Zero Knowledge Proofs

Its not a proof to say for any number you give me i can answer correctly each time. This a conjecture which is only true if you ASSUME what you're trying to prove.
For any amount of correct guesses you could have just got lucky.
It would be a proof if you answer correctly infinitely many times which is impossible.

If you know and say they're the same color,you should peek and then say the opposite.

Thank you! There is com from me somewhere from one year ago saying it would be hard for me to find another angle than your great video above to cover this :) I've finally created my version on my channel, in French but you might appreciate the first protocol: a real-life ZKP for Sudoku. As the video progresses, the protocol is modified toward a dematerialized version, which might make the French more of a problem but the first protocol I guess the visuals are enough :)

What happens if the secret is that both of the candy clouds are the same color?

I just rewatched this. I think this is the most intereesting thing I have ever seen.

So the fact that people are swindled by FTX and Luna means that cryptocurrency is proven to be a Zero knowledge scam?! 😂😂😂

Zero knowledge Proof?
Fermat joined the chat

any chance of getting a link to the original paper ?

I don’t see it in the comments but someone probably mentioned what if you hide both sweets in the same cup. They can be the same color… the honesty part is what seems a bit flawed. If you trust you are honest you don’t need proof you simply believe. I’m not saying zero proof is not a thing but that the example is flawed.

I thought about a different one. Assume there are four colors in the jar. Then add the remaining two colors. Now all the balls in the pool are different. I just need to prove that I initially had two balls... I guess this is a non-interactive one.

This proof is not complete. Now you could use different technology like magnets, sounds, cameras attached to your eye in order to lie about knowing which ball is which.

whats the relationship between zero knowledge proofs and random walks?

Thought Experiment.... A man claims inside a box he has a precious object, but only he has seen it but tells you about it.... you see the box, but never what's inside.... you assume that the man is telling the truth, but in reality nothing is inside the box.... you report that there is a precious object in the box, although it doesn't really exist.... the moral? This theorem only works if subject A is actually telling the truth that subject B is depending upon; therefore this theory is flawed from the onset because it depends on an honest person giving facts.

Another thought experiment... Imagine a man says that he is 35 years old, giving an exact birthdate, but by all appearances seems to be older or younger than what he states. You believe him to be younger or older, assuming he's lying, but is indeed 35 years old. Moral? An assertion can be true even if it goes against reason or logic or appearance.

Conclusion? This is nothing more than Godel's Incompleteness theorem with a little gambler's fallacy (inverse or otherwise) thrown in for good measure.

Jesus Christ Almighty God bless you all

Blockchain of privatecoins like e.g. Monero are still public, just encrypted. One issue of privatechains is the added complexity - also very few programmers have deep understanding of ring signatures and ZKPs, not to mention support in major cryptographic libraries and existence of any ZKP industry standards (is there anything like SHA-2 for ZKP ??).
The blockchain will likely be used for settlement-only as secure transactions will get way more expensive, then privacy is given by the fact thousands of real-time transactions will be combined in a single blockchain transaction. Of course if people won't fight for their privacy and freedom then no algorithm will help them.

The fact this seems so obvious after your explanation is testament to your powerful abilities as a communicator.

Where's the follow-up video?

I don't find cup method that impressive. She just swapped out one difference for another one. That's like saying "I can have a conversation with someone and we don't speak the same language". Sounds impressive until you realize I just hired a translator. This video was pretentious and bombastic.

Except that does not prove they are different colors, merely different, and in actuality not even that. They could be different shapes, or sizes, or textures, etc. For that matter, you could have cheated in any number of ways and still be able to tell whether the cups were switched, or not. Some simple ways:
1. You only placed 1 of the objects under 1 cup and palmed the other.
2. The objects are the same, but the cups have some simple, subtle marking
3. You can actually see when the cups are being switched
4. You have some unknown accomplice informing you of the switch
5. There is some other means of identifying which object is which
A hidden compass and hidden magnet would work for both 4 and 5, for example

Not only cryptocurrency scams are responsible for people losing giant sums of money. That, or one may say cryptocurrency itself is in a sense a scam. It barely escapes being a Ponzi scheme. It is at best a form of gambling. People do not typically purchase cryptocurrency simply because it is a means of trading for other items. Instead, it is putatively an investment, but unlike more traditional investments, it is not backed by any object with any intrinsic value. That is why it is deemed "currency". Unlike true currency, however, its purchasing ability is not backed by anything other than how much an unregulated public is willing to pay for it.

