The Moon and the Maths

Table of Contents

• Chapter 1 The Sea of Tranquility

  The basics of ZKP maths — sets, integers, modular arithmetic, and the ground rules for zero knowledge proofs.

• Chapter 2 Bay of Rainbows

  Polynomials — where we learn that every secret is just a point on a curve.

• Chapter 3 Ocean of Storms

  Finite Fields — the arithmetic that makes ZKPs possible.

• Chapter 4 Apennine Mountains

  Abstract Algebra — groups, rings, and the structures beneath the maths.

• Chapter 5 The Far Side

  Elliptic Curves — the cryptographic workhorses of modern ZKPs.

• Chapter 6 Sea of Moscow

  R1CS — rank-1 constraint systems and arithmetic circuits.

• Chapter 7 Crater Tycho

  Trusted Setup — the ceremony that powers SNARKs.

• Chapter 8 The North Pole

  Groth16 and True Zero Knowledge — the final destination.