Multi-Party Distributed Point Functions
summary
Constructs a multi‑party distributed point function in minicrypt by replacing BGI15’s deterministic combinatorial design with a randomized combinatorial design, dropping exponential 2^n blowup to a concrete n^3·√D share size (n parties, domain D) using PRG/one‑way‑function black‑boxes. The scheme samples degree‑2 neighbors (with replacement), needs about n^4 seeds overall and yields only weak (inverse‑polynomial) security that is amplified to full security via the standard Boyle et al. transformation, so it works but remains theoretically large.
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chapters (14)
- 0:00Multi-party DPF intro
- 1:57What is a DPF
- 3:46Two-party DPF constructions
- 5:11Multi-party DPF limits
- 6:40Why DPF matters
- 8:31Improved multi-party DPF
- 9:55New construction overview
- 14:39Two to three-party DPF
- 18:13Generalizing to any number of parties
- 23:50DPF combinatorial design
- 26:24Randomized design approach
- 30:29Results and efficiency
- 31:09Open problems
- 32:15Q&A
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