It is in fact rather like the tulip bulbs of the 1600s in Holland. Tulipmania, as it is sometimes called, began with the trading of real merchandise: tulip bulbs. Dutch people could purchase some number of tulip bubs, plant them, and then sell tulips from the mature plants for considerably more than the investment cost of the bulbs. This represented a very real investment strategy. Before too long, however, the prices of bulbs began to rise due to an artificial demand for the bulbs based not as much upon how many flowers a mature plant could produce, but rather upon the fact bulb prices were rising, and people could buy at one price and sell the same commodity later at a higher price. Such a situation is not indefinitely sustainable. It can only be maintained organically as long as the price of the bulbs was less than the total amount of profit obtained by raising the plants and harvesting the flowers. Above that point, the bulbs had no real additional value, and no one purchasing such a bulb should ever have expected to recover the entire cost of the bulb. Yet, because people saw the prices continue to rise due to poorly advised speculation, people continued to "invest" wildly. Some actually believed the situation could continue indefinitely. (The same sort of people who often invest in Ponzi schemes even today.) The rest were merely unscrupulous individuals who hoped to be able to wait long enough to sell before the market had reached its limit yet not so long the prices dropped. Prices skyrocketed to the point where some bulbs sold for over $1 million in today's money, yet the actual proceeds from successfully planting and growing a bulb was only a few hundred dollars. One day, a single high cost bulb failed to sell on the open market, and almost immediately the prices plummeted, and people began going bankrupt left and right. Now before anyone complains, there was a lot more involved than only speculative buying, but at the core the entire market was supported by virtually nothing of any intrinsic value. Neither is crypto.

Bitcoin prices peaked at $64,400 on November 12, 2021. Subsequently, prices dropped to a low of 15,452 on November 25, 2022, or just under a year later. Anyone who purchased any bitcoins between January 1, 2021 and June 3, 2022 and then subsequently sold them has lost a sizeable amount of their money, and no one since June 3 has so far made any sizeable amount by selling. These variations were not as a result of any changes in the bitcoin "industry". They were not as a result of any political maneuvering between two countries. There are no investment vehicles driving the prices. They were expressly due to people's willingness to pay the current prices of bitcoins. It certainly can happen a genuine investment vehicle can go bankrupt due to mismanagement or other imponderable issues, but ordinarily, barring bankruptcy, any investment in any hard business will still maintain some value after stock devaluation. Crypto has nothing to support it.

what's the music at the start of the video? it sounds like music from the pokemon tcg game

If the candy clouds are the same colour you can't see if the cups have been swapped or not...

You could also introduce a 3rd cup with a random candy color known or unknown to the person switching the cups around and asking if you(jade) if there's 1,2 or 3 duplicates of any color

Zero sum proofs are algorithms based on trust (faith). Your contention is a zero sum proof turns a NP into a P. It doesn't (and this was/is the giant problem with "virtual" money)

Using your example of figuring out 2 candies under a cup. You could have put 2 same color candies under the cups and marked one with your thumb.

If you use pieces of different color steel, that can't be marked, you could do it with "positioning" under the cup.

The fact there is NO "proof positive" makes it so this method can never arrive at P. Even if the proof narrows it down to .000000000000000000000000000000000000001, the "1" on the end makes it an open question. The odds might be stacked enormously in your favor, but that doesn't eliminate doubt. 1 of these days you could "hit the lottery". The more you play, the better the odds. But unless you purchase ALL the tickets, it will REMAIN a NP endeavor.

Even if there are 1,000,000 tickets, and you purchase 999,999 of them, their is still a "1 in a million chance" (just like with every one of the other tickets) you're wrong (not likely, but broke none the less)

Zero knowledge proofs are NOT enclosed "zero probability" chances of being wrong.

Another example of this is an algorithm used to track down criminals using a bunch of other "indicators". Things like education, social standing, credit score. I don't really know what went into the algorithm, I do know they got it wrong and arrested an innocent man.

The idea that a person's conviction must be unanimous (beyond the shadow of doubt) is exactly the same thing. It might be the best we can do in pursuit of justice, but it has failed miserably, many, many, times.

There is no "magic", turning an open question into a closed conclusion. Either you account for ALL possibilities or the question remains open.

(For some reason your example/demostration reminds me of Harry Houdini attending sooth sayers and "mystics" claiming to communicate with the dead, to see how they're pulling it off. Instead, you were there with the goal of "proving" the mystic (zero knowledge proof) correct.

The odds are with you, but the laws of logic are not. It remains an NP problem.

(Good luck on the lottery:)

Is it really zero knowledge? What if the proofer is lying and there is only one candy, and she puts that single candy under one of the cup, if the verifier can't have additional knowledge or assumption that there must be 2 candies, the proofer can still correctly tell whether the cup is switched, which ultimately fail to prove the statement "she has two candies of different colors"

This reminds me of the Altar at Mount Ebal. Nobody wants it to be proven true, but it's going to have to be. Like, they're just going to have to accept the fact, that it's true. Although, in this it's over a bunch of improprieties. Not the actual scholarship, but that some red tape wasn't heeded. Mainly, because the archeologist thought his discovery would get stolen. That's a crack? Too? He has a literal proof that the entire Bible is corroborated, but of course Academics are fighting it tooth and nail, because a few decorums were breached. It's bolix. That's the corruption of Academia in a nutshell. This should be Groundbreaking stuff, and on the discovery channel. It shouldn't be buried by red tape.

