
Engineering @solstrategies. Former founder. Solana, IBRL, ZK, & cryptography. 🥟 enthusiast.
Poznan, Poland
Joined October 2017
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I'm absolutely thrilled that Darklake and its proof tech will find a new home with @solstrategies. We keep building.
Solana.
vitorpy retweeted
The biggest risk is not being ambitious enough.
Beyond excited to expand our scope to founders building new technologies and creating new markets with @a16zfrontier.
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My best attempt to be mathematically accurate:
1) The set of all integer linear combinations of n-dimensional basis vectors forms a lattice.
2) A public key in lattice-based crypto is an "ugly" basis of a lattice: the basis vectors are almost parallel to each other.
3) Given an arbitrary n-dimensional point ℎ not on the lattice, it is hard to find an integer linear combination of the ugly basis that produces a lattice point close to ℎ.
My ELI5:
1) Imagine I put you on a map and I pull the corners of the map and stretch it in a weird way such that you were close to San Francisco before I stretched it and now you are suddenly close to Beijing and far from SF.
2) I ask you how to undo the stretch and return reality to normal -- but you can't because you can only see your immediate surroundings.
3) The way I warped the world stays secret.
Thanks for the nerdsnipe @EliBenSasson
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I suspect the real reason eMudhra is exiting the SSL business is Google indicated it is most likely going to drop eMudhra from being trusted by Chrome AT ALL, after observing inexplicable incompetence in how they mis-generated their private key for the CA certificate.
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eMudhra conducted a formal key-generation ceremony using FIPS 140-2 Level 3 hardware security modules. It went so bad!
The hardware generated strong keys.
The team tested exporting and importing keys. A bug in a script generated a set of weak keys.
Bad keys had labels similar to good keys.
Bad keys used to generate certificate signing requests.
eMudhra's root CA signed those requests. The result? Private keys: 4, 56, 66, 115, 155, 156, 230, 237.
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so I'm going to tell you a secret
our team actually cares an absurd amount about building private money without backdoors
if that means we have to keep out the terrorists, so we can have privacy for the good guys, so be it
we're cypherpunks, not anarchists 🫡
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6 years of TowerBFT: Solana is in beta mode
6 hours of Alpenglow: Kill the beta!
Maybe we wait until the first successful Alpenglow epoch change?
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this is fantastic, I've thought many times about trying to setup something for people to collaborate on finding that seed, I wish I would have just tried running it myself now :D hindsight 20/20 anthropic.com/research/ecdsa…
Next time add some gigantic reaction wheels and flip it with no thrusters!
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I should probably read the paper, but the duality that every compressor is a predictor and vice versa is well known for *decades*?
I mean, *I* knew this in 2019 and I'm usually the last for whom a penny drops.
Why care about Kolmogorov complexity?
LLMs = monotone compression
(and whether “monotone” is necessary hinges on whether one-way functions exist)
arxiv.org/pdf/2610.11031
ロシアがウクライナのデータセンターを相次いで攻撃
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ゼレンスキー大統領が報復を宣言。Yandexのデータセンターを相次いで攻撃
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サービスが一部停止。経済制裁により新たなGPUの入手難しく、復旧は絶望的
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この攻撃によりなぜかロシアのbotの半分が活動しなくなり、Xが少し平和になる←イマココ
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Problem is: companies say they want to hire someone like this
But in 9/10 cases unless said person is not a cofounder or founding eng, they won’t get the trust to do the risky + sometimes controversial stuff that is required to execute quickly and well to win vs competition
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AI is getting better at solving hard math problems, especially given recent drops. But what does that mean for the cryptography that protects everything from private messages to healthcare to banking and crypto wallets?
Stanford cryptographer Dan Boneh, with @eddylazzarin, @SuccinctJT, @liz_harkavy, and @smc90, makes sense of the warnings sounded recently. They cover:
- what’s fact vs. assumption
- what’s new and what risks cryptographers have long prepared for
- where quantum computing doesn't (and does) fit
- opportunities for builders
Highlights:
00:37 – What sparked the most recent debate about AI and cryptography
01:35 – Signal vs. noise: What the math does and doesn’t tell us
05:29 – Why cryptography depends on open problems
09:25 – Why the stakes go beyond blockchains
10:43 – How AI could strengthen confidence in cryptography
13:50 – Considerations for users and institutions
20:10 – Where AI and quantum threats overlap
22:32 – Building systems that can change cryptographic methods
23:59 – Hash-based versus lattice-based cryptography
33:07 – Opportunities for builders, and better security tools
38:14 – What comes next if there were a cryptographic break?
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The world’s war crimes tribunal is now the most closely watched IT project in Europe. The US has sanctioned the entire International Criminal Court, giving companies 180 days to stop doing business with the Hague tribunal. The court says it is prepared. It has replaced Microsoft with Germany’s openDesk and dropped its health insurer Axa. Europe is offering words and an EU law that would bar European firms from complying with US sanctions. The rest depends on whether openDesk works better than the blocking statute.
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I wasn’t going to comment since this is a really bad take IMO, but since it’s taken off I feel the need to. To my understanding, there is no evidence whatsoever pointing to a break of decades old hardness assumptions like elliptic curve cryptography. 1/n
Today I call upon the blockchain industry to calmly begin planning for "bunker mode". My personal recommendation is to set in motion a controlled mass migration of assets to fresh addresses, i.e. addresses whose pubkeys remain hidden behind a hash.
Holders, starting with large and sophisticated ones, should consider moving the bulk of their funds to addresses that have never signed a transaction. And when they do sign one, they should also move remaining funds to a new address (possibly generated from the same seed phrase).
Don't rush. While I believe there is cause for action a rushed migration would do more harm than good. Don't panic either. Moving assets to protected addresses is a simple, preventative step which does not require new cryptography or new wallets.
