If you own any crypto, list founder Ben Goertzel's comments on Google
cracking Bitcoin's ECDLP on a yet to be built quantum computer might be of
interest.

-- Matt Mahoney, [email protected]

---------- Forwarded message ---------
From: Ben Goertzel from Eurykosmotron <[email protected]>
Date: Wed, Apr 1, 2026, 2:26 PM
Subject: Google’s Quantum Crypto Paper Tells You Quite a Lot
To: <[email protected]>


On Responsible Disclosure, Leaked Search Spaces, and Why Quantum Is an
Asset Even More Than a Threat
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for more
Google’s Quantum Crypto Paper Tells You Quite a Lot
<https://substack.com/app-link/post?publication_id=349947&post_id=192877368&utm_source=post-email-title&utm_campaign=email-post-title&isFreemail=true&r=n870j&token=eyJ1c2VyX2lkIjozOTAxMzUwNywicG9zdF9pZCI6MTkyODc3MzY4LCJpYXQiOjE3NzUwNjc5NzEsImV4cCI6MTc3NzY1OTk3MSwiaXNzIjoicHViLTM0OTk0NyIsInN1YiI6InBvc3QtcmVhY3Rpb24ifQ.zmsI5rzJ1IVIIYzMGbbKdCRjwVhyM_ZRPWpFA2Ws6gM>On
Responsible Disclosure, Leaked Search Spaces, and Why Quantum Is an Asset
Even More Than a Threat

Ben Goertzel <https://substack.com/@bengoertzel>
Apr 1
<https://substack.com/@bengoertzel>

<https://substack.com/app-link/post?publication_id=349947&post_id=192877368&utm_source=substack&isFreemail=true&submitLike=true&token=eyJ1c2VyX2lkIjozOTAxMzUwNywicG9zdF9pZCI6MTkyODc3MzY4LCJyZWFjdGlvbiI6IuKdpCIsImlhdCI6MTc3NTA2Nzk3MSwiZXhwIjoxNzc3NjU5OTcxLCJpc3MiOiJwdWItMzQ5OTQ3Iiwic3ViIjoicmVhY3Rpb24ifQ.zYiQOzdkgrS9TCdzCrfUisTvwkay_1-kj7QDwHrgRqQ&utm_medium=email&utm_campaign=email-reaction&r=n870j>
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Last week Google Quantum AI dropped a 57-page whitepaper
<https://substack.com/redirect/2a792b6e-507e-4e2c-8cb6-a3d0dc3f86dd?j=eyJ1Ijoibjg3MGoifQ.He21_CkfOfKJxaU23rF_Os5N5_-qzSFgpejK31Q3t_8>that
should be keeping every blockchain developer awake at night. The headline
finding: Shor’s algorithm can break the 256-bit elliptic curve cryptography
underpinning Bitcoin, Ethereum, and most of the crypto ecosystem using
fewer than half a million physical qubits on a superconducting
architecture. Their circuits could execute in about nine minutes--within
Bitcoin’s average block time.

The online magazine *beincrypto.com <http://beincrypto.com>* interviewed me
on the topic and the headline they came up with was “ASI Alliance Can
Rebuild Google’s Secret Quantum Circuit, CEO Ben Goertzel Says
<https://substack.com/redirect/3d90310c-67f7-4a2b-a288-1d3481ce7b54?j=eyJ1Ijoibjg3MGoifQ.He21_CkfOfKJxaU23rF_Os5N5_-qzSFgpejK31Q3t_8>”
– an angle that I wasn’t really expecting, though I did indeed say that to
them, among a bunch of other things.

A number of people have asked me about this in the hours since the article
was posted, so I thought I’d write something here to clarify a bit.

Basically: Google withholds the specific quantum circuit they discovered in
the name of responsible disclosure, yet the paper itself constrains the
search space so tightly that reproducing comparable circuits is well within
reach for any serious quantum algorithms group. Including, I would say, our
team at SingularityNET, even though quantum is not our main shtick.

Another point I made to the journalists who asked me about this is: The
qubit counts that make these cryptographic attacks feasible are roughly the
same qubit counts that make quantum-enhanced AI feasible. So regarding
quantum computing, the threat and the capability will arrive on roughly the
same time-scale, and if you’re only looking at the threat side, you’re
missing half the picture--arguably the more important half.
*What the Paper Reveals*

Google’s ZK proof statements and the surrounding discussion disclose a
remarkable amount of architectural detail--more, perhaps, than the authors
fully appreciate. The circuits use kickmix architecture (classical
reversible logic gates combined with measurement-based uncomputation and
diagonal phase corrections), windowed arithmetic with a window size of 16,
the standard Shor phase estimation structure with qubit-recycled Quantum
Fourier Transform, and exactly 28 windowed point additions for 256-bit
ECDLP. They’re using Montgomery’s trick for modular inversion batching,
yoked surface codes for dense qubit storage, and reaction-limited execution.

