Pinned Tweet
[Repost] Recently there's been some renewed interest in "hash-friendly" cryptography schemes, brought forward by successful AI-assisted simplifications of hardness assumptions in post-quantum candidates. Over the last month I decided to dig deep into Binius, which is a proof system over "binary circuits" (functions that take binary inputs, what software/hardware naturally execute). While it is somewhat complicated, it's not that scary once you isolate the individual components and see how it's glued together (learning still in progress). The nice thing about it is that it's taking advantage of fundamental mathematical properties and is not based on structured algebra (discrete log, lattices, etc) that could be break unexpectedly.
I just created an initial overview chart, and will follow up with narrower ones that describe the math and core properties in more detail. A proper article about this might be worth it at some point, but I'm not sure yet. The audience for this is inherently small, but anyway.
Goodbye, Poseidon!
An epic 8-year, 8-figure rabbit hole in post-quantum cryptography reaches its dream conclusion. The Ethereum Foundation is abandoning Poseidon for L1, pivoting to SHA or BLAKE. This milestone unlocks ultimate security for lean Ethereum and foreshadows a golden era of hash-based cryptography.
Since 2018, the Ethereum Foundation has invested in magic cryptographic bricks, so-called "SNARK-friendly hashes". In 2019, Poseidon was born. It held strong and became the dominant SNARK-friendly hash, securing billions via zkrollups and zkVMs.
In a stunning reversal, breakthrough SNARK designs show that SNARK-friendly hashes aren't necessary after all. Off-the-shelf traditional hash functions like SHA2 and BLAKE2s can now match Poseidon in a SNARK. In hindsight the key was not SNARK-friendly hashes, but hash-friendly SNARKs.
The secret is doing maths over the smallest prime number: 2. So-called "binary fields" natively speak the language of bits, aligning with the boolean operations inside traditional hashes. This is a stark departure from "prime fields", where awkward large-prime arithmetic makes bit manipulation painfully expensive.
We're talking sci-fi cryptography. 1M traditional hash calls proven per second, on a laptop. Just 100x overhead vs native CPU boolean compute. Nobody predicted such performance, not even the handful of binary-field visionaries. Hat tip to the research geniuses: Jim and Ben with Binius in 2023; Ron, Benedikt and William with Flock in June.
With SHA2, the lean aesthetic of minimal assumptions reaches its climax. The EF's principled stance on pure hash-based cryptography has aged like fine wine. We now enjoy foundations the world can trust for decades and centuries, foundations worthy of the dream of an internet of value.
Speed of deployment is a secondary win. There's no longer a need to wait years for Poseidon cryptanalysis to bake. Emile and Thomas from the EF post-quantum team are moving at breakneck speed with binary fields. The strawmap now points to a production-grade leanVM in 2027, with CL, DL, EL deployments in 2028.
As AI becomes exceptional at cryptanalysis, the contrarian bet to avoid riskier structures like lattices and isogenies is visibly paying off. The past weeks have been brutal. Lattice-based "HAWK" and isogeny-based "SQIsign", both signature schemes in NIST's Round 3, have suffered blows. Sources I trust say more blood is coming.
On AI, the open autoresearch trend kicked off by ECDSA[.]fail is spreading fast, with amazing outcomes from zk[.]golf and SNARK[.]fast. Days ago SNARK[.]fast crossed 1.8M BLAKE3/sec proven on an M3 Max. Stay tuned for fresh autoresearch challenges dropping tomorrow.
Also tomorrow: Ethproofs call #10, dedicated to binary fields. Possibly the most noteworthy Ethproofs call yet. Experts leading the charge will present the future of hash-based SNARKs at 2pm UTC. What an incredible time to be alive. To witness history, DM me for a calendar invite :)
Today I can confidently claim that hash-based cryptography has won out for blockchain post-quantum signatures. SNARK succinctness compresses arbitrarily many signatures into one small proof per block. SNARK flexibility yields k-of-n threshold signatures, complex multisigs, and more.
Ultimate security. Uncompromising performance. Full programmability.
Believe in something. Believe in hashes.
I really cannot stand @TheAtlantic, but sometimes their artists drop bangers like this
agentic solutions are only viable if applied to a Fordian pipeline, which only occurs narrowly in industry. our complex socities, inherently formed around human desires, require constant input and readjustment. this is also the main argument against RSI taking over the world.
we've seen this before; time to learn accelerandese, buddy
The Latin alphabet is not how machines think in latent space nor ideally how they communicate
Created a custom 8,192-dimensional token alphabet for machines to communicate in token space directly
Inspired by the alphabet in @Grimezsz new Accelerando MV
1st img = encoded lyrics
Part two: Multilinear Extension (MLE)
xitter.cf/nebulayer/status/21042…
Everything that a computer can compute can be expressed uniquely by a (multilinear) formula. This is the basis on which zero-knowledge proof systems operate, and how computational logic becomes checkable. Next chart is about Sumcheck, which reduces a claim about said formula to a single check at a random point.
