> This is also why address reuse in Bitcoin is encouraged as to sign a transaction you need to reveal your public key. If you don't reuse an address after sending a transaction from the address, you don't need worry about the private key of that address being exposed.
Shouldn't that say "address reuse in Bitcoin is discouraged"? Otherwise I don't think I understand what he's trying to say.
The reason being without revealing public key, with only the bitcoin address the attacker first need to guess the public key from the address, then guess the private key from there. So just breaking one of the hash algorithm or ecdsa algorithm is not enough to steal funds. at least that's in theory, in reality if either algorithm is broken we have a much bigger problem.
ECDSA is vulnerable to a modified version of Shor's quantum integer factorization algorithm. However, nobody on Earth is known to be close to producing such a computer. Adiabatic quantum computers like the ones produced by D-Wave are not known to be capable of running Shor's algorithm. See https://en.wikipedia.org/wiki/Adiabatic_quantum_computation
SHA-256 and hashing algorithms have no known quantum attack against them, but one could theoretically gain a sqrt(n) advantage in brute-force search using Grover's quantum search algorithm. https://en.wikipedia.org/wiki/Grover%27s_algorithm
Bitcoin can soft-fork, allowing address generation with a different algorithm. It's not any sort of existential threat to Bitcoin. But it does require that you move your coins to a new address if you reuse an address, else you are vulnerable.
This burned sony, and burned people that had faulty wallet code that submitted transactions with the duplicate nonces.
If you only published, and signed a transaction once, you would be immune to fail by ECDSA nonce reuse.
Its good to rotate the publickey/address per transaction in bitcoin