The ZK proof statements go further, revealing exact resource counts per
point addition subroutine: 2.7 million and 2.1 million non-Clifford gates
for the two variants, on 1,175 and 1,425 logical qubits respectively. The
asymptotic scaling is stated explicitly: approximately 4.5n qubits for
n-bit ECDLP.

So what’s actually secret? The specific circuit implementation of the
elliptic curve point addition--the internal wiring of how they compute the
in-place addition using those ~2.1 million Toffoli gates on ~1,425 qubits.
That’s the crown jewel. Everything else is disclosed.
*The Search Space Is Narrower Than One Might Think*

The key optimizations in elliptic curve point addition circuits involve a
handful of well-understood design choices--modular arithmetic strategy
(Montgomery vs Barrett reduction, addition chain optimizations for field
multiplication), coordinate system selection (projective vs affine, which
inversions to defer), and ancilla management (how aggressively to use
measurement-based uncomputation to trade measurements for gate savings).
These are not obscure research frontiers; they are textbook topics in
quantum circuit optimization, well-mapped by the existing literature.

The prior work that Google is improving on--Litinski 2023, Häner et al.
2020, Gouzien et al. 2023, Chevignard et al. 2026--is entirely public and
establishes the design space. Google’s contribution is roughly an order of
magnitude improvement in spacetime volume over Litinski, achieved within
this known design space. Chevignard et al. already achieved 1,100 logical
qubits--fewer than Google’s low-qubit variant--at the cost of 100 billion+
Toffoli gates. So the qubit-efficient end of the tradeoff curve is already
published. What Google solved is getting the gate count down from 100
billion to 70–90 million while staying near the 1,200–1,450 qubit range.
(To connect the numbers: with 28 windowed point additions and ~2.7 million
non-Clifford gates per addition, 2.7 million × 28 ≈ 75.6 million total
gates, which lands right in that range.)

That’s impressive circuit engineering, but it’s an optimization within a
known framework, not a fundamental algorithmic breakthrough. The paper
tells you the target, the tools, and the constraints. Reverse-engineering
the wiring from there is a bounded search problem.
*Who Could Reproduce This?*

By my best guess, a team of three to five quantum algorithms researchers
with deep expertise in reversible arithmetic circuit synthesis, elliptic
curve cryptography, and quantum error correction could plausibly reproduce
circuits in the same ballpark--say within 2–3x of Google’s gate
counts--within six to twelve months. The field is small enough that the
highest levels of expertise in this precise subdomain are centered in
perhaps ten to twenty groups worldwide: ETH Zurich, CWI Amsterdam,
Microsoft Research, the French groups around Chevignard and Gouzien,
Quantinuum’s theory team, various university labs. However, none of this
knowledge is super secret lore, and teams like ours at SingularityNET with
adjacent quantum computing expertise could handle this sort of work too,
after a bit of getting up to speed.

Getting to exactly Google’s numbers is harder, because the last factors of
optimization in reversible circuit synthesis come from clever ancilla
scheduling, specific addition chain choices, and measurement-based
uncomputation placement decisions that constitute a large combinatorial
search--this is where automated circuit optimization tools and significant
compute for design space exploration matter, and where Google’s resources
give them an edge. But from a security perspective, “within 2x” versus
“exact match” doesn’t change the picture. A circuit with 140 million
Toffoli gates instead of 70 million still breaks your keys; it just takes
18 minutes instead of 9.
*Our Team Could Do This*

So what I said to beincrypto.com
<https://substack.com/redirect/a1632f29-094d-4314-94d9-6254c321a130?j=eyJ1Ijoibjg3MGoifQ.He21_CkfOfKJxaU23rF_Os5N5_-qzSFgpejK31Q3t_8>
was that I feel our team at SingularityNET team could mount a credible
effort to reproduce circuits of comparable efficiency – and we are not a
group that anyone would normally associate with quantum cryptanalysis.

