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How to compute a 256 bit elliptic curve key with 50M Toffoli gates

76 points| aburan28 | 2 years ago |arxiv.org

44 comments

order

genr8|2 years ago

"At 10% threshold, assuming a 10-μs code cycle and non-local connections, one key can be generated every 10 minutes using 6000 modules with 1152 physical qubits each."

1152 qubits sounds like the D-Wave chips. So does that mean 6000 D-wave chips ?

Even if you reverse the calculation, that would be 60000 minutes on 1 chip, which is about 42 days only, so. Quantum Too Good

fsh|2 years ago

The paper is about digital gate-based quantum computers. These have almost nothing in common with D-Wave's analogue quantum annealers. They certainly cannot run Shor's algorithm (they don't run algorithms at all).

curling_grad|2 years ago

If I remember correctly, the chips in D-Wave machines are for specific problems (optimization problems mostly), so it seems very unlikely they can run the quantum circuits proposed in the article.

consp|2 years ago

Can those even perform shor's? I've read somewhere those are not suitable but I'm limited by a lack of actual knowledge here.

Escapado|2 years ago

About 5 years ago I wrote my master thesis on quantum computing, specifically on the construction of quantum circuits. As these circuits are generally unitary matrices an interesting question is: Given a set of gates that operate on one qbit or two qubits (controlled gates) and a target unitary matrix (e.g. fourier transform or the hamiltonian of a physical system of interest such as an Ising model), can we find an optimal/minimal arrangement of those gates to approximate or exactly match the target matrix.

Back then I modelled the quantum circuit as a set of unitaries (by parametrizing them through their generator), that operate on one or two qubits, set a limit to the amount of steps and the amount of controlled gates and then threw different optimization algorithms at it. I got the best performance using simple dense neural networks. What's cool is that I could generate a training set really quickly since I could just randomly build tensor products of unitary matricies to create billions of unitaries of up to 7 qubits in minimal time and then just see how close I can get given a fixed length for the quantum circuit and a fixed number of control gates.

I really liked this approach and it was fun to work on. However it was ultimately limited as the size of the matrices scales exponentially with the number of qubits.

bob1029|2 years ago

I have a feeling the quantum-crypto conversation is going to take off like a rocket after IBM does their Quantum System 2 presentation later this year.

upofadown|2 years ago

IBM has been on the edge of a major breakthrough for quite some time now...

They like to make larger and larger quantum computers that don't do anything useful. A sort of progress I suppose...

tourist2d|2 years ago

I wouldn't hold your breath on IBM releasing anything amazing in 2023.

phas0ruk|2 years ago

Doesn’t this mean crypto has a major problem ?

bawolff|2 years ago

So its mostly just public-key encryption and its been a known issue since about 1994. We are still nowhere near making quantum computers that can crack them so its not an urgent thing. There has been a lot of research into alterantives though.

was_a_dev|2 years ago

In the realm of quantum computing, it always has

survirtual|2 years ago

Encrypted comms has a problem.

Crypto does not, for a lot of reasons, but biggest I can think of is that hashing is still one-way, public keys are hidden (until used, which is why it is important to expose your public key only when using funds).

When there is a viable ECC attack vector, it will not be much effort to migrate to a more mature PQC. Better to wait as long as possible, maybe even have a crypto built on PQC to field test it with money on the line -- a few billion in market cap goes a long way to incentivizing breaking the crypto involved.

some_furry|2 years ago

Subtext: This is about quantum computers, which have been known to break RSA and ECC for the order of 30-ish years now.

unsolved73|2 years ago

RIP Passkeys.

rhn_mk1|2 years ago

I'm sure if Passkeys are found to be susceptible to quantum cracking, they will move on post-quantum encryption.