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

Topics Covered:

• Definition of IND-CCA Security
• Application of NIZK: Construction of CCA-secure encryption scheme

Topics Covered:

• IP for Quadratic Non-Residuosity
• Non-interactive ZK
  • NIZK in The Common Random String(CRS) Model
  • Construction in CRS Model: Blum-Feldman-Micali’88 (quadratic residuosity)
  • NIZK for QNR
  • NIZK for 3SAT
• Proofs vs. Argument

Topics Covered:

• Sequential vs Parallel Repetition: reduce soundness error
• Proof of Knowledge
  • PoK of DLOG
• Non-Interactive ZK(NIZK)
  • NIZK in The Random Oracle Model
    • NIZK for 3COL
  • NIZK in The Common Random String Model (Lecture 16)

Topics Covered:

• Perfect ZK Proof for QR Language
• Perfect ZK Proof for Graph Isomorphism
• Comp. ZK Proof for 3Coloring
• All NP Languages have Comp. ZK Proofs
• Commitment Schemes

Topics Covered:

• Zero knowledge, definitions and example
• ZK Proof for QR Language.
  • honest-verifier ZK
  • malicious-verifier ZK

Topics Covered:

• Construction of CRHF from Discrete Log

• Digital Signatures only from OWF

• Direct Constructions:Trapdoor Permutation and the Hash-and-Sign Paradigm.

• Random Oracles.