Homomorphic Signatures and Pre-Processing NIZK

Explore homomorphic signatures and pre-processing NIZKs in this lecture by David Wu from the University of Virginia. Delve into lattice-based cryptography, focusing on new capabilities such as computing on encrypted and signed data. Examine the GSW Fully Homomorphic Encryption scheme, its homomorphic operations, and its application as a homomorphic commitment. Investigate the connection between commitments and proofs, leading to a discussion on NIZKs in the preprocessing model. Learn about additional concepts like lattice trapdoors and context-hiding for commitments. Gain insights into cutting-edge cryptographic techniques and their potential applications in secure computation and privacy-preserving technologies.

Intro
Cryptography from Lattices
Computing on Encrypted Data
Computing on Signed Data
The GSW FHE Scheme
Homomorphic Operations in GSW
GSW as a Homomorphic Commitme
From Commitments to Proofs
NIZKs in the Preprocessing Model
Back to Homomorphic Commitment
Another Ingredient: Lattice Trapdoo
Context-Hiding for Commitments