Secure Computation 3
Talkat Cryptography 10 Years Later: Obfuscation, Proof Systems, and Secure Computation Boot Camp 2025 · 2025-05-19..05-23·
summary
Shows a concrete route to sublinear 2PC: build homomorphic secret sharing for branching programs, use encrypted inputs plus secret-shared decryption key and a distributed discrete log step to convert multiplicative group shares into additive output shares. Under DDH the DD‑log step has 1/poly correctness error; switching to Paillier / Damgård–Jurik removes that and supports large message spaces. Result: fully succinct evaluation for branching programs and C / log C communication for layered circuits, with polynomial preprocessing and heavy exponentiation cost per gate. Multi‑party extensions remain limited.
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chapters (10)
- 0:00Breaking circuit size barriers
- 1:05FHE overview and limits
- 9:03Pre-processing model
- 14:28Homomorphic secret sharing
- 19:54DDH-based HSS
- 30:58Paillier-based HSS
- 38:06Two-party computation
- 42:48Multi-party HSS
- 54:24Open problems
- 56:32MPC adoption Q&A
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