1. 1. Community Guidelines
  2. 2. Zero Knowledge Proofs
    1. 2.1. Curated Resources
    2. 2.2. Video Lecture Series
    3. 2.3. Articles
      1. 2.3.1. ZK Introductory
      2. 2.3.2. Ingonyama Blogs
      3. 2.3.3. ZKSNARKS
      4. 2.3.4. STARKS
      5. 2.3.5. Applications
      6. 2.3.6. Vulnerabilities
    4. 2.4. Hands-On ZK
    5. 2.5. Protocols
    6. 2.6. Mathematics
      1. 2.6.1. Finite fields
      2. 2.6.2. Cryptographic primitives
        1. 2.6.2.1. Elliptic curves
        2. 2.6.2.2. Hash functions
        3. 2.6.2.3. Verifiable Delay functions
        4. 2.6.2.4. Arithmetization
        5. 2.6.2.5. Commitment Schemes
        6. 2.6.2.6. Secure Multi Party Computation
        7. 2.6.2.7. Proving Methods
      3. 2.6.3. Computational Primitives
        1. 2.6.3.1. Hardware acceleration
        2. 2.6.3.2. Discrete Fourier Transforms
        3. 2.6.3.3. Multi Scalar Multiplications
  3. 3. Homomorphic Encryption

Ingopedia

Finite fields

  • Number theory explained from first principles
  • An introduction to the theory of finite fields
  • MIT lectures -FInite Field arithmetic
  • Finite field arithmetic Doche Lange
  • Aztec emulated field and group operations
  • Extension fields: Entropy

Modular arithmetic

  • A Fast Large-Integer Extended GCD Algorithm and Hardware Design for Verifiable Delay Functions and Modular Inversion
  • Optimized Binary GCD for Modular Inversion
  • Library of Algorithms
  • Modular Multiplication and Hardware implementations - Review
  • Evaluation of large integer multiplications in hardware - Review
  • Hardware friendly modular mult
  • Montgomery REDC using positive inverse mod r
  • Low latency multipliers and cryptographic puzzles

Related Math

  • The Matrix cookbook
  • Ideal Class Groups

Polynomials

  • Finite fields and polynomials
  • Schwarz - Zippel Lemma
  • Curious History of Schwarz-Zippel lemma