Bitcoin's cryptography is based on elliptic curves and the difficulty of the discrete log problem, which is in NP. This would also be broken by quantum cryptography. Bitcoin's other main cryptographic element is hash functions. If P=NP then finding a (second) pre-image of a hash is easy, which means that merkle trees and therefore the blockchain itself are no longer authenticated data structures, and furthermore that proof of work isn't useful as a game theoretical construct anymore, since verifying the proof takes as much work as manufacturing it (though presumably it still proves some work happened).
Everyone seems to think that crypto currency will fall if we can resolve the sha256 algorithm. They seem to forget...the code can be altered to compensate.
I just wish that somebody had asked how would seems like try to research what our brains/mind (just like just another tool) can't know. What our toolmaker tool can't do?
It's much MUCH easier to say what computers _can_ do. They count (and thus handle all the arithmetic) and they can compare two quantities. That's it (!) But they do what they do blindingly fast, with clever (human generated) algorithms and large (mostly dedicated) databases. But that's all they can achieve - at least so far.
Not really. You are talking about some low level. Not the lowest, not the highest. It's like describing ability of human by ability of atoms. What you have to answer is: what can you do with these simple things. You know, very simple cells construct complicated organisms. Very simple operations construct complicated routines. This video was about how complicated these routines can be, not which are they made of.
2:08 RSA-2048 = 25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357 .. Anybody who wishes to factor this relatively SMALL "Dual-Prime Composite Number" can easily do so, of they download the excellent (and safe) "B-Calc" 10,051 digit Calculator by GF Cornwell. ... The first task is to establish a sufficiently accurate "INTEGER ASPECT RATIO". of which there are more suitable candidates than particles exist is any "MULTIVERSE" model of the Cosmos. Thankfully the asymptotic protocol is fully deterministic. The trick is to ignore the huge numbers and treat them with indifference. As with regular fractions, we need to find the common denominators, so that "LIKE MAY COMPARE WITH LIKE"... As these huge numbers are being posted to a "Clip-board" via the calculator, they only need to be labelled. It is more convenient a quicker to use 'aspect-ratio' integers that are 'odd' numbers, for speed and convenience. One even number requires that the product of the challenge 'Aspect Ratio' and the Dual-Prime Composite is multiplied by four. This is because 123456.499998987 is the square root of 123456 x 123457, and 246912.9999979 is the square root of 4 x 123456 x 123457 ... The product of two very similar aspect ratio integer dimension rectangles is going to be a close pseudo-square. This DETERMININISTIC PROTOCOL rejects the aspect ratio with the fewer "NINES" after the decimal point. ..... The Dual Prime Composite first needs to be "FORCED" into a pseudo-square. This is best achieved by obtaining the product of (PQ) x (PQ +1) Two square roots (P x Q) x (a1 x r1) x (P x Q) x (a1 x r1) +1, and challenge aspect ratio "2" (P x Q) x (a2 x r2) x (P x Q) x (a2 x r2) +1, ... by counting the string of nines. The more nines the more accurate the aspect ratio. ... By using common denominators, "Like is Compared To Like" . The CRITICAL TEST is to enlarge the square root o "Compound Dual Prime and Aspect Ratio Product from .9999 to the next integer. The Factors can then be obtained by simple algebra, if subtracting the D.P.C.*A.R. from the square of the enlarged square root, leaves a perfect integer square. What we are looking at visually is four vast pseudo-squares with a small square in the centre, rather like four playing cards placed in rotational symmetry. ... IT WOULD BE TH HEIGHT OF IRRESONSIBILITY TO PUBLISH THE RAW FACTORS. ... It could cause panic on the stock markets. RSA Public Key Encryption was only permitted by the Security Services, because is was very easy to crack.
You forgot to talk about Non-Deterministic Turing Machines. They actually can solve NP Complete, Exp-Space, and Halting problems, and Turing, Goedel, Von Neumann, and Schroedinger all acknowledged that incompleteness and undecideability could be addressed if our logical axioms were themselves incomplete. Indeed they are which is why NTMs have been discovered, developed, and employed (NTM-Corp.com). It turns out that if you discover a number set that indexes chaos, it’s pretty useful and demonstrates a non-deterministic solution to halting.
Non deterministic can't solve Halting problems... NP is contained in EXP-Time and you can't solve the Halting problem with infinite resources of time and space. Also Non deterministic aren't known to solve EXP-Space, but note that EXP-space is contained in EXP-time (as you need to perform at least one action on every bit of space you use) and EXP-time is contained in NP by bruteforcing all possible non deterministic desicions. So you were claiming that NP=EXP-time which is not known...
I felt cheated by him ducking the chaos question. Strange attractors are an interesting phenomenon and predicting the trajectory of a lorenz attractor is kind of in this domain. Can a computer predict when the trajectory will switch to the other lobe.
And this electron problem is NP problem? It is easy to verify, when we know solution? Where is electron is not problem where it is long to compute. It is problem where we can not measure.
![[#2024MAMA] ROSÉ (로제), Bruno Mars - APT. | Mnet 241122 방송](http://i.ytimg.com/vi/dgGqD28J6aQ/mqdefault.jpg)
It's NP-complete to understand why he thought those trousers were a good idea
Found this guy on "Math Life Balance" youtube interview. Seems like a great guy.
I've enjoyed the talk & Q/A. thank you
Bitcoin's cryptography is based on elliptic curves and the difficulty of the discrete log problem, which is in NP. This would also be broken by quantum cryptography. Bitcoin's other main cryptographic element is hash functions. If P=NP then finding a (second) pre-image of a hash is easy, which means that merkle trees and therefore the blockchain itself are no longer authenticated data structures, and furthermore that proof of work isn't useful as a game theoretical construct anymore, since verifying the proof takes as much work as manufacturing it (though presumably it still proves some work happened).