Part Three: Sumcheck
xitter.cf/nebulayer/status/21082…
Sumcheck is a checksum-like mechanism for computable logic, where a single input changes the entire structure of the final value. It allows the prover to claim to know such logic without revealing it in full, and the verifier can use a handful of challenges to force any falsehoods to surface in a checkable final value.
The next part will be on binary FRI, which allows us to perform the proper check of said final value. It will be the most complicated chart, but also the most important.
Sumcheck is a checksum-like mechanism for computable logic, where a single input changes the entire structure of the final value. It allows the prover to claim to know such logic without revealing it in full, and the verifier can use a handful of challenges to force any falsehoods to surface in a checkable final value.
The next part will be on binary FRI, which allows us to perform the proper check of said final value. It will be the most complicated chart, but also the most important.
[Repost] Recently there's been some renewed interest in "hash-friendly" cryptography schemes, brought forward by successful AI-assisted simplifications of hardness assumptions in post-quantum candidates. Over the last month I decided to dig deep into Binius, which is a proof system over "binary circuits" (functions that take binary inputs, what software/hardware naturally execute). While it is somewhat complicated, it's not that scary once you isolate the individual components and see how it's glued together (learning still in progress). The nice thing about it is that it's taking advantage of fundamental mathematical properties and is not based on structured algebra (discrete log, lattices, etc) that could be break unexpectedly.
I just created an initial overview chart, and will follow up with narrower ones that describe the math and core properties in more detail. A proper article about this might be worth it at some point, but I'm not sure yet. The audience for this is inherently small, but anyway.
It think that as crypto enthusiasts, we have to accept the idea that it's likely impossible to build open and truly free financial infrastructure where grifters and scammers are somehow excluded from. Can't have your cake and eat it too.
Nebulayer retweeted
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.
2050: the claim is the proof(?)
The evolution of block verification:
- 2010: download everything and re-execute
- 2030: sample the data with PeerDAS and verify a SNARK
We’re slowly changing what it even means to verify Ethereum.
vitalik.eth.limo/general/202…
Everything that a computer can compute can be expressed uniquely by a (multilinear) formula. This is the basis on which zero-knowledge proof systems operate, and how computational logic becomes checkable. Next chart is about Sumcheck, which reduces a claim about said formula to a single check at a random point.
[Repost] Recently there's been some renewed interest in "hash-friendly" cryptography schemes, brought forward by successful AI-assisted simplifications of hardness assumptions in post-quantum candidates. Over the last month I decided to dig deep into Binius, which is a proof system over "binary circuits" (functions that take binary inputs, what software/hardware naturally execute). While it is somewhat complicated, it's not that scary once you isolate the individual components and see how it's glued together (learning still in progress). The nice thing about it is that it's taking advantage of fundamental mathematical properties and is not based on structured algebra (discrete log, lattices, etc) that could be break unexpectedly.
I just created an initial overview chart, and will follow up with narrower ones that describe the math and core properties in more detail. A proper article about this might be worth it at some point, but I'm not sure yet. The audience for this is inherently small, but anyway.
Shielded Bitcoin is an L2, which uses the Bitcoin L1 for settlement + state reconstruction. Fundamentally it will face the same friction as any other L2 variant, which often is the death blow:
> Peg-in and peg-out are outside the scope of this paper.
Happy to be proven wrong.
Nebulayer retweeted
⚛️ Bitcoin does not have a quantum computer problem today. It has a migration problem, and migrations could take years to get right.
SHRINCS is the first Bitcoin-specific post-quantum proposal I have seen that makes a serious end-to-end trade-off, and it deserves to be read carefully rather than cheered or dismissed. Their work is the proposal.
I wrote an analysis of the challenges that come with it, the ones that only become visible when you look past the signature scheme and into the wallets that have to run it.
The migration really has three questions:
- which scheme Bitcoin should support
- what that scheme does to the protocol and the wallet ecosystem
- what happens to coins that have never been moved by their owner.
Almost all of the public discussion is still on the first one, which is probably the easiest of the three.
SHRINCS is conservative where it matters. It is hash-based, so it leans on the SHA-256 that Bitcoin already depends on instead of stacking a lattice assumption on top. A single 48-byte public key commits to both a compact stateful path (Flexible XMSS and WOTS+C) and a stateless SLH-DSA fallback.
