This course aims to teach learners about indistinguishability obfuscation from well-founded assumptions. By the end of the course, students will be able to understand learning parity with noise, PRGs in NC, implausibility of degree-2 PRGs, structured seed PRG, and the construction of SPRG. The teaching method involves theoretical explanations and examples. This course is intended for individuals interested in cryptography, computer science, and theoretical mathematics.
Indistinguishability Obfuscation from Well Founded Assumptions - Part 3
Overview
Syllabus
Intro
Overall Picture: Continuing From Part-2
Learning Parity with Noise BFKL 93, IPS 09 for some constant 8 € (0,1), and a prime modulus p.
PRGs in NC
What Structure? Computable using Bilinear Maps- Bilinear Maps Friendly.
Implausibility of Degree-2 PRGS BBKK 18, LV 18, BHJKS 19
Turning Point: "Degree-2.5" Integer PRGS A.JS 18, JLMS 19, AILMS 19 Input: An Integer vector
NEW! SPRG Overview Also degree 2.5, but boolean output!
SPRG: Simple Proof
Structured Seed PRG
How to Construct SPRG?
Key Intuition: Sparsity Helps SPRG Components
Correct T Errors (Failed First Attempt)
Problem: Can't Reveal BAD
Example: Correcting One Error
Correcting T =: Errors
Correcting T = Errors
What about Security?
Taught by
IEEE FOCS: Foundations of Computer Science
