I believe P=NP. Prove me wrong

[demanze]

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

[bassbity]

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.

[demanze]

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.

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

[Cnut237]

I believe P = NP. Anything that can be checked quickly, can be solved quickly.
[...]
Prove me wrong

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 security of Bitcoin is ensured by SHA-2 hashing and elliptic curve cryptography.

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.

[pixie85]

Also large thefts have occured like Mt. Gox, and smaller ones keep occuring in plain sight of everyone.

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.

The disaster was bound to happen as MtGox didn’t use any version control software. A system that is responsible for changes to computer programs, that is installed on top of the entire infrastructure. Without this software, the bad code had seeped into the system without ever being noticed.

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

[demanze]

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

Mark Karpeles is an asperger syndrome guy with around 200 IQ. I don't think he is dumb enough to let any employee or code get near his private keys at all. I think he was probably completely stunned when he realised the coins had moved without his consent, he didn't even know what to explain to Japanese police at first.

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.

I'm the one who stole the coins and never used them. Boom, you're wrong  

It's way easier to stealthily steal 20 coins than to claim any prize at all. The proof that P = NP would be the algorithm itself. But the algorithm would likely be easier to find than the proof that the algorithm is correct.

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.

Yes, but most of the known algorithms for problems in NP run not only in polynomial time, but also very quickly. 2SAT can be solved in N^2. XOR-SAT can be solved in N^3. That's about the most complex we can solve. If P = NP then the algorithm must be some sort of extension of Gaussian Elimination, which would run maybe in N^4 or N^5. I don't think large polynomials are relevant. If complexity could get up to N^1000, then it likely wouldn't stop there.

[Cnut237]

I don't think large polynomials are relevant. If complexity could get up to N^1000, then it likely wouldn't stop there.

For reference, 2^1000 is...

10,715,086,071,862,673,209,484,250,490,600,018,105,614,048,117,055,336,074,437,503,883,703,510,511,249,
361,224,931,983,788,156,958,581,275,946,729,175,531,468,251,871,452,856,923,140,435,984,577,574,698,574,
803,934,567,774,824,230,985,421,074,605,062,371,141,877,954,182,153,046,474,983,581,941,267,398,767,559,
165,543,946,077,062,914,571,196,477,686,542,167,660,429,831,652,624,386,837,205,668,069,376

And the estimated number of atoms in the observable universe is a mere 10^80, which is a comparatively tiny...

100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000




... but I agree with you that exposed public keys are where bitcoin is potentially vulnerable to future technology.

[pooya87]

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. 
Prove me wrong

Why should we prove your claims? The one making the claims should prove them also.
Here is a SHA256 hash: 00000000000000000002958a78bb4038b72cb1681aceab0fa17106b4e250a8f8 find a collision.
Here is a EC public key: 03cb8f9734f4dc2e423dad83d59f7f2e823a9ab4df0e1fa1b18690f8bd0376cd9b "forge" it whatever it means!

I also believe that someone already knows and is using this knowledge at their own advantage.

I also believe there are super advanced aliens among us who are watching over SHA256 and ECC and will evaporate that "someone" who knows more.
Prove me wrong

[demanze]

Why should we prove your claims? The one making the claims should prove them also.
Here is a SHA256 hash: 00000000000000000002958a78bb4038b72cb1681aceab0fa17106b4e250a8f8 find a collision.
Here is a EC public key: 03cb8f9734f4dc2e423dad83d59f7f2e823a9ab4df0e1fa1b18690f8bd0376cd9b "forge" it whatever it means!

Why should I prove my claims? It would be a great sacrifice.

If I do have a working solution, then I have no incentive to prove it. Since everyone believes the system works anyway, I can steal coins in a very targeted manner and be rich as long as nobody reveals the truth. You forget to take into account the most important thing, which is the violence, greed, dishonesty inherent to every being living in a competitive and cruel world like the human world.

