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

Multi scalar multiplications

Algorithms and methods

  • Fast Multi-scalar Multiplication Methods on Elliptic Curves with Precomputation Strategy Using Montgomery Trick
  • Faster batch forgery identification See section 4 for MSM, bucket method
  • Pippenger’s exponentiation algorithm - Bernstein
  • Efficient multi-exponentiation
    • implementation in Python
  • Multi-scalar multiplication: state of the art & new ideas with Gus Gutoski
  • Improved Fast exponentiations - Bodo Moller
  • Fast exponentiation with precomputation - Brickell Gordon et al
  • Matter labs -ALgorithms
  • Ryah Henry - Thesis
  • Efficient Multi exponentiation: Bucket method - Bootle

Implementations

  • pipezk
  • MSM with FPGA -Connor Masterson thesis
  • PipeMSM
  • EdMSM
  • CycloneMSM
  • Cuzk
  • Zprize MSM implementations