Ryan Henry
0d22946a0e
Ship the TLS mesh, composer, Beaver/Yao/leaf MPC, prep/online paths, apps, and docs so the tree is pushable before elevating share_expr, security_mode, and prep resume. Co-authored-by: Cursor <cursoragent@cursor.com>
41 lines
2.5 KiB
Markdown
41 lines
2.5 KiB
Markdown
# Multiparty & 3-server {#multiparty}
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<div class="eli5"><b>ELI5.</b> make_dpf3 is two ordinary spines per party and a Shamir payload, so any two parties open and the third key is independent of the value. make_it_dpf3 shares the whole truth table instead, and all three shares are required. Doerner–Shelat and geneval are the two-party, no-dealer alternatives.</div>
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\endhtmlonly
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Two-party keys are the default. The library also builds three-evaluator
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`(2,3)` keys, information-theoretic three-server DPFs, and dealer-free
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two-party keygen when the index is already shared.
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| Construction | Parties | Header |
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| --- | --- | --- |
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| [dpf::make_dpf3](@ref dpf/dpf3.hpp) | Any two of three open (Shamir / dual spine, [ePrint 2024/1658](@ref bib_dpf3)) | `dpf3.hpp` |
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| [dpf::make_dpf3_doerner_shelat](@ref dpf/dpf3_ds.hpp) | Same keys from XOR shares of `alpha` | `dpf3_ds.hpp` |
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| `make_dpf3_cmp` / `make_dpf3_ic` / `make_multipoint3` | Comparisons, intervals, multipoint | `dpf3_cmp.hpp`, `dpf3_multipoint.hpp` |
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| [dpf::make_it_dpf3](@ref dpf/it_dpf3.hpp) | Information-theoretic 3-server DPF ([ePrint 2023/028](@ref bib_itdpf)) | `it_dpf3.hpp` |
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| [dpf::make_dpf_doerner_shelat](@ref dpf/doerner_shelat.hpp) | Two parties, shared index, no dealer for the point | `doerner_shelat.hpp` |
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| [dpf::geneval_*](@ref dpf/geneval.hpp) | Answer shares for one query, no reusable key | `geneval.hpp` |
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| [dpf::shamir::deal](@ref dpf/shamir.hpp) | (K,N) Shamir. `(2,3)` is the `make_dpf3` payload | `shamir.hpp` |
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The payload inside `make_dpf3` is degree-1 Shamir on the points `1`, `2`,
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and `3`. That access structure is `shamir::two_of_three`, the type
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`shamir_share`. The same split takes other thresholds:
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`shamir::deal<T, K, N>` and `shamir::share_secret`. `make_dpf3` stays
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`(2,3)`. See [secret shares](@ref secret_shares) and `examples/mwe/shamir.cpp`.
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```cpp
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auto [k1, k2, k3] = dpf::make_dpf3(std::uint8_t{42}, dpf::fp61{7});
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auto opened = dpf::reconstruct(
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dpf::as_share(k1, dpf::eval_point(k1, std::uint8_t{42})),
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dpf::as_share(k2, dpf::eval_point(k2, std::uint8_t{42})),
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dpf::as_share(k3, dpf::eval_point(k3, std::uint8_t{42})));
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```
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Party meshes and socket walks live under [trio.hpp](@ref dpf/net/trio.hpp)
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and the `party/` harnesses. Application-shaped sketches include
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[3-party Duoram](@ref app_duoram) and [three-server PIR](@ref app_pir3).
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**Go deeper:** [guided tour — three evaluators](@ref tour_dpf3),
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[Doerner–Shelat](@ref tour_ds), [evaluating DPFs](@ref evaluation),
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[bibliography](@ref bibliography).
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