In the best case, if I'm a good hearted person, I could issue some warnings on bitcointalk and say "I told you" after the truth is revealed intentionally or accidentally by someone else. That would be a funny thing to do also.

As said in The Matrix, "denial is the most predictible of all humans responses". Remember Neo's reactions: https://youtu.be/lBo_mVV81n8?t=238

[Cnut237]

If I do have a working solution, then I have no incentive to prove it.

Is the $1,000,000 millennium prize not sufficient incentive for proving your 'solution' to P vs NP? You'd also achieve worldwide fame and recognition as a genius, and if you're eligible then a Fields medal would seem likely, too.

[demanze]

Is the $1,000,000 millennium prize not sufficient incentive for proving your 'solution' to P vs NP? You'd also achieve worldwide fame and recognition as a genius, and if you're eligible then a Fields medal would seem likely, too.

What if I would be arrested for the coins I have stolen or would be suspected of stealing? Or simply for destroying value?

The mainstream financial elites are very interested in Bitcoin. Elon Musk, MicroStrategy are pouring billions of dollars into purchasing bitcoins. Revealing such a secret would destroy their investments and their companies. They would have two options. 1. Accept their failure and walk away. 2. Blame the person who "caused" the event.

When trillions of dollars are at stake, how much of an honest reaction can we expect from people who were attracted to this by greed in the first place?

If Satoshi Nakamato is an individual then maybe they have very very very very very very very good reason of hiding.

[Vod]

For reference, 2^1000 is...

10,715,086,071,862,673,209,484,250,490,600,018,105,614,048,117,055,336,074,437,503,883,703,510,511,249,
361,224,931,983,788,156,958,581,275,946,729,175,531,468,251,871,452,856,923,140,435,984,577,574,698,574,
803,934,567,774,824,230,985,421,074,605,062,371,141,877,954,182,153,046,474,983,581,941,267,398,767,559,
165,543,946,077,062,914,571,196,477,686,542,167,660,429,831,652,624,386,837,205,668,069,376

And the estimated number of atoms in the observable universe is a mere 10^80, which is a comparatively tiny...

100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

I think that post sucked and does not deserve any merit. Prove me wrong.

[demanze]

I think that post sucked and does not deserve any merit. Prove me wrong.

At least you have been warned.    

1. Never reuse addresses. As I explained in details above, nobody will dare to steal anything from an address with zero outputs. As it would create an obvious anomaly. So you are safe as long as you follow this advice and no one wants to reveal anything.
2. When the supervillains decide to move out of shadow, be the first one to sell all of your coins or accept the losses.

It doesn't cost anything to understand the warnings. I'm not doing any blackmailing. I'm not some evil AI trying to pull off Roko's basilisk. Unlike the real villains.  

[Murpheus]

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.

In mathematics it is called Modula operations...

its like an "equal to" sign... but with 3 strokes instead

like 4=2 answer will be 0
or 7=3 answer will be 1


I think thats it...
but like you...
its been long I touched my mathematics textbook

[Cnut237]

For reference, 2^1000 is...

10,715,086,071,862,673,209,484,250,490,600,018,105,614,048,117,055,336,074,437,503,883,703,510,511,249,
361,224,931,983,788,156,958,581,275,946,729,175,531,468,251,871,452,856,923,140,435,984,577,574,698,574,
803,934,567,774,824,230,985,421,074,605,062,371,141,877,954,182,153,046,474,983,581,941,267,398,767,559,
165,543,946,077,062,914,571,196,477,686,542,167,660,429,831,652,624,386,837,205,668,069,376

And the estimated number of atoms in the observable universe is a mere 10^80, which is a comparatively tiny...

100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

I think that post sucked and does not deserve any merit. Prove me wrong.

I don't need to prove you wrong, I agree with you. It was a simple demonstration to the OP that N^1000 is a big number even with N=2, and a counter-argument to his statement that "I don't think large polynomials are relevant."

Nothing merit-worthy really, and I wasn't seeking any. Bit confused by your reaction. Also a bit harsh to say it sucked; I thought it was a fair contribution to the discussion.

