Zero Knowledge Concept<\/p>\n
Zero knowledge proofs sounds mystical, academic and a little bit untouchable. At least for me<\/strong> they were in this\u00a0manner.<\/p>\n Most explanations either too easy or too complicated like:<\/p>\n Stay at the \u201cAli Baba cave\u201d level forever (don\u2019t worry if you don\u2019t know \u201cAli Baba cave\u201d, I\u2019ll explain it in this\u00a0post)Or jump straight into elliptic curves and polynomial commitments<\/p>\n Neither builds a real and solid intuition.<\/p>\n Let\u2019s fix it. No heave math at the beginning. No magic. No any vague metaphors.<\/p>\n We\u2019re trying to build a clean and solid mental model\u00a0of:<\/p>\n What a proof actually\u00a0isWhat can \u201cZero Knowledge\u201d guaranteeWhy it\u00a0worksAnd why it\u2019s important with some real life\u00a0usecases<\/p>\n Before any touch to concepts like zkSNARKs<\/strong> or systems like Zcash<\/strong> and TornadoCash<\/strong> (TornadoCash was once the nightmare of Anti Money Laundering agencies).<\/p>\n in practice, a proof must convince someone that something is\u00a0true.<\/p>\n In computer science, a proof is more\u00a0precise:<\/p>\n A protocol between a prover<\/strong> and a verifier<\/strong>\u00a0.The prover claim a statement is\u00a0trueThe verifier checks the\u00a0claim<\/p>\n Example:<\/p>\n Prover: \u201cI know the password\u201d<\/p>\n Verifier: \u201cProve\u00a0it\u201d<\/p>\n In a normal system, you prove that you know the password by revealing it. It works, but with a cost. It leaks the\u00a0secret<\/strong>.<\/p>\n So the main question<\/strong> is that, is there any way to prove we have an information (like password) without revealing it?<\/p>\n Let\u2019s check some everyday\u00a0proofs:<\/p>\n Example 1 (Password)<\/strong><\/p>\n To prove you know the password:<\/p>\n You type\u00a0itThe server checks\u00a0it<\/p>\n Problem: The secret was revealed during the verification.<\/p>\n A normal proof can cause data\u00a0leakage<\/p>\n Example 2 (Bank\u00a0Balance)<\/strong><\/p>\n To prove that you can afford a\u00a0car:<\/p>\n you show your bank\u00a0balance<\/p>\n Problem: You has revealed your financial details.<\/p>\n Example 3 (Age Verification)<\/strong><\/p>\n To prove you\u2019re over\u00a018:<\/p>\n you show you ID\u00a0cardIt reveals your birthdate, address, ID\u00a0numberBut the only thing needed\u00a0was:Is age \u2265\u00a018?<\/p>\n Everything else was unnecessary information leakage.<\/p>\n This is where Zero Knowledge becomes powerful.<\/strong><\/p>\n Can you\u00a0prove:<\/p>\n \u201cI know a secret that satisfying some condition\u201d<\/strong><\/p>\n Without revealing the secret\u00a0itself?<\/p>\n This is Zero Knowledge. <\/strong>as you see the idea of Zero Knowledge is very\u00a0easy.<\/p>\n The Idea behind Zero Knowledge<\/p>\n To understand zero knowledge intuitively, let\u2019s look at famous \u201cAli Baba cave\u201d\u00a0example.<\/p>\n Imagine a circular cave shaped like a\u00a0ring.<\/p>\n There\u2019s an entrance that splits into 2\u00a0paths:<\/p>\n Path A\u00a0(left)Path B(right)<\/p>\n At the end of the cave, the 2 paths reconnect, but with a locked door<\/strong> can be opened with a secret\u00a0number.<\/strong><\/p>\n Only someone who knows the secret number can open the\u00a0door.<\/p>\n The situation<\/p>\n Bob (the prover)\u00a0claims:<\/p>\n \u201cI know the secret and can open the\u00a0door\u201d<\/p>\n Alice (the verifier) does not trust him (she has trust\u00a0issues).<\/p>\n So she wants proof, unless she can not\u00a0sleep.<\/p>\n But Bob refuses to the secret number (or open the door in front of her, since it has the risk of secret\u00a0leakage)<\/p>\n So how can Bob convince\u00a0Alice?<\/p>\n Alice waits outside the\u00a0caveBob enters the cave and randomly chooses one path (A or\u00a0B)Alice then enters and shouts from which path she wants Bob to return\u00a0from\u201cCome out from path A!\u201d\u00a0or\u201cCome out from path\u00a0B!\u201d<\/p>\n now:<\/p>\n If Bob actually knows the secret number, he\u00a0can:Open the door if necessary,<\/em>and exit from whichever path Alice\u00a0requests<\/em>If he does not know the\u00a0secret:He can only exit from the path he origianlly choseHe has a 50% chance of guessing correctly<\/p>\n If Bob is cheating, his chance for fooling Alice at each experiment is\u00a050%.<\/p>\n So if they repeat the experiment 10 times, and in all Bob success the experiment the chance that he cheating would\u00a0be:<\/p>\n (1\/2)\u00b9\u2070 =\u00a01\/1024<\/p>\n that is about 1 in\u00a01000<\/p>\n (After each successful round the chance that Bob is cheating becomes\u00a0half)<\/p>\n After enough rounds, Alice becomes convinced. without seeing the\u00a0secret.