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# 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– < / div >
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Two-party keys are the default. The library also builds three-evaluator
`(2,3)` keys, information-theoretic three-server DPFs, and dealer-free
two-party keygen when the index is already shared.
| Construction | Parties | Header |
| --- | --- | --- |
| [dpf::make_dpf3 ](@ref dpf/dpf3.hpp ) | Any two of three open (Shamir / dual spine, [ePrint 2024/1658 ](@ref bib_dpf3 )) | `dpf3.hpp` |
| [dpf::make_dpf3_doerner_shelat ](@ref dpf/dpf3_ds.hpp ) | Same keys from XOR shares of `alpha` | `dpf3_ds.hpp` |
| `make_dpf3_cmp` / `make_dpf3_ic` / `make_multipoint3` | Comparisons, intervals, multipoint | `dpf3_cmp.hpp` , `dpf3_multipoint.hpp` |
| [dpf::make_it_dpf3 ](@ref dpf/it_dpf3.hpp ) | Information-theoretic 3-server DPF ([ePrint 2023/028 ](@ref bib_itdpf )) | `it_dpf3.hpp` |
| [dpf::make_dpf_doerner_shelat ](@ref dpf/doerner_shelat.hpp ) | Two parties, shared index, no dealer for the point | `doerner_shelat.hpp` |
| [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` |
The payload inside `make_dpf3` is degree-1 Shamir on the points `1` , `2` ,
and `3` . That access structure is `shamir::two_of_three` , the type
`shamir_share` . The same split takes other thresholds:
`shamir::deal<T, K, N>` and `shamir::share_secret` . `make_dpf3` stays
`(2,3)` . See [secret shares ](@ref secret_shares ) and `examples/mwe/shamir.cpp` .
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```cpp
auto [k1, k2, k3] = dpf::make_dpf3(std::uint8_t{42}, dpf::fp61{7});
auto opened = dpf::reconstruct(
dpf::as_share(k1, dpf::eval_point(k1, std::uint8_t{42})),
dpf::as_share(k2, dpf::eval_point(k2, std::uint8_t{42})),
dpf::as_share(k3, dpf::eval_point(k3, std::uint8_t{42})));
```
Party meshes and socket walks live under [trio.hpp ](@ref dpf/net/trio.hpp )
and the `party/` harnesses. Application-shaped sketches include
[3-party Duoram ](@ref app_duoram ) and [three-server PIR ](@ref app_pir3 ).
**Go deeper:** [guided tour — three evaluators ](@ref tour_dpf3 ),
[Doerner– ](@ref tour_ds ), [evaluating DPFs ](@ref evaluation ),
[bibliography ](@ref bibliography ).