Nope! Not convinced.. because those two objects could be the same color but their shape is different :D

A good video as usual. Just a small typo you might want to correct: Reimann => Riemann

Awesome 😎

📺💬 They want same as this.
🥺💬 I gives them many for their expectations sample + Symbols ( add symbols ) and more but they need to think about it please continue the lessons.
📺💬 Some of them may read plus symbols 🥺💬 Yes, assemble can be read it too see the picture topics and explanation I clearly explain but now reading about the mathematics you teaching.

what if you picked 2 of the same color?

I like this video

Reminds me, "We show that the entire history of the earth would have to berepeated over and over again in the order of 64^80,000 times in order for them to be a substantiac chance that complex living entititeswould evolve even once" -Richard Thompson, from the book"Demonstration by Information Theory That Life cannot Arise from Matter"

Thanks. Please make the video about coloring in graphs and Riemann hyppothesis.

Nine

That doesn't work with everything tho. for example if there is a clone of one person which behaves exactly like him but isn't conscious. Is it then possible for that person to prove that he is conscious and real person and other one is clone at not conscious.

The irony is this type of scheme is used to keep the nuclear launch codes secret 🤔

In the example given, I wonder how do I prove to someone that the colours I picked are the same color?

We always want more of Up and ⚛!

Isn't it game theory?

Once you tell people you have a secret it's no longer a secret,
for a secret is only a secret if it's known by exactly one person or entity.
Tell people that you know a secret is already a partial reveal,
and thus allows for finding out.
To truly keep it a secret you can't tell anyone, nor reveal that you know the secret.

I found a 5 point encryption on the Trojan curve as a rectangle formed by 4 tangent lines to the knob of the Trojan curve symmetrically placed on the curve where the tangents are vertices of the rectangle formed. This has then 3 intercepts to the curve for any line of the rectangle. Lines tangent to the curve intercept in double points and the same goes for the 2 diagonal lines. Any 2 of the 3 intercepts are said to sum to the 3rd, which can be made algebraic, with the last condition that the 3rd point sum is flipped over the line of symmetry of the Trojan curve. All this can be imagined as a side view of a curved door handle. The 5th point of this finite Galois field is the point at infinity where the 2 points to be summed are across the line of symmetry of the Trojan curve so intersecting the Trojan curve asymptotes. Such 2 asymptotes are considered 1 point as in projective geometry and behave as the 0 in this field of 5 points. Adding either asymptote to any vertex of the rectangle then is the intercept across the axis of symmetry, but flipped back to the vertex again, showing the infinite point is the geometric 0 and this is the algebraic result as well, once such sum action is encoded.
I have only been able to find such pleasing field conditions to illustrate Trojan curve encryption for the 5 point field. Since only addition is defined, multiplication is by repeated addition. This verifies field closure for any point added to itself 5 times. Then division isn't a tractable operation and is why the key cant be determined from the number of times a point was added to itself and the resulting point so obtained, to find the point beginning the sum, which is the encryption key.
I believe this is a complete description of Trojan curve encryption conceptually in geometric format. The sum formula is presented in standard treatments to complete this algebraically.
I'm interested in knowing if such a simple tangent diagram for this geometric result exists in any other order Galois finite field.

actually they could have the same color but a slightly different shape.

Cool video and clear explanation. Thanks.

It seems to me that the process also depends on the entity that is "swapping" items isn't being eavesdropped upon i.e. the swapping process is not being looked in on by the entity with the secret. If there were a backdoor into that process (or at least to have the information to determine if something was swapped or not swapped) then the secret holder need only reply with what it knows that process resulted in not do anything with their own cups and items.

In your demonstration it requires you to cover your eyes so you can't see whether the person moving the cups actually swapped their positions or didn't. If you had a friend who was watching while your eyes were closed, and could tip you off as to the result of that process, then you wouldn't need to evaluate the content of your own cups but simply repeat back to the cup swapper, what they did. Given the original secret is never known there would be no way for the tester to know there was a problem unless they discovered your friend.

I love Brady over on Numberphile and enjoyed his video on zero-knowledge proofs, but this video actually demonstrated a practical, easily understood actual example of a zero knowledge proof and now I understand them much better! Cheers!

You pick a third Candy Cloud from the jar without showing its colour, but that is different from the other two. If you were speaking the truth, then you can prove it by showing all three Candy Clouds have a different colour. This does not reveal what colour you picked, because each of the three colours could have been picked at the start. If you were lying then at least two of the three will be the same colour and this will also reveal which colour you picked at the start.

You shouldn't have used candy clouds, you should have used M&M or something like that, which is more likely to have no other identifiable difference than color. As it were, your soundness is compromised....
Won't any hashed password storage be an application zero knowledge proof? The prover knows the password, the verifier provides the hashing algorithm and have the hashed result. The verifier doesn't know what the password actually is (zero knowledge).

When asked "What is greater than God, More evil than the devil, The poor have it, The rich don't need it, And if you eat it, you'll die?",
I didn't want to give it away to the others. So I said: "I think I know the answer. I say nothing".
It took them a few more minuts to find the answer. I guess I failed. What would be your zero knowledge proof?