AI Advances in Mathematics Spark Debate on Crypto Security

Original | Odaily Planet Daily (@OdailyChina)

Author | Azuma (@azuma_eth)

AI has once again achieved remarkable progress in the field of mathematics.

On the morning of October 7 Beijing Time, OpenAI unveiled a series of mathematical achievements generated by its internal state-of-the-art models, ultimately compiling 722 manuscripts and 372 result families on GitHub, covering multiple fields including number theory, geometry, combinatorics, and theoretical computer science—among them significant mathematical directions such as the Milnor rationality conjecture, algebraic specialization, the quasi-Riemann hypothesis, and Hilbert’s tenth problem. OpenAI revealed that approximately 4,000 questions were posed to the model throughout the evaluation process, with each result requiring an average computational effort equivalent to about three hours of ChatGPT Pro reasoning.

That same night, Ethereum Foundation researcher and tech expert Justin Drake issued a bold call: the crypto industry should begin calmly planning for "bunker mode"—gradually moving assets to new addresses that have never previously signed a transaction.

Drake's logic is straightforward: the rapid evolutionary pace of AI's mathematical capabilities could crack the Elliptic Curve Digital Signature Algorithm (ECDSA) before quantum computing becomes truly mature, directly threatening the security of accounts on major blockchains like Bitcoin and Ethereum.

For a long time, the cryptocurrency industry has focused its account security defenses on the distant hypothetical “Q-day”—the day quantum computing breaks modern public-key cryptography. But Drake is warning that AI-driven mathematical superintelligence could prematurely doom ECDSA on classical hardware—this risk can no longer be measured in terms of “decades from now”; the most pessimistic projections suggest it could occur within months or years, where attackers might只需 call upon a large GPU cluster to directly reverse-engineer private keys in as little as a week.

Drake’s concerns are not entirely unfounded—the rapid evolution of AI’s mathematical capabilities is evident. In May this year, OpenAI revealed AI-generated counterexamples to the Erdős unit distance conjecture; in August, it announced progress on several long-standing open problems; in September, it further declared that its internal model had solved the Navier-Stokes millennium problem; and now, it has publicly released hundreds of mathematical research results all at once…

Drake, in his call to action, mentioned that we may be at a turning point where "weeks could span centuries of mathematical progress." If AI can challenge humanity's long-standing judgments on the difficulty of mathematical problems in an extremely short time, then there may also be undiscovered shortcuts to problems in cryptography that we currently consider sufficiently hard.

ECDSA is particularly dangerous because it possesses a rich mathematical structure. Tools such as Schoof’s algorithm, the Frobenius endomorphism, and pairings are all built upon this structure, whereas one of the design goals of cryptographic hash functions is to minimize exploitable mathematical structure—the richer the structure, the more likely there exist undiscovered “shortcuts” in theory.

Therefore, Drake proposed a rather extreme assumption, one he believes is worth preparing for in advance: future AI could discover a classical algorithm similar to Shor’s algorithm, enabling attackers to rapidly derive private keys from public information without relying on quantum computers. If this were to happen, assets protected by ECDSA could be directly exposed.

Against this backdrop, Drake proposed the so-called "bunker model." For ordinary token holders, the core recommendation is to gradually migrate assets to new addresses that have never previously initiated a transaction. The reason is that the public key for such addresses has not yet been directly exposed on-chain—the address itself is only hashed—and once the address signs a transaction, the public key may become public. If a novel attack against ECDSA emerges in the future, attackers could theoretically gain additional exploitable information. For key signers such as exchanges, custodians, oracles, and L2 security councils, he offered more aggressive recommendations, including strengthening cold wallets, periodically rotating ECDSA public keys, and, where feasible, adopting hash-based signature schemes for multisignature setups.

Drake emphasized that this process should be done "slowly," without panic or hasty large-scale migrations, as the migration itself can introduce new operational risks. In particular, addresses holding fewer than 50 BTC are somewhat implicitly protected by the "Satoshi Shield"—the 20,000 addresses, each containing 50 BTC, that are known to be owned by Satoshi and whose public keys have been exposed.

Drake concluded by stating that, for the industry to safely exit bunker mode in the future, it will need a set of "post-AI cryptography" capable of addressing the AI era. He recommended fully committing to hash-based cryptography and completely avoiding any mathematical assumptions with structure, since any reliance on complex mathematical structures should be assumed vulnerable to future AI-driven attack pathways.

After Drake issued a warning, Ethereum co-founder Vitalik Buterin shared his own perspective on the matter.

