Homomorphic Commitments & Signatures

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" summary

Constructs homomorphic signatures for arbitrary circuits (leveled) where certificate size depends on circuit depth but not data size, built from equivocable homomorphic commitments derived from GSW-style homomorphic ops and LWE/SIS trapdoors. Setup uses a long public random string; signing is trapdoor-based equivocation, verification runs a homomorphic evaluation on public commitments then checks a short opening. Scheme achieves selective security and extensible fixes (chameleon hashes, ZK), but needs heavy preprocessing and lacks bootstrapping.

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" chapters (13)

1. 0:00Intro
2. 0:44Recall the GSW FHE
3. 3:47Homomorphic Computation on Commitments and Openings
4. 15:01SIS Trapdoor with Correct Distribution [GPV08, MP12, LW15]
5. 17:13Summary: Homomorphic Commitments
6. 18:37Homomorphic Signatures: Motivation
7. 20:16Homomorphic Signatures (HS)
8. 24:58Constructions of Homomorphic Signatures
9. 27:50Other Solutions
10. 31:11Warm-Up: 1-Time, 1-Bit Signature
11. 32:33Warm-Up: 1-Time, Multi-Bit Signature
12. 37:45Extensions
13. 39:25Open Problems

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