the math break · cryptographic risk audits
AI is solving math’s hardest problems. Blockchains rest on one.
Every blockchain key is safe only while one math problem stays unsolved, and nobody has proven it can’t be. AI is now disproving 80-year-old conjectures. We find where your math assumptions are weak, how hard each would be to replace, and what to fix first.
Until RSA and elliptic-curve signatures would be disallowed
NIST IR 8547 (draft, 2024) proposes disallowing quantum-vulnerable public-key algorithms after 2035. Most systems need years to migrate.
01 · the threat
The threat: AI is on a run
Cryptography rests on problems everyone believes are hard, such as factoring large numbers or finding a private key from a public one. None of those beliefs is proven. They hold because no one has found a faster algorithm yet.
Since 2022, AI systems have started finding new algorithms and new mathematics. In 2026 they began producing results working mathematicians call significant, and the field is now debating how to verify them.
None of this has broken real-world cryptography: as of October 2026 we found no published machine-learning attack on standard post-quantum parameters. But the work that would break them is exactly the work AI is getting better at.
- 2022
AlphaTensor finds new algorithms
DeepMind’s system discovered matrix-multiplication methods faster than the best known human ones for some sizes.
AI inventing algorithms, the core of cryptanalysis
- 2022
SALSA attacks lattice cryptography
Researchers used transformers to recover secret keys from lattice-based schemes, at small, non-standard parameters.
lattices underpin the new post-quantum standards
- 2023
FunSearch makes new discoveries
An AI-guided search found cap-set constructions larger than any previously known: new mathematics, not recall.
results humans hadn’t found
- 2024
AlphaProof reaches olympiad level
AlphaProof and AlphaGeometry 2 scored at silver-medal standard at the International Mathematical Olympiad, with machine-checked proofs.
rigorous, verifiable reasoning
- 2025
AlphaEvolve beats a 1969 record
It multiplied 4×4 complex matrices with 48 multiplications, improving on Strassen’s 49 from 1969.
a 56-year-old record fell to an AI agent
- 2025
Gold at the Olympiad
AI systems reached gold-medal level at the International Mathematical Olympiad.
top-human problem solving
- 2026
An 80-year-old conjecture falls
In May, an internal OpenAI model disproved Erdős’s 1946 unit-distance conjecture. Mathematicians including Noga Alon and Tim Gowers verified and simplified the proof, and Google DeepMind reported resolving nine more open Erdős problems that month.
results mathematicians call significant
- 2026
A Millennium Prize problem, contested
In September, OpenAI announced a blow-up result for the Navier–Stokes equations with smooth forcing, backed by a Lean formalization. Whether it settles the prize problem is disputed, and 25 Fields Medalists, including Terence Tao, warned against treating open problems as AI benchmarks.
the field is arguing about how fast this is moving
- 2026
Hundreds of results at once
On October 6, OpenAI released 722 AI-written manuscripts from about 4,000 problems in pure mathematics, theoretical computer science and mathematical physics. Only about a fifth are formally checked, and three were withdrawn for errors.
discovery at industrial scale
- next?
The problem behind every blockchain key
Bitcoin and Ethereum keys are safe only while recovering a private key from a public one stays impossible: the elliptic-curve discrete logarithm problem. Nobody has solved it. Nobody has proven it can’t be solved.
if it falls, every exposed public key is at risk at once
02 · the speed gap
Discovery is accelerating. Migration isn’t.
AI is getting faster at finding weaknesses. The infrastructure built on cryptography isn’t getting faster at changing.
AI finds what people missed
Google’s Big Sleep AI agent found an exploitable memory-safety bug in SQLite that existing fuzzing had missed. In 2025 it found a flaw known only to attackers before they could use it.
Olympiad-level mathematics
AI systems reached gold-medal level at the International Mathematical Olympiad.
One hash, a quarter century
SHA-1: first published attack 2005, first real collision 2017, NIST retirement planned for 2030.
Default: about 9 years until NIST’s 2035 cutoff. Illustrative planning model, not a prediction.
Start by 2029
That leaves 3 years of slack before the weakness is expected to be usable.