<\/p>\n She is convinced because after enough rounds, statistically it\u2019s impossible for Bob to succeed without knowing the\u00a0secret.<\/p>\n After each round the false statement probability becomes\u00a0half<\/p>\n It\u2019s very important to know that this protocol is working because Bob does not know which path Alice is going to\u00a0choose.<\/strong><\/p>\n So the randomness that Alice use to choose the path is why it\u2019s working. A zero-knowledge proof must satisfy three properties.<\/p>\n 1- Completeness<\/strong><\/p>\n If the statement is true, an honest prover can convince an honest verifier.<\/p>\n Example: 2- Soundness<\/strong><\/p>\n If the statement is false, a cheating prover cannot convince the verifier (except with tiny probability that is not practical in real\u00a0world).<\/p>\n Example: 3- Zero Knowledge<\/strong><\/p>\n The verifier learns nothing beyond the fact that the statement is\u00a0true.<\/p>\n Example: Yes \u2192\u00a0allowedNo \u2192\u00a0denied<\/p>\n They do NOT\u00a0learn:<\/p>\n Your birthdateYour ID\u00a0numberYour address<\/p>\n Only the truth of the statement.<\/p>\n Instead of\u00a0proving:<\/p>\n \u201cThe password is 78%68Uifokman#\u201d<\/p>\n You prove:<\/p>\n \u201cI know a value such that hash(value) = stored_hash\u201d<\/p>\n This will change the structure of the statements. You\u2019re not proving the\u00a0data.<\/p>\n you\u2019re proving:<\/p>\n There\u2019s a secret input that satisfies a known condition (without revealing the\u00a0secret)<\/p>\n The above is the shape of almost all zero knowledge systems.<\/p>\n Proving you know a secret password without revealing it<\/p>\n Imagine you\u2019re at a private\u00a0office.<\/p>\n There\u2019s a secure WiFi\u00a0network.<\/p>\n You tell the\u00a0admin:<\/p>\n \u201cI know the WiFi password.\u201d<\/em><\/p>\n The admin doesn\u2019t want you\u00a0to:<\/p>\n Say it out\u00a0loudWrite it\u00a0downOr leak it in any\u00a0way<\/p>\n But they want proof that you actually know\u00a0it.<\/p>\n So how could you prove\u00a0it?<\/p>\n an interactive way to show you know the wifi password without revealing the\u00a0password<\/p>\n Here\u2019s a clever\u00a0method:<\/p>\n The admin generates a random number (a challenge)You take the WiFi password (secret) and combine it with that random\u00a0numberYou compute a cryptographic hash of the combinationYou send the result\u00a0back<\/p>\n The admin knows the correct password.<\/p>\n So they:<\/p>\n Combine the real password with the same random\u00a0number.Compute the same\u00a0hash.Compare your\u00a0result.<\/p>\n If they match, you must know the password.<\/p>\n But you never revealed\u00a0it.<\/p>\n In early zero-knowledge systems, proofs were interactive.<\/p>\n Structure:<\/p>\n Prover commitsVerifier sends random challengeProver respondsRepeat<\/p>\n Each round reduces cheating probability.<\/p>\n If a cheater has a 50% chance of faking one\u00a0round:<\/p>\n After 20\u00a0rounds:<\/p>\n (0.5)\u00b2\u2070 \u2248\u00a00.000001<\/p>\n Cheating becomes nearly impossible. Security comes from probability, not exposure.<\/p>\n Blockchains can\u2019t run interactive conversations.<\/p>\n They need:<\/p>\n A single\u00a0proofThat anyone can verify\u00a0laterWithout talking to the\u00a0prover<\/p>\n Modern systems convert interaction into a single cryptographic object.<\/p>\n So instead\u00a0of:<\/p>\n Prover \u2194 Verifier (many\u00a0rounds)<\/p>\n We get:<\/p>\n Prover \u2192 Proof \u2192\u00a0Verifier<\/p>\n This is what zkSNARKs\u00a0achieve.<\/p>\n But conceptually?<\/p>\n It\u2019s still:<\/p>\n Convince me you know a valid solution.<\/em><\/p>\n Let\u2019s simplify how privacy coins like Zcash use this\u00a0idea.<\/p>\n Bitcoin is transparent, but Zcash is fully anonymous<\/p>\n Instead of revealing:<\/p>\n SenderReceiverAmount<\/p>\n You prove:<\/p>\n The sender owns the\u00a0funds.The input notes exist (input note are UTXOs actaully).The total input equals total\u00a0output.No double spending\u00a0occurs.<\/p>\n All without revealing amounts or addresses.<\/p>\n The blockchain verifies correctness.<\/p>\n But sees nothing sensitive.<\/p>\n Many think ZK = privacy\u00a0coin.<\/p>\n That\u2019s narrow.<\/p>\n You can\u00a0prove:<\/p>\n You passed KYC without revealing documentsYou voted once without revealing your\u00a0voteA smart contract executed correctlyA machine learning model was evaluated correctlySecure gambling without any trust to a third\u00a0party<\/p>\n Zero knowledge separates:<\/p>\n Truth from\u00a0data.