Are BTC/ETH keys or BLS/KZG signatures actually at risk from recent AI math breakthroughs? The short answer: Not yet. Adding the technical analysis behind this discussion below. The October 7 snapshot of @OpenAI math results contains 722 manuscripts across 372 result families. We conducted a focused review of 8 selected families (10 manuscripts), not an exhaustive audit. Assuming their stated theorems hold, here is what they claim and what follows for cryptography: • #142 + #029: deterministic polynomial-time factoring of polynomials over prime fields, relying on #029’s uniform Hecke zero-free theorem. This is not RSA integer factoring. Randomized polynomial factoring was already efficient; no new reduction of secp256k1 key recovery or RSA factoring to this task is supplied. • #107: dense matrix-multiplication bounds improve, including finite-field results. The headline is ω ≤ 2.25 over ℂ; separate bounds give ω < 2.371055 over every fixed field. But NFS/TNFS uses sparse linear algebra modulo subgroup order r: roughly w·N² field operations for an N×N system with average row weight w. Applicability, sparse-solve gains and competitive finite-size costs remain to be established. No cheaper complete BLS/KZG attack is demonstrated by these results. • #103: among polynomial-time deterministic simulations, workspace improves from O(log² n) to O(log n). A major space-complexity result—but no polynomial-time randomized log-space solver for the cryptographic target is supplied. Such a solver would itself already be a polynomial-time attack. • #279: exact quantum integer factoring over a fixed finite gate set. Stronger ideal-circuit guarantees, without demonstrated practical resource savings or a new classical attack. Shor already provides quantum factoring and discrete-log algorithms; this result does not establish a cheaper ECC attack. • #109: an asymptotic integer-multiplication improvement, with no demonstrated speed gain at cryptographic sizes. The construction has enormous constants and thresholds, with schoolbook multiplication below its cutoff. • #002 / #030: our abstract/main-theorem review found global elliptic-curve arithmetic advances, without an effective algorithm extracting the finite-group secret d from Q = dG. What this means for Bitcoin and Ethereum: The reviewed manuscripts do not provide a practical way to recover a wallet’s private key from its public key. If such a method were found for secp256k1—the curve used by Bitcoin and Ethereum accounts—an attacker could forge ECDSA and Schnorr signatures and potentially spend funds wherever the exposed key and wallet’s spending rules allow. This includes Bitcoin’s Taproot signatures. Could they undermine Ethereum’s validators or data verification? Ethereum’s validator signatures (BLS) and blob commitments (KZG) use the same curve, BLS12-381. A practical attack that recovers secrets in the relevant groups could therefore threaten both: impersonating validators and producing false blob proofs that pass verification. There is also a narrower route: recovering KZG’s secret setup value, τ, would enable false proofs under that setup, without recovering validator keys. The reviewed results demonstrate neither attack; any network-level consequences would depend on the attack’s scope and the protocol. How much cheaper have these results made an attack? We found no demonstrated reduction in the total work needed to break these targets. For secp256k1, a representative generic classical attack takes roughly 2^128 group operations. None of the reviewed results establishes a reduction to 2^100 or 2^80—or another lower end-to-end estimate. Some results improve theoretical guarantees or asymptotic bounds, but none of the reviewed results demonstrates a cheaper complete attack on these targets. BLS and KZG require separate, attack-specific estimates. This is a statement about the evidence available, not a prediction of how soon a break could happen. 📝 Working research notes & full attack map: raullenchai.github.io/ai-mat… (Originally compiled for our own use). 🛠️ We welcome feedback from cryptographers (github.com/raullenchai/ai-ma…), e.g., have we missed a concrete way to turn these results into a cheaper attack? Could #142’s internal tools help recover keys in a deployed group, or could #107 reduce the total cost of attacking BLS or KZG?

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