We have researchers with strong backgrounds in mathematical optimization,
formal methods, and algorithmic complexity. We have one quantum AI expert,
a couple team members with PhDs in particle physics, and a load of strong
computer scientists many of whom studied physics in depth at some point in
their lives. We have a small but active quantum AI research side-project,
aimed mostly at exploring novel algorithms approaches at the toy scale on
quantum computers currently available via API. We have extensive experience
with large-scale automated search over combinatorial spaces-- with various
novel algorithms precisely designed for this class of problem. We have the
compute resources, through ASI:Cloud and our broader infrastructure
partnerships, to run extensive circuit optimization campaigns – though to
be clear, we aren’t wealthy enough to direct a lot of resources to this
sort of problem just for the fun of it.

The point isn’t that SingularityNET is going to reverse-engineer Google’s
circuit; we have a lot of other fish to fry, like building beneficial
decentralized AGI capable of launching beneficial superintelligence, and so
forth. The point is that if we could credibly do this, so could any
well-funded national laboratory, defense contractor, or state-sponsored
research group. China’s quantum computing program, which has published
extensively on Shor’s algorithm implementations, certainly has the
expertise. So do groups in France, the Netherlands, Israel, Singapore.

As an adjacent side-point, I would note that while our own R&D team is
working hard toward AGI and superintelligence and making interesting
research progress, so far we have not withheld any of our code for safety
reasons, though we have discussed the possibility internally. Our position
is that secrecy in this domain has very limited tactical value because of
the clear routes to parallel discovery--keeping capabilities secret buys
you at most a fairly short window. The idea that withholding the circuit
diagrams provides meaningful security against determined adversaries is, I
would say, way optimistic.

This isn’t a criticism of Google’s team--their instinct toward caution is
correct, and the ZK proof approach makes total sense. But the crypto
community should not interpret “responsible disclosure” as “the attack
details are safely locked away.” They are locked behind a door that any
competent team can pick, and the paper itself hands you the lockpicking
tools.
*The Real Barrier Isn’t the Circuit*

Even if every quantum algorithms group on Earth had Google’s exact circuit
files tomorrow, the attack still requires roughly 500,000 physical
superconducting qubits with 10⁻³ error rates and a fast classical control
system. That is a hardware engineering challenge measured in billions of
dollars and years of fabrication iteration, not millions and months. The
circuit is a necessary but far from sufficient condition for an actual
attack.

Google’s own paper makes this point implicitly by noting the distinction
between fast-clock architectures (superconducting, photonic, silicon) and
slow-clock architectures (neutral atom, ion trap). The circuit doesn’t help
you if you can’t run it fast enough. And nobody today has a
half-million-qubit superconducting machine.

However, compute technology is advancing very quickly. The paper analyzes
qubit requirements across multiple cryptographic standards, not just ECDLP,
and the trend lines are sobering across the board. The paper’s Figure
3--showing the dramatic decade-long decline in physical qubit requirements
for breaking RSA-2048--should give everyone pause. The finish line is
moving toward us as fast as we’re moving toward it. And as the paper warns,
the first indication that a cryptographically relevant quantum computer
exists might not come from a press release--it might be detected on the
blockchain itself.
*The Qubit Coincidence*

There is another highly relevant point that I have not seen anyone else in
the crypto discourse seriously engage with: the qubit counts needed for
useful quantum AI and the qubit counts needed for these cryptographic
attacks are very concretely in the same ballpark.

Google’s crypto-cracking circuit requires around 1,200–1,450 logical qubits
(realizable using 500K or so physical qubits on the architectures they are
thinking about – waving hands around fairly freely). The kind of quantum
logic network reasoning we’ve been designing for Hyperon’s PLN and ECAN
subsystems--nontrivial quantum-enhanced probabilistic inference, the sort
of thing that would actually give you qualitatively new AI capabilities
rather than just marginal speedups--would do serious work with 5,000–10,000
logical qubits. That’s a gap of roughly 4–8x, not orders of magnitude. And
if you use block-factorized designs--decomposing quantum computations
across a network of classically connected quantum processors, which is the
direction our architecture has been heading anyway for other reasons--you
could quite possibly achieve meaningful quantum AI with individual nodes of
1,000–2,000 logical qubits. Which is essentially the same scale as the
crypto-cracking circuit.

So basically: The hardware generation that can break your elliptic curve
keys is the same hardware generation that can run quantum-enhanced
reasoning engines. This is not a coincidence--both cryptographic attacks
and quantum AI applications are bottlenecked by the same resources:
coherent qubit counts, gate fidelity, and error correction overhead. Both
demand circuits of nontrivial depth on a thousand-plus logical qubits. The
difference is in what you do with those qubits--Shor’s algorithm to crack
the discrete log problem, or quantum amplitude amplification and quantum
walks over inference graphs to accelerate probabilistic reasoning.

