Topic: Mining scripts on quantum computers (Read 327 times)

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I don't follow how this becomes easier to crack than RSA though.

Shor's algorithm works on ECDSA, way easier than breaking RSA in fact[1] (I think 2x easier?). You can modify the algorithm slightly to defeat ECDSA which shouldn't be a problem.

This only works on RSA keypairs (and any other cryptosystem that uses prime factoring) and it is inapplicable to the elliptic curve cryptography that Bitcoin uses.

Elliptic curves take their private key as an extremely large number and multiply that by a curve point to get the public key. It's completely different from getting two primes and multiplying together to derive the private key, public key and other parameters, which is what Shor's algorithm applies to.

This only works on RSA keypairs (and any other cryptosystem that uses prime factoring) and it is inapplicable to the elliptic curve cryptography that Bitcoin uses.

Elliptic curves take their private key as an extremely large number and multiply that by a curve point to get the public key. It's completely different from getting two primes and multiplying together to derive the private key, public key and other parameters, which is what Shor's algorithm applies to.

The quantum Shor algorithm is a much more powerful approach than Grover, and can be used to destroy public-key cryptography.
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But, IMO, unfortunately QC wouldn't work for any task other than generating enormous amounts of noise.

Mining can potentially be much quicker with QCs.
The current PoW difficulty system can be exploited by a Quantum Computer using Grover’s algorithm to drastically reduce the number of computational steps required to solve the problem. The theorised advantage that a quantum computer (or parallelised QCs) have over classical computers is a couple of orders of magnitude, so ~x100 easier to mine. This isn’t necessarily a game-changer, as this QC speed advantage is likely to be some years away, by which time classical computers will surely have increased speed to reduce the QC advantage significantly. It is worth remembering that QCs aren’t going up against run-of-the-mill standard equipment here, but rather against the very fast ASICs that have been set up specifically for mining.

Re-used BTC addresses are 100% vulnerable to QCs.
Address Re-Use. Simply, any address that is re-used is 100% vulnerable because a QC can use Shor’s algorithm to break public-key cryptography. This is a quantum algorithm designed specifically to solve for prime factors. As with Grover’s algorithm, the key is in dramatically reducing the number of computational steps required to solve the problem. The upshot is that for any known public key, a QC can use Shor’s approach to derive the private key. The vulnerability cannot be overstated here. Any re-used address is utterly insecure.

Processed (accepted) transactions are theoretically somewhat vulnerable to QCs.
Theoretically possible because the QC can derive private keys from used addresses. In practice however processed transactions are likely to be quite secure as QCs would need to out-hash the network to double spend.

Unprocessed (pending) transactions are extremely vulnerable to QCs.
As above, a QC can derive a private key from a public key. So for any unprocessed transaction, a QC attacker can obtain the private key and then create their own transaction whilst offering a much higher fee, so that the attacker’s transaction gets onto the blockchain first, ahead of the genuine transaction. So block interval and QC speed are both crucial here – it all depends on whether or not the a QC can hack the key more quickly than the block is processed.

If quantum computers ever work, then by using Groover's algorithm mining difficulty would be square root of the usual one.