IMO it is now reasonable to brace for the possibility that ECDSA breaks before qday, in the worst case in months not years. By "break" I mean fast private key recovery (e.g. in one week) on available hardware (e.g. a large GPU cluster).
Recent days have been humbling for human mathematical intuition. Long-held, unquestioned hypotheses have fallen. This includes the n log(n) bound for integer multiplication and the 3SUM conjecture. In hindsight, May's unexpected disproof of the Erdős unit distance conjecture was our warning shot.
Yesterday's OpenAI drop made it clear that mathematical superintelligence is upon us. They say there are weeks where decades happen. We are about to live through weeks where centuries of mathematical progress happen. Could our magic 64-byte ECDSA signatures be too good to be true? Was it just security through obscurity all this time?
Elliptic curves feel especially vulnerable to superintelligence. Curves carry rich structure, with room for fancy tricks like Schoof, Frobenius, pairings. (By contrast, hashes are designed to minimise algebraic structure.)
Separately, as Ewin Tang can attest, an efficient quantum algorithm sometimes foreshadows an efficient classical one. We should be open to the possibility of a classical counterpart to Shor that breaks elliptic curves and RSA at once.
Also noteworthy is the striking under-representation of cryptographic breakthroughs among the 722 mathematical results OpenAI published. I've witnessed first-hand the US government censoring academic quantum cryptanalysis results. Backroom interventionism is my base case.
I urge large, sophisticated actors to lead by example. Project11's "risq list" (bitcoin-risq-list.projecteleven[.]com) is a great tracker of exposed BTC pubkeys. Binance, Bitbank, Robinhood, Bitfinex, and Tether have an opportunity to harden their cold storage. Next month I'll address institutions in London in a live Q&A (forum.ethereuminstitutional[.]org/london-2026).
Again, please do not rush. Wallets holding under 50 BTC enjoy partial cover from "Satoshi's shield", i.e. his 20K exposed addresses that hold 50 BTC each. Load-bearing signers like oracles and L2 security councils should consider rotating ECDSA pubkeys with every signed message and/or multi-signing with a hash-based schemes like SPHINCS.
Exiting bunker mode safely will require post-AI cryptography. My inclination is to go all-in on hash-based cryptography and avoid structured mathematical assumptions entirely, whether from curves, lattices, or isogenies. A single battle-tested hash (e.g. from the SHA or BLAKE families) yields plausible post-AI security.
The Ethereum roadmap on strawmap[.]org fully embraces hash-based cryptography with end-to-end formal verification as a response to the quantum threat. Those timelines must now be revisited and accelerated in light of mathematical superintelligence. I'll be pushing for maximum defensive acceleration.
Hi. If elliptic curves are broken so that any exposed public key leads to compromise and it's by a financially-motivated hacker who’s top priority is to steal crypto, the entire fucking world is going to zero.
Having your magic internet coins in bunker mode is not going to help you.
It would mean some random ass fucking cyber criminals > every developed nation state and private corporation in the world.
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What happens when a single day of AI research produces more mathematics than humanity can absorb in a century?
Imagine millions of superhuman research agents at work. Formal systems may verify the proofs, but humans won’t have enough context to understand the underlying web of machine-invented concepts.
Mathematics could split into two layers:
Machine mathematics: vast, verified, mostly consumed by AIs.
Human mathematics: a compressed “effective theory” of the machine frontier—the small subset of ideas we can understand.
Physics may follow the same path: AIs could explore huge spaces of theories and derive correct predictions using structures no human physicist fully understands.
The key question is whether AI can compress knowledge as fast as it creates it.
My guess: the detailed frontier becomes permanently machine-native, while selected parts are periodically compressed into human-comprehensible principles.
Eventually even deciding what is worth understanding may require AI.
At that point AI is no longer just a scientific tool. Humans are receiving selected explanations from a much larger intellectual civilization they cannot independently grasp.
A number of these results are in theoretical or mathematical physics!
For example: A proof of spontaneous magnetization in quantum Heisenberg ferromagnets (Lean-verified)
If it survives scrutiny, it would be the first rigorous proof of quantum ferromagnetic order and a landmark in mathematical physics, with or without AI.
Claude:
The question is whether, at a low but nonzero temperature and with no external field, an infinite magnet spontaneously picks a direction and becomes magnetized. Physicists have assumed the answer is yes since Bloch's spin-wave theory in the 1930s. Proving it rigorously has been another matter:
Dimensions 1 and 2: the Mermin–Wagner theorem shows it can't happen, so the question is only for 3 or more dimensions.
The classical version (spins as ordinary arrows) was proved by Fröhlich, Simon and Spencer in 1976 using "infrared bounds."
The quantum antiferromagnet (neighbors anti-align) was proved by Dyson, Lieb and Simon in 1978 with a related technique called reflection positivity.
The quantum ferromagnet is the case that stayed open. Reflection positivity doesn't give the needed bound there, which Dyson–Lieb–Simon pointed out themselves. The paper notes that Lieb listed it as an open problem in 1999. Results since then, such as Correggi–Giuliani–Seiringer's 2015 free-energy asymptotics, controlled thermodynamics and finite length scales but never produced an ordered state.
What's claimed
For every dimension d ≥ 3 and every spin S (½, 1, 3/2, …), at all sufficiently low temperatures, there is a translation-invariant infinite-volume equilibrium state (a KMS state, the rigorous definition of "thermal equilibrium" for infinite quantum systems) whose spin expectation is at least S/4. In other words, a genuinely magnetized phase exists.
For spin ½, the paper also derives a consequence for lattice bosons: a form of the long-range order associated with Bose–Einstein condensation.





































