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- The second article about zk-proofs is ready, but I can't post it due to the image uploading problem ๐ญ
https://hey.xyz/posts/0x8218-0x0298
@yoginth.lens
In the meantime, if you haven't already, you can dive into the first part of my zk-proofs series:
https://hey.xyz/posts/0x8218-0x0280-DA-b047fd5f
- ****Learning zk-Proofs: A Beginner's Guide 2/x****
Previous posts:
****0.****ย Introduction: https://hey.xyz/posts/0x8218-0x0279
****1.****ย Learning zk-Proofs: A Beginner's Guide 1/x: https://hey.xyz/posts/0x8218-0x0280-DA-b047fd5f
Hello, there!
In the previous post, we delved into the fundamental tools of zk-proofs: Prime Numbers, Modulo, and Finite Fields. Now, let's explore the core principle of zk-proofs and understand why they stand apart from conventional proofs. In this post, we'll illustrate these concepts with real-life examples.
****What's a Proof?****
Seems like a simple question, right? In fact, you engage in proving things every day because it's vital for human communication. You prove to your mom that you had your school lunch. You prove to your boss that your work is satisfactory. You prove to the government that you've paid your taxes.
But how do you accomplish these proofs? Well, one way is by revealing certain pieces of information you possess.
With your mom, you might describe precisely what you ate, and she'd know you're fine because it matches what she prepared. To your boss, you present the tangible results of your work: a comprehensive report, a functional website, or maybe a repaired car. To the government, you provide your paychecks.
In these scenarios, you take on the role of theย ****Prover****ย (a child, an employee, a taxpayer), and the other party becomes theย ****Verifier****ย (a mother, a supervisor, a government entity).
****What's a zk-proof?****
https://en.wikipedia.org/wiki/Zero-knowledge_proof
This concept may seem a bit more complex, but not much. Essentially, a zero-knowledge proof is a unique kind of proof that discloses no information other than the answer to the question at hand.
As you dive further into zk-proofs, you'll come across several common thought experiments, and I'm about to introduce you to one of them.
****The Tale of Two Balls and the Color-Blind Friend****
Picture this: you have a friend named Victor (the Verifier), but there's a twist - he's color-blind, unable to tell red from green. You possess two balls, one red and one green, which, to Victor, appear identical.
Your mission as the Prover is to prove to Victor (the Verifier) that these balls are indeed different in color. Shouting didn't work; it only got you a punch in the face. Calmly explaining it also didn't cut it, as Victor now doubts you after your earlier shouting episode. So, let's put on our logical hats and think this through.
****1.****ย First, you hand Victor the balls: the red one in his left hand, and the green one in his right hand.
****2.****ย Victor can then shuffle the balls behind his back, as he pleases. Importantly, he must remember which hand holds which ball to distinguish them.
****3.****ย Next, Victor shows you one of the balls. Your task is to correctly identify its color.
****4.****ย You repeat steps 2 and 3 as many times as necessary.
Victor can verify your honesty in this process because he knows which hand holds the ball he's showing. If, for example, he shows you the ball from his left hand and you declare it as green in one instance and red in another, he can conclude that you're not being truthful. After all, the balls can't magically change colors. On the flip side, if your responses consistently match the actual colors, his confidence in your statements about the balls' colors grows with each repetition (or round).
These proofs rely significantly on chance. In the first round, you have a 50% chance of fooling Victor. In the second round, it drops to 25%, then 12%, 6.25%, and so on. This percentage of being misled is called theย ****soundness****ย of the proof.
But here's the key: Victor still doesn't know which ball is which. He merely concludes that the left ball is likely red, and the right ball is probably green. If you were to take the balls back, shuffle them, and present them again, Victor wouldn't be able to distinguish them. In essence, you haven't revealed information about the colors; you've provided a convincing argument that the balls have different colors. This is why we can classify the experiment asย ****zero-knowledge****.
Modern proof systems improve the odds by relying on various mathematical functions that offer only a few correct answers and thousands of incorrect ones.
- Uniswap added 0.15% trading fee on UI, makes totally sense
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- Applications for a16z's Crypto Startup School close this Friday.
If you haven't applied yet, here are 5 reasons to consider doing so.
https://levy.mirror.xyz/D-6HrjlrJJcf9H7WpJJiClFakTNs-lqchsm21Lex0go
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Through music, there is no race, culture, background, or any other thing to split us
Music makes us one๐น
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Create the art that expresses who you are. Create the art that mirrors your values and beliefs. Create art that celebrates you for who you are
F)ck external pressures such as social media. They mean nothing
It is just you and your art
And the right people will come, but funny enough, they will only come when you create for the sake of art more than for anything else๐น
- Create the art that you love. Create the things that ignite your soul
Create the art that expresses who you are. Create the art that mirrors your values and beliefs. Create art that celebrates you for who you are
F)ck external pressures such as social media. They mean nothing
It is just you and your art
And the right people will come, but funny enough, they will only come when you create for the sake of art more than for anything else๐น
- Create the art that you love. Create the things that ignite your soul
Create the art that expresses who you are. Create the art that mirrors your values and beliefs. Create art that celebrates you for who you are
F)ck external pressures such as social media. They mean nothing
It is just you and your art
And the right people will come, but funny enough, they will only come when you create for the sake of art more than for anything else๐น
- Create the art that you love. Create the things that ignite your soul
Create the art that expresses who you are. Create the art that mirrors your values and beliefs. Create art that celebrates you for who you are
F)ck external pressures such as social media. They mean nothing
It is just you and your art
And the right people will come, but funny enough, they will only come when you create for the sake of art more than for anything else๐น
- Create the art that you love. Create the things that ignite your soul
Create the art that expresses who you are. Create the art that mirrors your values and beliefs. Create art that celebrates you for who you are
F)ck external pressures such as social media. They mean nothing
It is just you and your art
And the right people will come, but funny enough, they will only come when you create for the sake of art more than for anything else๐น
- Create the art that you love. Create the things that ignite your soul
Create the art that expresses who you are. Create the art that mirrors your values and beliefs. Create art that celebrates you for who you are
F)ck external pressures such as social media. They mean nothing
It is just you and your art
And the right people will come, but funny enough, they will only come when you create for the sake of art more than for anything else๐น
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These voices and stories are what keep the stages alive๐น
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What's going on @stani ser?
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