Topics:

• Poly-commit based on Error-correcting Codes
• Argument for Vector-Matrix Product
  • Proximity Test
  • Consistency Test
• Linear-time encodable code based on expanders
  • Lossless Expander
  • Recursive Encoding with constant relative distance

Topics:

• KZG poly-commit based on bilinear pairing
  • KZG scheme
  • Powers-of-tau Ceremony
  • Security Analysis
  • Knowledge of exponent assumption
  • Variants: multivariate; ZK; batch openings
• Bulletproofs poly-commit based on discrete logarithm

Topics:

• Preprocessing SNARK
• KZG Poly-Commit Scheme
• Proving Properties of committed polys
  • ZeroTest
  • Product Check
  • Permutation Check
  • Prescribed Permutation Check
• Plonk IOP for General Circuits

Topics:

• Differences between Interactive Proofs and SNARKs
• Outline of SNARKs from IP
• Brief intro to Functional Commitments
• SZDL Lemma
• Multilinear Extensions
• Sum-check Protocol and its application.
  • Counting Triangles
  • SNARK for Circuit-satisfiability