#ZeroKnowledgeProofs

1 week ago

Zero-Knowledge Proofs Explained: How to Prove Everything Without Revealing Anything

Zero-knowledge proofs are reshaping Web3 by enabling private transactions, secure authentication, and scalable blockchains — all without exposing user data. #zeroknowledgeproofs

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The New Oil

@thenewoil.org

1 month ago

How Zero-Knowledge Proofs Work This is another article in my series on Privacy Enhancing Technologies. Let’s talk about how we can using some clever techniques to assert the truth of a statement without divulging personal data that proves the assertion. ## What problem are we solving? This is the question we need to always ask first. And there are several problems that might be solved by zero-knowledge proofs. But for the purposes of this article, we’re going to focus on this: maximizing privacy. We want to prove a fact about ourselves while revealing as little personal information as possible. The use case that sticks out most today is age verification. Many sites are now required by law to verify that all users are over a given age. Australia has banned social media for anyone under the age of 16. The UK, France, Italy and many US states have required porn sites to verify the age of their visitors. Utah has required mobile app stores to verify users’ ages, as well. But we can envision other use cases like verifying a user’s location, nationality, student or employment status, etc. But verifying that someone is over a certain age is a good example, so let’s stick with that. (Note that age-gating has a lot of important issues which I’m not going to address here – the EFF has a lot of articles on this.) The first thing to note is that I did not say that a user must prove their _exact age_. All of these age-gating laws set a _minimum_ age. If written properly, these laws also should not require your identity. We simply need to prove, to some reasonable degree, that we are at least X years old – that’s it. Many of these systems fail, from a privacy perspective, by requiring the user to provide more information than is strictly required. ## Example: Entering a Bar Let’s use a common example: you need to be 21 or older to enter a bar. You could prove this by providing a government-issued ID to a bouncer at the door. However, that bouncer would then see your name, address, date of birth, and more. And if that bouncer uses an internet-connected scanner to check your ID, then you’ve also shared that information with some company you’ve never heard of. (And who knows who _they_ might share it with.) So how could we prove that we’re at least 21 without handing over our ID? You could instead go to a mutually trusted third party to check your ID who could issue you a wristband that indicates you’re 21+ and show _that_ to the bouncer. Or you could have an ID scanner that’s not connected to the internet and stores no data that simply lights up red (rejected) or green (approved). Of course, this requires the trusted third party or device – and this is sometimes how “zero knowledge” systems are implemented. It would be technically feasible for Apple and Google to securely and privately store a government-issued digital ID that would allow you to prove that you are over a given age without revealing any further information. This would be based on the assumption that the holder of the phone is the person identified by the ID it contains. ## What is a Zero-Knowledge Proof? There are logically rigorous definitions of a zero-knowledge (ZK) proof, but I’m going to try to simplify it greatly here. I want to be able to convince someone of the truth of a statement without revealing the facts that prove it. And after convincing them beyond a shadow of a doubt that this thing is true, I also do not want that person to be able to prove it to anyone else. For example, I want to prove to you that I’m over 21, but I don’t want you to be able to prove this to anyone else because no one else needs to know. The easy button “solution” is to use a trusted third party that reviews the private data and only reveals the answer to the posed question. And for some types of problems, you _need_ a third party involved. For example, to determine your age, you at least need some official, mutually-trusted entity to issue a birth certificate with a date of birth. But there are types of ZK proofs that require no third party whatsoever – ways to prove that you know a secret without revealing that secret. For example, proving that you know a password without giving up the password or that your bank balance is over a minimum amount without revealing how much money you have. These proofs can be absolute or probabilistic. Let’s look at a fun, contrived example of each type. ## Where’s Waldo? We’re all familiar with the Where’s Waldo (or Wally) books: you have a large drawing with hundreds of people in it, and you have to find one particular person: Waldo. So let’s say I claim to know where Waldo is and you don’t believe me. Furthermore, I want to prove I know Waldo’s location without revealing the location to you in the process. How might I do this? Let’s assume the image including Waldo is square, two feet on a side. I put the image on a big table and tell you to leave the room. I get a big piece of paper, at least four feet square. I cut a Waldo-sized hole in the dead center of the paper, and then adjust the paper over the image to reveal Waldo’s face. I tell you come back in. You see Waldo’s face in the cutout. I definitely know where Waldo is – I’ve shown him to you. But because the paper is much larger than the image, you can’t see where the image is under the paper – that is, how it’s oriented relative to the cutout. You therefore learn nothing about Waldo’s location in the image. And furthermore, you can’t _prove_ to anyone else that I know where Waldo is. Another version of this involves a deck of cards. I choose a card and tell you that it’s red. You don’t believe me. I then set my card to the side, face down, and take the rest of the deck and reveal 26 black cards. A standard 52-card deck has exactly 26 red and 26 black cards in it. If all the black cards are still in the deck, then I must have pulled a red card. And yet, you don’t know which _specific_ red card I pulled. ## Ali Baba’s Cave Sometimes we can’t prove something is absolutely true, but it’s sufficient to show that something is statistically highly likely to be true – usually to an arbitrary degree of the verifier’s choosing. This example is called Ali Baba’s Cave. This is trickier to envision, so let’s use some images. **Ali Baba’s Cave** source: Wikimedia (click the image) There’s a circular cave with a door at the back of the cave, preventing anyone from going through. That door is locked with a pass code. Peggy (the “prover”) wants to convince Victor (the “verifier”) that she knows this pass code without revealing the code itself. The cave has one entrance, on the opposite side of the locked door. There are two paths to the locked door at the back of this cave: A and B. This is shown in the first image. Peggy tells Victor to wait outside, where he can’t see which path Peggy takes. Peggy randomly chooses path A or B – it doesn’t matter which, but let’s say she chooses B. She calls Victor into the mouth of the cafe where he can see both paths, A and B (but not the door at the back of the cave). Victor tells Peggy to come out using Path A (the second image). And a short while later, Peggy emerges from Path A (third image). Now, Peggy could have gone down Path A, in which case she could appear via this path without first unlocking the door. She had a 50% chance of just getting lucky. However, if Victor is sent back out and we repeat this same experiment over and over, and Peggy reliably comes out using the path that Victor specifies, every single time without fail, then – statistically speaking – it becomes very hard to believe Peggy could be that lucky. The math is simple: you multiply 0.5 (50%) for each time you run the experiment. If she got it right 10 times in a row, there’s only a 1 in 1024 chance she did that based on pure luck. After 40 trials, the odds are over a trillion-to-one. Is it possible? Sure. But is it likely? No. So we conclude that Peggy must indeed know the code. And while Victor has observed this and now believes this, he can’t _prove_ this to anyone who wasn’t also there. #### Need practical security tips? Sign up to receive Carey's favorite security tips + the first chapter of his book, _Firewalls Don't Stop Dragons_. Don't get caught with your drawbridge down! **Get started**

How #ZeroKnowledgeProofs Work

firewallsdontstopdragons.com/how-zero-knowledge-proof...

#ZKP #privacy

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‘Unrealistic but fascinating’ — the feeling people had when hearing his talk. In that very feeling, the future was hiding. #zeroKnowledgeProofs #ZKP #HalFinney

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