And I believe the onus of proof in this thread is on the OP. If none is forthcoming, then: OP < P vs NP.

[demanze]

I don't need to prove you wrong, I agree with you. It was a simple demonstration to the OP that N^1000 is a big number even with N=2, and a counter-argument to his statement that "I don't think large polynomials are relevant."

Nothing merit-worthy really, and I wasn't seeking any. Bit confused by your reaction. Also a bit harsh to say it sucked; I thought it was a fair contribution to the discussion.

And I believe the onus of proof in this thread is on the OP. If none is forthcoming, then: OP < P vs NP.

For a sec I thought he was saying my post sucks.

I think you misunderstood what I was saying with N^1000. I'm talking about the complexity of the algorithm that solves a NP-complete problem. I was saying the degree of the polynomial has little chance of being exactly 1000 and then stopping there - if you find a problem with complexity N^1000, then it is likely you can find one at 1001, 1002 and so on ... Until N^N which is definitely worse than simple 2^N exponentiality.

So there's no point discussing large polynomials. The algorithm is N^3, N^4, N^5 or does not exist. That's how evil the problem is.

If you want deeper technical arguments about this, I wrote an answer on stackexchange a while ago: https://cs.stackexchange.com/questions/47300/what-is-the-evidence-that-p-could-equal-np/131282#131282

[Cnut237]

For a sec I thought he was saying my post sucks.

No, it was mine. I can kind of understand it as a wall of numbers is a bit irritating. I was just trying to demonstrate how large N^1000 can be, and that possible doesn't mean easy.

I think you misunderstood what I was saying with N^1000. I'm talking about the complexity of the algorithm that solves a NP-complete problem. I was saying the degree of the polynomial has little chance of being exactly 1000 and then stopping there - if you find a problem with complexity N^1000, then it is likely you can find one at 1001, 1002 and so on ... Until N^N which is definitely worse than simple 2^N exponentiality.

So there's no point discussing large polynomials. The algorithm is N^3, N^4, N^5 or does not exist. That's how evil the problem is.

If you want deeper technical arguments about this, I wrote an answer on stackexchange a while ago: https://cs.stackexchange.com/questions/47300/what-is-the-evidence-that-p-could-equal-np/131282#131282

But you still need to prove your assertion that P=NP. It's not up to other people to disprove an "I think". You can argue the case either way, certainly, I'm just not convinced that "I believe x. Prove me wrong" is a solid basis to start from.

[demanze]

But you still need to prove your assertion that P=NP.

But if I do then everything you love will be worthless in one minute. You do love bitcoin, don't you? So you will hate me if I destroy it with a bitcointalk post.

Besides, Bitcoin is maybe the only weapon against elites and governments. Why shouldn't it live up to its peak? I would be a traitor on the level of Ephialtes of Trachis, if I revealed anything.

[pixie85]

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

Mark Karpeles is an asperger syndrome guy with around 200 IQ. I don't think he is dumb enough to let any employee or code get near his private keys at all. I think he was probably completely stunned when he realised the coins had moved without his consent, he didn't even know what to explain to Japanese police at first.

Here's the problem, you don't think he's dumb enough to let it happen.

His mistake was that the exchange software was built for magic cards. It wasn't meant to operate a multi million dollar exchange and lacked real security.

He did not allow anyone near his private keys but allowed people to modify the exchange code and add fake fiat balances that were never deposited, use it to buy bitcoin and withdraw.

His private keys were not hacked in any way.

[Twentyonepaylots]

I don't think your theory can be proven correctly or incorrectly at this point considering the lack of evidence jn both sides of the spectrum. However, what I believe to be the biggest threat in the security of people's bitcoins is the existence of a quantum computer that can run under certain algorithms faster than a normal computer would ever be. Since it can crunch an unbelievably long amount of research into 10-15 minutes of running scripts and codes, anyone who possesses it can easily hack into and steal bitcoins from other people.