Compared to Drake’s alarmist warnings, Vitalik’s stance is notably more cautious. He first clearly stated that he supports keeping funds in brand-new addresses that have never signed a transaction, as long as the process isn’t overly complicated. However, he advised against hastily moving assets today due to breakthroughs in AI mathematics, as migrating keys carries inherent operational risks—incorrect migration could even result in greater losses than a hacker attack.

But this does not mean Vitalik believes the risk can be ignored. On the contrary, Vitalik thinks the industry should seriously consider a possibility that has not been adequately factored into risk models: not only could elliptic curves be vulnerable to AI-accelerated mathematics, but even the much-anticipated "post-quantum cryptography" may not be entirely secure.

Vitalik specifically highlighted ML-DSA, FHE, and lattice-based cryptography. While the industry has traditionally believed that quantum computing primarily threatens elliptic curve and RSA cryptography, and that lattice-based schemes could serve as the next-generation security foundation, Vitalik has noted that, under the assumption of AI accelerating mathematical progress, this distinction may not be as solid as previously thought.

Vitalik explained that similar situations have repeatedly occurred throughout human history—a problem once thought to require extremely high computational complexity was eventually found by mathematicians, after decades of research, to have hidden structures that dramatically reduced the difficulty of breaking it. If AI can compress what would have taken humans decades of mathematical exploration into just a few years or even months, then there may also be undiscovered shortcuts within lattice-based cryptography.

Like Drake, Vitalik is more optimistic about pure hash-based cryptography. In his view, schemes such as elliptic curves and lattice-based cryptography rely on specific mathematical structures, whereas the design goal of hash functions is precisely to avoid such exploitable structures. If AI’s strength lies in uncovering hidden mathematical structures, then a cryptographic system with “no structure to discover” is clearly more trustworthy.

However, pure hashing alone cannot permanently solve all problems. Signatures and proofs can be fully transitioned to pure hashing, but the real bottleneck lies in public key encryption (PKE)—which underpins secure website access, encrypted communications, VPNs, and the entire security foundation of the internet. Mathematical theorems have long proven that it is impossible to construct a public key encryption system using only hash functions with no algebraic structure; achieving this requires introducing mathematical structures with traps. As soon as such structure exists, we must assume that AI will eventually find ways to break through it. Faced with this practical dilemma, Vitalik’s recommendation is that if you want a lattice-based cryptographic system to remain theoretically secure in the long term, the simplest solution is to directly increase the parameters and key sizes by a factor of ten.

Regarding Vitalik’s recommendations for the operational side, in addition to advising users against hastily transferring funds, Vitalik proposed two defensive strategies for on-chain applications. First, privacy protocols should avoid hardcoding encrypted notes directly on-chain and instead prioritize off-chain third-party channels. Second, multisignature wallets should prioritize completing signature verification off-chain to prevent signers’ public keys from being prematurely exposed to the entire network. In this way, even if the underlying ECDSA suffers an irreversible mathematical attack, the multisig system would only “gracefully degrade” into a single-signature model controlled by the signature collector—far preferable to the catastrophic scenario where anyone can freely withdraw funds.

Whether it’s Justin Drake, who advocates extreme defense, or Vitalik Buterin, who emphasizes engineering realism, the consecutive warnings from these two core minds of Ethereum at the same moment have posed a heavier philosophical question to the entire cryptocurrency world: When AI begins to lead mathematical research, is the very foundation upon which the industry stands truly secure?

For over a decade, “In Math We Trust” has been the foundational totem of decentralized belief. We have long assumed that intricate algebraic structures serve as secure havens, pushing the unknown risk of cryptanalysis into a distant future. Yet, OpenAI’s progress on hundreds of mathematical conjectures brutally reveals a truth—what humans perceive as “unbreakable” may merely be the result of our own computational limitations moving too slowly through the labyrinth of mathematics.

When AI begins to extrapolate vulnerabilities at a pace spanning centuries in weeks, the balance between attack and defense is already disrupted. Future defenses may have no choice but to embrace a return to simplicity—a minimalist approach that abandons reverence for complex, intricate structures in favor of a purely hash-based model with no structure at all.

This may be the first true collision between blockchain and artificial intelligence at the foundational security level. For ordinary individuals caught in this shift, there is no need to panic, but it is essential to abandon blind faith in static security. In this new era, where mathematical superintelligence is dawning, staying alert and maintaining reverence for unknown attack surfaces is the best “bunker” for protecting on-chain wealth.