Everyone seems to think that crypto currency will fall if we can resolve the sha256 algorithm.
They seem to forget...the code can be altered to compensate.
"you need the bitcoins to buy drugs on the intern... you know that right?"
"On that point we'll draw things to a close."
That was amazing. No wonder they did not allow any more questions after that:D
I was quite amused. He obviously invested his bitcoins well before the show.
I just wish that somebody had asked how would seems like try to research what our brains/mind (just like just another tool) can't know. What our toolmaker tool can't do?
1:38 what of this 617 digit number factoring contest?
Wiki RSA numbers.
He said that it lapsed.
It's much MUCH easier to say what computers _can_ do. They count (and thus handle all the arithmetic) and they can compare two quantities. That's it (!) But they do what they do blindingly fast, with clever (human generated) algorithms and large (mostly dedicated) databases. But that's all they can achieve - at least so far.
Not really. You are talking about some low level. Not the lowest, not the highest. It's like describing ability of human by ability of atoms. What you have to answer is: what can you do with these simple things. You know, very simple cells construct complicated organisms. Very simple operations construct complicated routines. This video was about how complicated these routines can be, not which are they made of.
@@KrzysiuNet
This video was about how fast those complicated routines can run.
2:08 RSA-2048 = 25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357 .. Anybody who wishes to factor this relatively SMALL "Dual-Prime Composite Number" can easily do so, of they download the excellent (and safe) "B-Calc" 10,051 digit Calculator by GF Cornwell. ... The first task is to establish a sufficiently accurate "INTEGER ASPECT RATIO". of which there are more suitable candidates than particles exist is any "MULTIVERSE" model of the Cosmos. Thankfully the asymptotic protocol is fully deterministic. The trick is to ignore the huge numbers and treat them with indifference. As with regular fractions, we need to find the common denominators, so that "LIKE MAY COMPARE WITH LIKE"... As these huge numbers are being posted to a "Clip-board" via the calculator, they only need to be labelled. It is more convenient a quicker to use 'aspect-ratio' integers that are 'odd' numbers, for speed and convenience. One even number requires that the product of the challenge 'Aspect Ratio' and the Dual-Prime Composite is multiplied by four. This is because 123456.499998987 is the square root of 123456 x 123457, and 246912.9999979 is the square root of 4 x 123456 x 123457 ... The product of two very similar aspect ratio integer dimension rectangles is going to be a close pseudo-square. This DETERMININISTIC PROTOCOL rejects the aspect ratio with the fewer "NINES" after the decimal point. ..... The Dual Prime Composite first needs to be "FORCED" into a pseudo-square. This is best achieved by obtaining the product of (PQ) x (PQ +1) Two square roots (P x Q) x (a1 x r1) x (P x Q) x (a1 x r1) +1, and challenge aspect ratio "2" (P x Q) x (a2 x r2) x (P x Q) x (a2 x r2) +1, ... by counting the string of nines. The more nines the more accurate the aspect ratio. ... By using common denominators, "Like is Compared To Like" . The CRITICAL TEST is to enlarge the square root o "Compound Dual Prime and Aspect Ratio Product from .9999 to the next integer. The Factors can then be obtained by simple algebra, if subtracting the D.P.C.*A.R. from the square of the enlarged square root, leaves a perfect integer square. What we are looking at visually is four vast pseudo-squares with a small square in the centre, rather like four playing cards placed in rotational symmetry. ... IT WOULD BE TH HEIGHT OF IRRESONSIBILITY TO PUBLISH THE RAW FACTORS. ... It could cause panic on the stock markets. RSA Public Key Encryption was only permitted by the Security Services, because is was very easy to crack.
Well...that's why you don't use
RSA....and how exactly are the authority forbidding that?
Good talk!
Sir, NP(beginning) = P(end)
You forgot to talk about Non-Deterministic Turing Machines. They actually can solve NP Complete, Exp-Space, and Halting problems, and Turing, Goedel, Von Neumann, and Schroedinger all acknowledged that incompleteness and undecideability could be addressed if our logical axioms were themselves incomplete. Indeed they are which is why NTMs have been discovered, developed, and employed (NTM-Corp.com). It turns out that if you discover a number set that indexes chaos, it’s pretty useful and demonstrates a non-deterministic solution to halting.
Non deterministic can't solve Halting problems...
NP is contained in EXP-Time and you can't solve the Halting problem with infinite resources of time and space.
Also Non deterministic aren't known to solve EXP-Space, but note that
EXP-space is contained in EXP-time (as you need to perform at least one action on every bit of space you use) and EXP-time is contained in NP by bruteforcing all possible non deterministic desicions. So you were claiming that NP=EXP-time which is not known...
I felt cheated by him ducking the chaos question.
Strange attractors are an interesting phenomenon and predicting the trajectory of a lorenz attractor is kind of in this domain. Can a computer predict when the trajectory will switch to the other lobe.
I wouldn't say he ducked the question. He admitted he did not know much about chaos so he could not answer the question.
P = np äs t goes to infinity. Ñp hard will always remain an approximation. Never a solution.. where is the electron?? And what is its momentum.
if t can go to infinity, that's bigger than any polynomial or super polynomial finite number, by definition.
No. This Is about solving a real problem. a computer cannot solve these problems yet. Want an example?
And this electron problem is NP problem? It is easy to verify, when we know solution? Where is electron is not problem where it is long to compute. It is problem where we can not measure.
I said np hard