And this means that if you’re a blockchain project whose entire quantum
strategy is “swap in post-quantum crypto and hope for the best,” you are –
oh let’s see, what would be the right metaphor? – let’s say: responding to
the news your rival tribe has invented bronze and discovered gunpowder by
rebuilding the fence around your village with bigger sticks!
*Quantum as Opportunity*

While quantum machines with thousands of logical qubits are a ways off,
these issues are still pertinent to current software design decisions, at
both the AI and the infrastructure level. Along these lines, at
SingularityNET and the ASI Alliance we have been designing (our new
AI-oriented L1 blockchain) ASI:Chain from the ground up to be strongly
quantum-oriented …. and I want to be precise about what I mean by that,
because it is a distinction that most of the crypto ecosystem has not yet
grasped and it’s quite relevant to the current conversation about quantum
and crypto and AI. Quantum-oriented does not mean quantum-resistant.
Quantum-resistant means you’ve plugged in lattice-based or hash-based
signature schemes and you’re hoping nobody finds efficient quantum attacks
on those too. Quantum-oriented means you are architecting your system to
actually leverage quantum computation as a resource--to run on quantum
hardware, not just defend against it.

MeTTa, our smart contract language, incorporates quantum type
systems--meaning that quantum states and operations are first-class
citizens in the language’s type hierarchy, so that AI agents running on
MeTTa can natively compose quantum subroutines into their reasoning
pipelines rather than treating quantum computation as an external oracle
call. We have worked out quantum versions of the core AI algorithms of our
Hyperon AGI architecture --attention allocation, probabilistic logic,
evolutionary learning. When quantum processors with 1,000–2,000 logical
qubits become available--the same machines that could threaten classical
crypto--our infrastructure is designed to harness them for reasoning,
inference, and autonomous decision-making at speeds that classical systems
cannot match. Quantum-enhanced smart contracts that can perform
probabilistic reasoning over complex state spaces. Quantum-accelerated
consensus mechanisms. Quantum machine learning integrated directly into
on-chain decision-making. This is the future we’re building toward, and the
qubit coincidence I described above means the timeline for that future is
the same as the timeline for the cryptographic threat.

Making quantum-safe encryption truly efficient--on par with classical
encryption performance--will likely require either new mathematical
breakthroughs in post-quantum cryptographic schemes or custom hardware
optimized for these operations. Our Hyperon AI system may itself contribute
to the mathematical side of this problem, which has an elegant recursion to
it: AI helping to discover the cryptography that protects the
infrastructure that runs the AI. Whether that particular recursion actually
plays out or not, the broader point stands--projects that understand
quantum computing as a computational resource to be harnessed, rather than
merely a threat to be survived, are the ones that will define the next era
of decentralized intelligence.
*What This Means for the ASI Alliance and the Broader Crypto Ecosystem*

It is worth emphasizing for those who are not familar with our work at the
ASI Alliance that the ASI:Chain is totally *not *EVM-compatible, nor is it
based on legacy Bitcoin software structures. It is its own chain with its
own architecture, built on a Rholang/RChain lineage with a totally new AI
programming language called MeTTa as the smart contract language. We do not
inherit Ethereum’s quantum vulnerabilities. The Google paper’s analysis of
Ethereum’s five distinct vulnerability categories--Account, Admin, Code,
Consensus, and Data Availability--is a roadmap of mistakes to avoid, and we
have been avoiding them from day one because ASI:Chain’s encryption layer
is modular. Quantum-safe cryptographic primitives can be plugged in without
redesigning the reasoning infrastructure. The cost is computational
overhead, which is a real engineering challenge but not an architectural
one.

Smart contract platforms that rely on ECDLP-based precompiles, as Ethereum
does, are building on a foundation with an expiration date. The “on-setup”
attack category described in the paper--where a single quantum computation
on fixed protocol parameters creates a reusable classical exploit--is the
most insidious threat, and any system using KZG commitments or
trusted-setup-based SNARKs should be migrating to hash-based alternatives
(STARKs, FRI) immediately. Key rotation mechanisms are non-negotiable;
Ethereum’s lack of expedient validator key rotation is a glaring weakness.

