Functional Commitments

on YouTube ↗01h 00m

" summary

Defines functional commitments (commit, local opening, check) and proves two security tiers: function binding (local consistency) vs stronger extractability (rewinding or ideal-oracle extractors). Gives concrete constructions: a pairing-based KZG-style scheme with one-group-element commitments and one-group-element proofs, linear-size SRS, checking via two pairings and reduction to the Q-Power SDH assumption; and a Pedersen/matrix scheme with square-root proof tradeoff (public-coin setup, larger proofs but smaller SRS). Open problems: post‑quantum short proofs and public setups.

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" chapters (12)

1. 0:00Functional commitments intro
2. 1:19Why they matter
3. 3:05Defining schemes
4. 7:24Security properties
5. 16:55Extractability vs binding
6. 25:32Hiding properties
7. 36:50Commitment constructions
8. 41:05Polynomial commitments overview
9. 42:31KZG construction
10. 49:11Matrix-based commitments
11. 54:31Open questions
12. 56:01Q&A

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