Nobody has shown AI breaking ECDSA or SHA-256. You don’t have to believe it will. You only have to plan for the day a weakness is found faster than you can swap.
03 · the foundation
Three assumptions hold up every crypto business
Signatures prove who authorized something. Hashes prove nothing changed. Randomness keeps secrets secret. If any one fails, the money moves.
Only the key holder can sign
ECDSA and Ed25519 authorize every withdrawal, transfer and contract call.
No two inputs share a fingerprint
SHA-256 and Keccak-256 bind blocks, addresses and documents together.
Secrets can’t be guessed
Keys and one-time nonces must come from a generator nobody can predict.
04 · the record
The math rarely breaks. The way it’s used does.
None of these were exotic breakthroughs. Every one would have shown up in an inventory of how the math was wired in.
- 2010
Sony reused one ECDSA nonce
The same random value signed every PlayStation 3 update.
master signing key recovered
- 2013
Android’s RNG repeated nonces
A random-number bug in wallet apps produced repeated signatures.
bitcoin stolen from phones
- 2017
Infineon’s weak RSA keys (ROCA)
Chips generated keys with hidden structure that made them factorable.
national ID cards and TPM keys replaced
- 2017
First practical SHA-1 collision
Google and CWI produced two different files with the same SHA-1 hash.
a trusted hash retired for good
- 2022
Profanity’s 32-bit seed
A vanity-address tool seeded keys from too little randomness.
Wintermute lost about $160M
05 · the exposure map
Follow a transaction. Find the weak points.
Every blockchain payment passes through the same six stages. Each one rests on a different piece of math, and each fails in a different way. Pick a stage to see the exposure, the proof and the fix.
Predictable randomness
A private key is just a very large random number. If the generator behind it is weak, someone else can generate the same key.
Profanity, 2022
A vanity-address tool seeded keys from only 32 bits of randomness. Wintermute lost about $160M.
Trace every key to its source
- Inventory each key generator, including vendor SDKs
- Require a vetted, OS-level random source
- Flag and rotate keys made by weak tools
Reused or biased nonces
Each signature needs a fresh one-time secret. Reuse it once and the private key can be worked out from public data.
Sony PlayStation 3, 2010
The same nonce signed every update, and the master signing key was recovered. See it live.
Make the nonce impossible to repeat
- Deterministic nonces (RFC 6979) or Ed25519
- Known-answer tests on every signing path
- Monitor signatures for repeated values
Keys live in the wrong place
Hot keys sit in app servers and backups, and hardware modules carry firmware nobody tracks.
Infineon ROCA, 2017
Chips generated factorable RSA keys. National ID cards and TPM keys had to be replaced.
Map custody end to end
- Where every key lives, who can use it, how it’s backed up
- Move signing into an HSM or KMS with a rotation plan
- Track vendor firmware advisories
Hashes hold up well
SHA-256 and Keccak-256 link blocks and derive addresses. No practical attacks are known, and quantum computers only modestly reduce their margin.
SHA-1, 2005 to 2017
Hashes do age: SHA-1 went from first attack to real collision in 12 years.
Document and watch
- Confirm no legacy hashes (MD5, SHA-1) remain anywhere
- Record where each hash is fixed in protocol
- Re-score as research lands
Verification code you can’t change
Contracts check signatures themselves, and a missed check can accept forged approvals. Immutable contracts can’t be patched.
A common audit finding
Signature checks that accept a malleable signature or don’t reject an invalid one regularly appear in smart-contract audits.
Audit the checks, plan the exit
- Review every on-chain signature check
- Use well-tested libraries for verification
- Design an upgrade or migration path before it’s needed
Public keys are already on-chain
Once an address spends, its public key is public forever. Today’s signatures could be attacked later.
NIST IR 8547
RSA and elliptic-curve signatures are disallowed after 2035, and post-quantum standards (FIPS 203, 204, 205) are already published.
A post-quantum roadmap
- Rank systems by how long migration will take
- Build in crypto-agility so algorithms can be swapped
- Plan the move to ML-DSA (FIPS 204) signatures
06 · the deadlines
The math itself also has a clock
NIST publishes its first post-quantum standards: FIPS 203, 204 and 205.
