YouTube Courses

The Kilian-Micali Protocol: Using CRH Functions with Local Openings and PCP - Lecture 5

Examines how collision-resistant hashes with local openings and PCPs yield interactive arguments.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Succinct Non-Interactive Arguments for Batch NP from Learning with Errors - Part 1 - Lecture 8

Builds batch NP arguments from LWE using locally opening statistically binding commitments and PCPs with fast online verification.

• YouTube
• 1 hour 22 minutes
• Self-Paced
• Free Video

Doubly Efficient Interactive Proofs in Cryptography - Lecture 2

Explains doubly efficient interactive proofs through triangle counting, low-degree extensions, and the GKR protocol for bounded-depth computations.

• YouTube
• 43 minutes
• Self-Paced
• Free Video

GKR Protocol and IP=PSPACE - Lecture 3

Examines corollaries of the GKR protocol and applies the IP = PSPACE result.

• YouTube
• 1 hour 22 minutes
• Self-Paced
• Free Video

Succinct Non-Interactive Arguments for Batch NP from Learning with Errors - Lecture 8

A construction of succinct non-interactive arguments for batch NP from learning with errors, with local openings and fast PCP verification.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Soundness of the Fiat-Shamir Paradigm in the Standard Model - Part 1

Examines how CI hash functions affect Fiat–Shamir soundness, contrasting their existence in the random oracle model with a plain-model counterexample.

• YouTube
• 1 hour 34 minutes
• Self-Paced
• Free Video

Fiat-Shamir Paradigm and Zero-Knowledge Proofs - Lecture 6

Shows how the Fiat–Shamir paradigm removes interaction in zero-knowledge proofs and how to establish the Kilian–Micali protocol’s soundness in the random oracle model.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Probabilistically Checkable Proofs via GKR and Interactive Arguments - Lecture 4

A construction of probabilistically checkable proofs from GKR, leading into interactive succinct arguments for NP.

• YouTube
• 1 hour 30 minutes
• Self-Paced
• Free Video

The Kilian-Micali Protocol Using Collision Resistant Hash Functions and PCP - Lecture 5

See how collision-resistant hashes and probabilistically checkable proofs combine to construct interactive arguments.

• YouTube
• 1 hour 45 minutes
• Self-Paced
• Free Video

BARGs Implies SNARGs and Connection to Non-Signaling PCPs - Lecture 9

Examines how BARGs imply SNARGs and connects these succinct arguments to non-signaling probabilistically checkable proofs.

• YouTube
• 1 hour 27 minutes
• Self-Paced
• Free Video

Soundness of the Fiat-Shamir Paradigm in the Standard Model - Lecture 7

Examines when the Fiat–Shamir paradigm remains sound in the standard model, contrasting random-oracle existence with a plain-model counterexample.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Elimination and Factorization A = CR

See how elimination reveals dependent columns and produces the column-row factorization A = CR.

• YouTube
• 37 minutes
• Self-Paced
• Free Video

The Four Fundamental Subspaces and Least Squares

See how the four fundamental subspaces reveal when a matrix equation has no exact solution, then use the pseudoinverse to find its least-squares solution.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Convergence Tests for Series and Power Series - Lecture 8

Uses limsup and liminf to state general convergence tests and define the radius of convergence for power series.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

Extreme and Intermediate Value Theorem - Metric Spaces - Lecture 11

Uses sequences to prove the extreme and intermediate value theorems, then extends convergence and Cauchy sequences to metric spaces.

• YouTube
• 1 hour 22 minutes
• Self-Paced
• Free Video