The broader ecosystem matters too, and this is where things get
uncomfortable even for those of us who are building our own decentralized
systems on more solid foundations. If Bitcoin or Ethereum suffer a
quantum-driven crisis, the contagion effects on crypto markets would hit
everyone, including ASI. Google models a 41% success rate for quantum
on-spend attacks against Bitcoin’s ten-minute block window, and any attack
success rate above single digits is deeply problematic for a store-of-value
chain. Once rational actors believe there is a meaningful probability that
a transaction can be reversed or an address drained during the confirmation
window, the game-theoretic assurances that underpin Bitcoin’s security
model collapse. The saving grace is that the hardware to execute this at
scale does not yet exist, but the mathematical writing is on the wall, and
the Bitcoin community’s lack of a coordinated upgrade path makes this a
serious medium-term risk.

The paper’s analysis of Algorand, QRL, and Abelian as examples of
successful PQC deployment is encouraging. The path is technically clear.
What’s less clear is whether the broader crypto ecosystem has the political
will to walk it before the window closes.
*The Responsible Disclosure Dilemma*

Beyond the specifics of quantum attacks on encryption, there’s a deeper
philosophical issue here that resonates with themes I’ve been thinking
about for years in the context of AGI safety. Google’s paper embodies a
genuine tension: they want to warn the community loudly enough to motivate
action, but quietly enough to avoid giving adversaries a head start. The ZK
proof is an elegant attempt to resolve this tension
cryptographically--proving you have the weapon without showing the
blueprints.

And I think the ZK approach actually does satisfy the crypto community’s
core epistemic standard, which is not “see everything” but “don’t take
claims on faith.” A well-constructed ZKP lets you verify that someone has
the capability without them handing you the exploit. That said, the
community should demand that the proof itself is rigorously audited by
independent cryptographers, and Google should expect skepticism until that
happens. I do not think we need to see the circuit to believe the result,
but we do need the ZKP to be examined by people who are not Google.

But information has a way of escaping containment--in AGI safety we talk
about this in terms of the difficulty of boxing superintelligent systems.
In quantum cryptanalysis the analog is simpler: the design space is finite,
the prior literature maps most of it, and the paper itself provides enough
constraints to turn an open research problem into a directed engineering
effort. The default should be openness, because the security benefits of
open review and decentralized scrutiny vastly outweigh the marginal risk
reduction of secrecy in a world where parallel discovery is the norm. If
something posed a specific, acute, short-term danger, we would hold it
back--we are not ideologues about this. But the general case strongly
favors disclosure.
*Does the Quantum Threat Kill the Decentralization Thesis? (No!)*

No, of course it doesn’t – but it raises the stakes enormously. If a
centralized actor cracks dormant Bitcoin and captures hundreds of billions
in assets, that is a massive centralizing force--no question. Over 1.7
million BTC in Satoshi-era P2PK wallets can never be migrated, and those
coins are going to be cracked by someone eventually. The question is
whether you want a legal framework around it or a lawless scramble. On
principle, giving governments a legal pathway to crack private wallets sets
a catastrophic precedent for digital property rights--the entire value
proposition of crypto rests on the idea that your keys are your coins. I
lean toward the position that dormant coins should remain inviolate as a
matter of principle, and the ecosystem should price in their eventual
vulnerability rather than invite government seizure regimes.

But the decentralization thesis was never premised on the idea that legacy
cryptography would last forever. It is premised on the idea that open,
distributed systems are more resilient, more innovative, and more aligned
with human flourishing than centralized ones--and that has not changed. The
quantum threat accelerates the timeline for crypto infrastructure to
evolve, and it will punish projects that were not forward-looking. But
projects that were designed with quantum computing as a first-class
consideration--as a computational resource to harness, not just a threat to
defend against--are positioned to come out stronger. The decentralization
thesis survives if decentralized projects out-engineer centralized ones on
the quantum transition – which is for sure the approach we’re taking in the
ASI Alliance.
*The Clock Is Running*

The paper’s own conclusion is the one that matters: the crypto community
should begin migration to post-quantum cryptography immediately, because
the margin for error is narrowing and the timeline is uncertain. Whether
the specific circuits leak, get independently rediscovered, or remain
secret for another few years is, in the scheme of things, a second-order
question. The first-order question is whether we’re building post-quantum
systems fast enough.

But I’d add a corollary that Google’s paper doesn’t quite state: there is a
further question of whether we’re building quantum-leveraging systems at
all. The hardware generation that threatens classical cryptography is the
same hardware generation that enables quantum AI. It seems very likely that
the projects that understand this--that are engineering for quantum
advantage, not just quantum survival--are the ones that will define the
next era of decentralized intelligence. The ones that treated quantum as
purely a defensive problem will find themselves with hardened walls and
nothing interesting inside them.

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