NIST’s draft transition plan proposes deprecating RSA-2048 and other 112-bit-strength public-key algorithms.
It proposes disallowing all quantum-vulnerable public-key algorithms, including RSA, ECDSA and EdDSA. 2035 is also the federal migration target set by NSM-10.
Source: NIST IR 8547, initial public draft (November 2024). A later NIST draft (CSWP 39) moves the 112-bit date to 2031; final dates are still being set. They apply to US federal systems and set the pace for regulated industry.
07 · the real question
How fast could you swap it out?
The same algorithm can be a ten-minute fix in one place and a multi-year migration in another.
| Where the primitive lives | Swap difficulty | What a swap takes |
|---|---|---|
| Software library | Low | Update the dependency and redeploy |
| Upgradeable smart contract | Medium | A governed upgrade through the proxy |
| Hardware secure element or HSM | High | Replace or re-provision devices |
| Immutable smart contract | High | Move users and funds to a new contract |
| Customers’ own keys | Very high | Every holder has to act |
08 · the audit
Security teams secure systems. We audit the math underneath them.
Find every assumption
Every signature scheme, hash, key store and random source, including the ones inside vendors and contracts.
Rate each one
How breakable it is, including how it’s implemented, and how hard it would be to replace.
Plan the swap
A ranked plan to fix misuse now and rotate primitives before they fail, not after.
Sample deliverable
| Primitive and use | Where it lives | Breakability | Swap | Priority |
|---|---|---|---|---|
| ECDSA, hot-wallet signing | Library and HSM | Medium nonce source unaudited | High | 1 · Fix now |
| RSA-2048, API certificates | Load balancer | Low today, quantum-exposed | Low | 2 · Plan by 2030 |
| Keccak-256, addresses | Immutable contract | Low | Very high | 3 · Monitor |
| Ed25519, service auth | Library | Low | Low | 4 · Routine |
Illustrative sample, not a client finding.
09 · engagements
Start small, go deep, stay ahead
Inventory plus the top risks, ranked. The fastest way to know where you stand.
Every primitive scored, with a rotation roadmap your team can execute.
Ongoing monitoring of new attacks and deadlines, with re-scoring as they land.
On blockchain rails
Stablecoin issuers, cross-border settlement and tokenized assets.
Trust is the product
Exchanges, wallets, custody firms and DeFi protocols.
Underwriting the risk
Know the real exposure behind a policy or a case.
10 · founding clients
Three scans at case-study pricing
In exchange for an anonymized write-up. Findings are written to the standard of a forensic declaration: specific, reproducible and defensible.
Joshua Bullock
Forensic declarations and litigation support, offensive security, and platforms built under FCRA, GLBA and DPPA.
Qualifications →sources
Check our work
Every claim on this page links to its original source. Where results are disputed, we say so.
- AlphaTensor: Discovering faster matrix multiplication algorithms (Nature, 2022)
- SALSA: Attacking Lattice Cryptography with Transformers (NeurIPS 2022)
- FunSearch: Mathematical discoveries from program search (Nature, 2023)
- AlphaProof and AlphaGeometry 2: silver-medal standard at IMO 2024 (Google DeepMind)
- Big Sleep finds an exploitable SQLite bug (Google Project Zero, 2024)
- AlphaEvolve: 4×4 complex matrices in 48 multiplications (arXiv, 2025)
- Gemini Deep Think officially achieves IMO 2025 gold (Google DeepMind)
- Remarks on the disproof of the unit distance conjecture (arXiv 2605.20695, 2026)
- Why the legendary Erdős problems are falling to AI (Quanta, 2026)
- Advancing mathematics research with AI-driven formal proof search (Google DeepMind, arXiv 2605.22763)
- On the Navier–Stokes Millennium Prize Problem (OpenAI, 2026)
- Navier–Stokes lost in translation: a critique of the Lean formalization (arXiv, 2026)
- OpenAI’s math breakthrough points beyond math (Axios, October 2026)
- NIST IR 8547 initial public draft: Transition to post-quantum cryptography standards (2024)
Sources checked October 2026.