Topic: I believe P=NP. Prove me wrong - page 2. (Read 338 times)

You think that someone broke into GOX wallets knowing their public keys?

Gox coins were probably stolen with inside help from an employee who helped them to change the code of the exchange and add backdoors that would allow them to apply changes to the site from the outside. They were changing balances and withdrawing coins through the site for many years.

https://anycoindirect.eu/en/blog/what-is-mt.-gox-how-850.000-bitcoins-got-stolen

Firstly, this is silly. P vs NP is not something where you can knock up a quick proof. I think P ≠ NP. Prove me wrong.
If you can demonstrate a proof, then go and claim the millennium prize and pick up a Fields medal while you're at it.

Secondly and less frivolously, even if P = NP, this does not mean that anything can be solved quickly, it just means that anything can be solved in polynomial time. Not necessarily quick at all.



The biggest potential threat to bitcoin security is probably a sufficiently powerful quantum computer (which we don't have yet) running Shor's algorithm to derive a private key from a known public key. This can be done quickly (if you have the powerful QC). ECC can be broken.
Hashing, on the other hand, is more resistant to quantum attack.

Sure, I can explain more.

The security of Bitcoin is ensured by SHA-2 hashing and elliptic curve cryptography. The security works because those functions are one-way functions (https://en.wikipedia.org/wiki/One-way_function). You can quickly compute the output, but it seems very hard to do it the other way around and get a valid input for a selected output. This is why empirically, bitcoin works.

However, at the mathematical level, one functions functions are not proven to exist. In fact, if the solution to the P versus NP problem is equality (https://en.wikipedia.org/wiki/P_versus_NP_problem), one way functions are guaranteed to not exist at all. Thus, the reason why Bitcoin works might be because no one has publicly revealed how to proceed to solve NP problems quickly.

I believe that at least one person in this civilisation has this knowledge and is manipulating everyone.

I will not speculate whether the manipulator is Satoshi Nakamoto himself, or a government, or misanthropic aliens.

However, there are things to observe in practice. To steal bitcoins from a random address, and avoid getting noticed, the attacker must have the public key of the target bitcoin address. The public key of a bitcoin address is revealed only after the first transaction spending coins from that address. Therefore, the thief must only attack private keys where coins have already been spent (reused bitcoin addresses).
If the attacker steals from a bitcoin address where the public key is not revealed, the forged private key will still work, but will likely correspond to a different public key, the owner of the coins will be able to notice that the private key is a forged one and prove it to the world by reusing the same address with a different private key. The same bitcoin address will have transactions with two different public keys and that's statistically impossible unless one of the keys was forged.

In practice we observe that there are multiple official warnings against reusing addresses (https://en.bitcoin.it/wiki/Address_reuse). Also large thefts have occured like Mt. Gox, and smaller ones keep occuring in plain sight of everyone.

Prove me wrong

We are not sure whether your speculation is right or wrong, because so far it seems that the calculations and the power used are still in a very logical stage. honestly I'm not good at calculating math. maybe you can explain it more simply and easily understandable by those of us who still don't understand how the flow of your statement actually corner mining or certain communities.

I believe P = NP. Anything that can be checked quickly, can be solved quickly. SHA-2 collisions are feasible. Secp256k1 keys can be forged. One-way functions do not exist.  

I also believe that someone already knows and is using this knowledge at their own advantage. They're laughing at the world and how easily humans can be manipulated into investing their hard earned money into something worthless at the mathematical level. They will never reveal the secret and will keep stealing large amount of coins again and again from reused keys like they did with Mt. Gox.

Prove me wrong