Homomorphic Signatures and Pre-Processing NIZK
summary
Shows that GSW ciphertexts function as a homomorphic commitment with GSW ciphertext = homomorphic commitment, exposing two concrete homomorphisms: an input-independent evaluator on ciphertexts and an input-dependent linear relation on randomness. Uses lattice gadget trapdoors and pre-image sampling to build a designated-prover NIZK in a preprocessing (correlated‑randomness) model and to derive homomorphic signatures; simulation switches A between LWE and uniform to get context‑hiding. Works for bounded-depth circuits, has large public parameters, and leaves fully homomorphic commitments and SA‑free well‑formedness proofs open.
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chapters (12)
- 0:00Intro
- 0:27Cryptography from Lattices
- 1:54Computing on Encrypted Data
- 3:28Computing on Signed Data
- 5:45The GSW FHE Scheme
- 8:59Homomorphic Operations in GSW
- 17:44GSW as a Homomorphic Commitme
- 26:25From Commitments to Proofs
- 39:10NIZKs in the Preprocessing Model
- 49:42Back to Homomorphic Commitment
- 51:09Another Ingredient: Lattice Trapdoo
- 54:29Context-Hiding for Commitments
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