Verification is the pleasant surprise. It is mostly SHA-256, and the draft reports a worst-case cost per signature byte below BIP340 Schnorr.
The stateful path uses one-time keys, and each one must sign exactly once. The counter must never move backwards, it must be committed to persistent storage before the signature leaves the device, and it must never be restored from a backup. Sign two different messages from the same slot and an observer can steal your fund.
SHRINCS handles this better than a purely stateful scheme. If the state is lost or merely uncertain, the seed still derives the stateless key, so you lose efficiency rather than funds. The cost is that wallet state stops being application data and becomes cryptographic state whose rollback can take user funds: hundreds of counters for hundreds of UTXOs, across several devices and several software wallets, on hardware where hash-based keygen already takes minutes.
There are also capabilities we do not get back. Non-hardened BIP32 derivation, and with it watch-only wallets as we build them today. Compact Schnorr-style threshold signing.
None of this makes SHRINCS a bad proposal, and the spec is honest about its own status: non-standard SLH-DSA parameters, constructions outside the NIST standard, security proof pending. It does mean the cost of this migration cannot be only measured in signature bytes. The stateful aspect of SHRINCS would be very challenging in terms of security and UX.
The uncomfortable part is that picking the signature scheme may be the easiest question here.
ledger.com/blog-shrincs-bitc…
Nebulayer retweeted
allow me to reintroduce SHRINCS:
- groups.google.com/g/bitcoind…
- github.com/SHRINCS/shrincs-b…
- youtube.com/watch?v=n-jGPICZ…
hypergraph mentioned
Major update from us @extropic
Announcing Torx and Thermalizers, basically our version of PyTorch + kernels, but for Thermo hardware
Also: Z1 is now taped out and in fabrication! Will be available on 0.5M pbit sticks, and 4M pbit PCIe cards
+1 more thing at the end... enjoy!
we built a bitcoin dark pools prototype 🪄
tl;dr - we built a privacy-preserving, bitcoin exchange using @mercurylayer, nostr, and a zk-execution network. the bitcoin transfer is completed offchain via a blind co-signer. the stablecoin network only reveals hashes of inputs and outputs, no amounts or user addresses. orders are matched peer-to-peer using nostr identities. exchange is atomic & privacy-preserving. deets:
this protocol is built on the following:
- statechains, a way to transfer ownership for bitcoin utxos offchain by reassigning spending keys
- private stablecoin network with flexible zk-circuits/contracts that lock funds to a specific sha256 hash
- a blind co-signer that facilitates ownership transfer for bitcoin utxos offchain per a specific order
the exchange builds upon mercury layers’ latch protocol. the seller locks their offchain "utxo" into an order that they create. the order specifies that an offchain transfer to the buyer’s offchain address should occur after buyer & seller commit to it. an order with a hash is created.
the order hash is then used to lock stablecoins on the zk network. meaning, the buyer must lock their funds into an escrow contract where the funds are only claimable by revealing the preimage for the order’s sha256 hash (or they refund the buyer after a timelock).
after these stables (or any other shitcoin, tbh) are locked on the zk side, the buyer submits the tx hash to the seller. after verifying that stables are locked in escrow, the seller calls the co-signer to unlock the transfer to the buyer. after verifying that the seller has committed this, the buyer also calls the co-signer to unlock the transfer. the co-signer reassigns the statechain multisig spending key to the buyer and tweaks their keyshare. the co-signer then deletes their key with the seller.
after the statechain transfer, the co-signer then reveals the preimage for the order to the seller. the seller uses that to claim the stables on the zk network out of the escrow contract. swap completed. buyer trusts signer deleted their keyshare up until the point the exit the statechain back to bitcoin.
we’ve taken this swap protocol and developed an RFQ protocol using nostr identities. in the exchange application, users create a nostr identity and submit buy and sell orders. only their npub, and the amount of their respective order, is revealed. no bitcoin addresses or other pii is exposed. when a user finds an suitable offer in the orderbook, they submit an encrypted firm quote with exact amounts and prices. only the counterparty in the trade can decrypt this message.
from an onchain perspective, there is no onchain bitcoin transaction. on the stablecoin side, zk magic only see hashes of inputs and outputs publicly available. you can’t even discern which token was involved in the trade.
the co-signer is blind and dumb. validation is done peer-to-peer between countparties. co-signer only signs when its told to.
this is a demo and opinionated design. in our view, it’s extremely privacy-preserving and makes nice tradeoffs wrt user self-custody.
we’ll building more optimized versions that make different tradeoffs, but wanted to share this example. all code will be open-sourced in the future.
🪄



























