4. ZK Math - Modular Arithmetic

In this video we cover one of the most important topics in this entire series, modular arithmetic. Before you can understand how any zero knowledge proof system actually computes, you need to understand how numbers behave inside a modulus, the "clock math" that every ZK circuit is built on. In this video you will learn: ✅ What modular arithmetic is, using a simple clock analogy ✅ How the mod operation works and how to compute it by hand ✅ Congruence notation (≡) and what it really means ✅ How addition, subtraction, and multiplication behave inside a modular system ✅ Why every operation inside a modular system stays inside the same closed range ✅ Why every ZK circuit computes inside mod p, using the same massive prime from the last video By the end of this video you will understand the engine that every ZK proof system runs on, and why every signal in a Circom circuit lives inside this wrapped-around number system. 🔢 This series covers the math foundations you need for: — Circom circuit development — R1CS and QAP — Groth16 and trusted setups — PLONK, STARKs, and KZG commitments — Elliptic curves and bilinear pairings — Halo2, arkworks, and more 📌 Full series playlist:    / @zk.cryptographer   📌 Previous video — Divisibility, Factors & Primes:    • 3. ZK Math - Divisibility, Factors & Primes   📌 Next video — Modular Inverses & Fermat's Little Theorem: Coming 🕐 Timestamps: 00:00 — Introduction 00:30 — The clock analogy 01:45 — The mod operation 03:00 — More mod examples 04:00 — Congruence notation 05:00 — Addition inside mod 05:40 — Subtraction inside mod 06:20 — Multiplication inside mod 07:00 — Why ZK uses modular arithmetic 07:30 — Summary Tags: zero knowledge proofs, ZK math, modular arithmetic, mod operation, congruence, cryptography math, circom tutorial, groth16, zk circuits, math for developers, blockchain cryptography, finite fields, BN254, number theory, mathematics foundations, ZK beginners, learn ZK, Circom, snarkjs, arithmetic circuits, clock arithmetic Hashtags: #ZeroKnowledgeProofs #ZKMath #ModularArithmetic #Cryptography #Circom #BlockchainDevelopment #MathForDevelopers #ZKProofs #LearnCryptography #NumberTheory