ZK

This repository includes all the code implementations for zk-snark verifying systems from simple arithmetics behind it to the circuit design and working.

prove(inputs, algorithm_description) -> (encrypted_inputs, proof, public_output)

verify(encrypted_inputs, proof, algorithm_description) == public_output

Languages Used :

• Sage (for solving equations over a field and plotting)
• Python (for visualising the proofs of theorems and polynomial operations)
• Circom (to design zk circuits)
• Markdown (for readme)

Modules :

• ZK Arithmetics
  • Zk-Arithmetics-1.ipynb
    • Basic Operations
    • Eucledean Division
    • Extended Eucledean Division (G.C.D.)
    • Number Representation
  • Zk-Arithmetics-2.ipynb
    • Modular Arithmetics
    • Fermat's little theorem
    • Solving Equations (using compatibility theorems)
    • Chinese Remainder Theorem
    • Remainder Class Representation
    • Modular Arithmetic & Operations
  • Zk-Arithmetics-3.ipynb
    • Polynomial Arithmetic
    • Operation on polynomial equations
    • Eucledean Division with polynomials
    • Irreducable Polinomial (prime factoring in polynomials)
    • Lagrange Interpolation
• Zk Algebra
  • Zk-Algebra-1.ipynb
    • Hashing Functions
    • Hashing to group
    • SHA256
  • Set Theory
    • Binary Operations in set theory
• ECC (Eliptical Curve Cryptography)
  • ECC_1.ipynb
    • ECC under finite field
  • ECC_2.ipynb
    • ECC under cyclic group
  • ECC_3.ipynb
    • Generator Points
    • ECC addition and modular addition homomorphism
    • Accosiativity
  • ECC_4.ipynb
    • ZK Proof Example using ECC
    • ECDSA malleability attack
• Bilinear Pairings
  • BP_1.ipynb
    • Bilinear Pairing Concepts
  • precompile_test/
    • 0x08 Precompile implementation
    • Simple test for working
• R1CS
  • main.ipynb
    • Transformation of Different Equations
    • Addition with constants
    • Multiplication with constants
  • circuit/
    • Multiply2()
    • witness generation
  • circuit2/
    • Multiply4()
• Q.A.P
  • main.ipynb
    • Example showing addition of two vectors is homomorphic to addition of two polynomials
    • Example showing hadamard product of two vectors is homomorphic to multiplication of two polynomials
    • Ex : Multiplying a vector by a scalar is homomorphic to multiplying the polynomial by the same scalar

Setup :

# For running the sage compiler
sage -n jupyter

Sources :

• Moon Math manual
• zkSecureum puzzles
• RareSkills ZK book
• 0xPARC

Dev Tools :

• Hardhat Circom
• Online Circom Compiler
• CircomLib