Number Field Sieves are still the best method, and the techniques are three or more decades old with only incremental improvements. (Of course there might be an incredible breakthrough tomorrow.)

▲

tiahura 6 days ago | parent [-]

best published method

▲

consp 6 days ago | parent | next [-]

Are the bitcoins in the first wallets gone? No? I will assume it's still the best method without any irrefutable evidence.

▲

tripplyons 6 days ago | parent | next [-]

Bitcoin uses ECDSA to sign transactions, not RSA.

In addition, selling information to a government on how to break either system would be more valuable than the amount of bitcoin you would able to sell before exchanges stop accepting deposits or the price crashes.

▲

aleph_minus_one 6 days ago | parent | next [-]

> In addition, selling information to a government on how to break either system would be more valuable

Honest question because one can find such claims very often on forums like HN:

Does there really exist a "feasible" way how some "lone hacker" could sell such information to some government and become insanely rich?

I know that people who apparently have some deep knowledge about how exploit markets work claimed on HN that "if you have to ask how/where to solve your exploit (i.e. you have the respective contacts), you are very likely not able to".

This latter observation seems a lot more plausible to me than the claim often found on HN that some "lone individual" would be able to monetize on it if he found a way how to break ECDSA or RSA by selling it to some government.

	▲	dfedbeef 6 days ago \| parent [-]
		Yes. Start what's known as "a company".

▲

close04 6 days ago | parent | prev | next [-]

If a government knows you have such information they’ll take it not buy it.

So your best bet would probably be to try to sell as many BTC as possible then give away the solution for free to your/a government.

	▲	6 days ago \| parent \| next [-]
		[deleted]
	▲	echelon 6 days ago \| parent \| prev [-]
		> If a government knows you have such information they’ll take it not buy it. They would probably kill you so you couldn't tell others. If a government can break crypto, that's worth more than money. Especially if it can remain peerless and undetected.

▲

cyberax 6 days ago | parent | prev [-]

A method to efficiently factor large numbers will also break the ECDSA.

▲

CamperBob2 6 days ago | parent [-]

No, ECDSA relies on the hardness of the discrete logarithm problem. Nothing to do with factoring, at least not in the classical sense.

On a quantum computer, my understanding is that Shor's algorithm could potentially target both problems, though.

	▲	cyberax 6 days ago \| parent [-]
		Both systems are an example of a hidden Abelian subgroup problem. That is also why Shor's algorithm equally applies to both: https://en.m.wikipedia.org/wiki/Shor%27s_algorithm#Shor's_al... So a hypothetical classic algorithm that breaks the RSA is also highly likely to break the ECDSA.

▲

capitainenemo 6 days ago | parent | prev [-]

Well, this discussion is about prime number factorisation, and bitcoins use elliptic curve...

▲

littlestymaar 6 days ago | parent | prev [-]

True, we can never know what state actors know that we don't, and my cryptography professor at university taught us that NSA likely had 20 years of mathematical advance over the academic crypto community.

That being said, NFS is almost thirty years old so maybe the NSA doesn't have anything better still.