Explore the third part of a comprehensive lecture on indistinguishability obfuscation from well-founded assumptions. Delve into advanced cryptographic concepts, including Learning Parity with Noise, PRGs in NC, and the implausibility of degree-2 PRGs. Examine the turning point of "Degree-2.5" Integer PRGs and discover the new Simple PRG (SPRG) overview. Gain insights into SPRG construction, key intuitions about sparsity, and error correction techniques. Analyze security considerations and challenges in revealing information about errors.
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
