Non-Interactive Zero-Knowledge in Pairing-Free Groups from Weaker Assumptions

Explore a groundbreaking paper on Non-Interactive Zero-Knowledge Proofs (NIZKs) in pairing-free groups presented at Eurocrypt 2020. Delve into the authors' innovative approach to constructing NIZKs under weaker assumptions, examining key concepts such as Sigma Protocols, Correlation-Intractable Hash Functions, and the Short-Exponent Discrete Logarithm problem. Gain insights into the step-by-step construction process, from the initial Sigma Protocol for LOH to the final transformation into NIZKs for NP. Understand the significance of this research in advancing cryptographic techniques and its potential impact on secure communication systems.

Intro
Non-Interactive Zero-Knowledge Proofs (NIZKS)
NIZKs in Pairing-Free Groups - Known Results
Our Improvements
Construction Overview
Key Intuition
Sigma Protocol for LOH
Step 2 CI Hash Function to NIZK
Step 2 Correlation-Intractable (CI) Hash Function
From NIZKH to NIZKs for NP
Our Second Contribution
Key Idea for Step 3
Short-Exponent Discrete Logarithm