<\/p>\n That\u2019s huge.<\/p>\n Traditionally:<\/p>\n To prove something \u2192 reveal information.<\/p>\n Zero knowledge breaks that coupling.<\/p>\n You get:<\/p>\n Verification without transparencyIntegrity without disclosureTruth without\u00a0exposure<\/p>\n This is why zero knowledge is becoming infrastructure.<\/p>\n Not a\u00a0feature.<\/p>\n Infrastructure.<\/p>\n A zero-knowledge proof\u00a0is:<\/p>\n A structured argumentThat proves knowledge of a\u00a0secretSatisfying specific constraintsWithout revealing the\u00a0secretWith overwhelming confidence<\/p>\n Under the hood, modern systems\u00a0convert:<\/p>\n Computation \u2192 Mathematical constraints<\/p>\n And prove:<\/p>\n \u201cThere exists an input such that these constraints hold.\u201d<\/em><\/p>\n That\u2019s it.<\/p>\n Not magic.<\/p>\n Not mystical\u00a0math.<\/p>\n Just carefully structured cryptographic reasoning.<\/p>\n So far, we\u00a0avoided:<\/p>\n Arithmetic circuitsR1CSPolynomial commitmentsTrusted setup<\/p>\n Because none of that matters without this foundation.<\/p>\n In the next post, we\u2019ll move from philosophy to mechanism:<\/p>\n How does code become constraints?<\/p>\n How does computation become something provable?<\/p>\n And how does a tiny proof convince an entire\u00a0network?<\/p>\n That\u2019s where zkSNARKs\u00a0begin.<\/p>\n If you\u2019re building in Web3 today, understanding zero knowledge at this level isn\u2019t optional.<\/p>\n It\u2019s the difference between using infrastructure\u2026<\/p>\n And understanding it.<\/p>\n Zero Knowledge Proofs Explained: Build a Strong Mental Model Before the Math<\/a> was originally published in Coinmonks<\/a> on Medium, where people are continuing the conversation by highlighting and responding to this story.<\/p>","protected":false},"excerpt":{"rendered":" Zero Knowledge Concept Zero knowledge proofs sounds mystical, academic and a little bit untouchable. At least for me they were in this\u00a0manner. Most explanations either too easy or too complicated like: Stay at the \u201cAli Baba cave\u201d level forever (don\u2019t worry if you don\u2019t know \u201cAli Baba cave\u201d, I\u2019ll explain it in this\u00a0post)Or jump straight […]<\/p>\n","protected":false},"author":0,"featured_media":150980,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-150979","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-interesting"],"_links":{"self":[{"href":"https:\/\/mycryptomania.com\/index.php?rest_route=\/wp\/v2\/posts\/150979"}],"collection":[{"href":"https:\/\/mycryptomania.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mycryptomania.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/mycryptomania.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=150979"}],"version-history":[{"count":0,"href":"https:\/\/mycryptomania.com\/index.php?rest_route=\/wp\/v2\/posts\/150979\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mycryptomania.com\/index.php?rest_route=\/wp\/v2\/media\/150980"}],"wp:attachment":[{"href":"https:\/\/mycryptomania.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=150979"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mycryptomania.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=150979"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mycryptomania.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=150979"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}What is a Proof in Computer\u00a0Science?<\/h3>\n
The Core Problem: Proofs Usually Reveal Information<\/h3>\n
The Big\u00a0Question<\/h3>\n
The Ali Baba Cave: The Classic Zero-Knowledge Story<\/h3>\n
The protocol<\/strong><\/h4>\n
Why Repetition Matters<\/h4>\n
If the randomness Alice using is leaked, Bob can fool her. So randomness is the\u00a0key.<\/strong><\/p>\nThe Three Properties (With Practical Meaning)<\/h3>\n
If you really know the password, verification should\u00a0succeed.<\/p>\n
If you don\u2019t know the password, you shouldn\u2019t be able to fake\u00a0it.<\/p>\n
You prove you\u2019re over 18.
The verifier\u00a0learns:<\/p>\nMental Shift: Proving Knowledge of a\u00a0Solution<\/h3>\n
Example: Proving You Know the WiFi Password Without Revealing It<\/h3>\n
The Challenge-Based Verification<\/h4>\n
Interactive Proofs: Why Repetition Works<\/h3>\n
From Interaction to One\u00a0Proof<\/h3>\n
Example: Private Transactions<\/h3>\n
Zero Knowledge Is Bigger Than\u00a0Privacy<\/h3>\n
The Deep\u00a0Insight<\/h3>\n
The Mental Model You Should\u00a0Keep<\/h3>\n
Where We Go\u00a0Next<\/h3>\n