable private, verifiable computation, opening up new paradigms for decentralized applications.
Ethereum’s long-term roadmap also includes robust preparations for the advent of quantum computing. The integration of post-quantum cryptographic primitives is a critical undertaking to ensure the network’s resilience against future quantum attacks that could potentially compromise current cryptographic standards. Formal verification, through initiatives like better.codes, provides the highest assurance that these complex systems and their underlying cryptographic components are free from design flaws or unproven assumptions. By fostering a community-driven approach to formal proof, the Ethereum Foundation is not only shoring up the security of its immediate ecosystem but also contributing fundamental research to the broader field of cryptography, benefiting all blockchain and decentralized technology initiatives. This investment underscores a deep-seated belief in the power of open science and collaborative innovation to solve the most challenging problems at the intersection of mathematics, computer science, and digital trust.
Implications and the Path Forward
The implications of the better.codes challenge extend far beyond the immediate goal of proving a specific soundness bound. For the field of cryptography, successfully closing the gap between conjectured and proven security for Reed-Solomon codes will significantly strengthen the theoretical foundations of SNARKs. This will, in turn, enable the deployment of even more robust, trustworthy, and scalable blockchain systems, fostering greater confidence among users and developers. For instance, a fully proven 128-bit security guarantee for koalaIRS12 would solidify the cryptographic underpinnings of systems like zk-rollups, directly impacting their real-world security assurances.
Moreover, better.codes represents a powerful demonstration of the burgeoning role of Artificial Intelligence in fundamental mathematical research and formal verification. The challenge explicitly invites participants to point their own AI agents at the problem, showcasing how AI can act as a force multiplier in the discovery and validation of complex proofs. This collaborative human-AI model could revolutionize how mathematical conjectures are approached, accelerating discovery in areas traditionally reliant on painstaking human effort. The continuous upstreaming of new lemmas and proof techniques ensures that AI models can learn and adapt, pushing the boundaries of automated theorem proving.
From the perspective of open science, the autoresearch model championed by better.codes sets a precedent for transparent, verifiable, and incrementally progressing research. By making all submissions and their associated proofs publicly available and git-backed, the initiative fosters an environment of collective learning, where researchers can build upon each other’s work without duplicating efforts or encountering hidden pitfalls. This aligns with the decentralized and open-source ethos that defines the broader blockchain and Web3 movements.
Looking ahead, while today’s launch focuses squarely on the soundness challenge to elevate the proven lower bound for koalaIRS12 to the target of 128 bits, the architects of better.codes envision a future where this platform hosts a series of additional challenges. These future problems will likely tackle other critical cryptographic conjectures and formal verification hurdles pertinent to the ongoing development of secure and scalable decentralized systems. The program’s terms regarding eligibility, evaluation, awards, and payments are established to be dynamic, allowing for adjustments as the challenge evolves and new research frontiers emerge. The collective effort initiated by better.codes is poised to not only secure the present but also forge the future of cryptographic guarantees. Interested participants are encouraged to begin their journey into this cutting-edge realm of autoresearch at better.codes.
