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https://github.com/OpenMined/PSI

Private Set Intersection Cardinality protocol based on ECDH and Bloom Filters
https://github.com/OpenMined/PSI

c cpp golang javascript private-set-intersection

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Private Set Intersection Cardinality protocol based on ECDH and Bloom Filters

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# PSI



Private Set Intersection protocol based on ECDH and Golomb Compressed Sets or

Bloom Filters.



## Protocol



The Private Set Intersection (PSI) protocol involves two parties, a client and a

server, each holding a dataset. The goal of the protocol is for the client to

determine the intersection between their dataset and the server's dataset,

without revealing any information about their respective datasets to each other.



The protocol proceeds as follows:



1. Setup (server)



The server encrypts all its elements `x` under a commutative encryption scheme,

computing `H(x)^s` where `s` is its secret key. The encrypted elements are then

inserted into a container and sent to the client in the form of a serialized

protobuf and resembles* the following:



```

[ H(x_1)^(s), H(x_2)^(s), ... , H(x_n)^(s) ]

```



2. Request (client)



The client encrypts all their elements `x` using the commutative encryption

scheme, computing `H(x)^c`, where `c` is its secret key. The client sends its

encrypted elements to the server along with a boolean flag,

`reveal_intersection`, indicating whether the client wants to learn the elements

in the intersection or only its size (cardinality). The payload is sent as a

serialized protobuf and resembles* the following:



```

[ H(x_1)^(c), H(x_2)^(c), ... , H(x_n)^(c) ]

```



3. Response (server)



For each encrypted element `H(x)^c` received from the client, the server

encrypts it again under the commutative encryption scheme with its secret key

`s`, computing `(H(x)^c)^s = H(x)^(cs)`. The result is sent back to the client

in a serialized protobuf and resembles* the following:



```

[ H(x_1)^(cs), H(x_2)^(cs), ... , H(x_n)^(cs) ]

```



4. Compute intersection (client)



The client decrypts each element received from the server's response using its

secret key `c`, computing `(H(x)^(cs))^(1/c) = H(x)^s`. It then checks whether

each decrypted element is present in the container received from the server, and

reports the number of matches as the intersection size.



It's worth noting that the protocol has several variants, some of which

introduce a small false-positive rate, while others do not generate false

positives. This behavior is selective, and the false-positive rate can be tuned. The selection has implications on communication costs as well.



__NOTE resembles*__: The protocol has configurable **containers**. Golomb

Compressed Sets (`Gcs`) is the default container but it can be overridden to be

`BloomFilter` or `Raw` encrypted strings. `Gcs` and `BloomFilter` will have

false positives whereas `Raw` will not. Using `Raw` increases the communication

cost as it is sending raw strings over the wire while the other two options

drastically reduce the cost at the price of having false positives.



## Security



See [SECURITY.md](SECURITY.md).



## Requirements



There are requirements for the entire project which each language shares. There

also could be requirements for each target language:



### Global Requirements



These are the common requirements across all target languages of this project.



- A compiler such as clang or gcc

- [Bazel](https://bazel.build)



## Installation



The repository uses a folder structure to isolate the supported targets from one

another:



```

private_set_intersection//

```



### C++



See the [C++ README.md](private_set_intersection/cpp/README.md)



### JavaScript



See the [JavaScript README.md](private_set_intersection/javascript/README.md)



### Go



See the [Go README.md](private_set_intersection/go/README.md)



### Python



See the [Python README.md](private_set_intersection/python/README.md)



### Rust



See the [Rust README.md](private_set_intersection/rust/README.md)



## Usage



To use this library in another Bazel project, add the following to your

WORKSPACE file:



```

load("@bazel_tools//tools/build_defs/repo:git.bzl", "git_repository")



git_repository(

   name = "org_openmined_psi",

   remote = "https://github.com/OpenMined/PSI",

   branch = "master",

)



load("@org_openmined_psi//private_set_intersection:preload.bzl", "psi_preload")



psi_preload()



load("@org_openmined_psi//private_set_intersection:deps.bzl", "psi_deps")



psi_deps()



load("@rules_python//python:pip.bzl", "pip_parse")



pip_parse(

    name = "pip_deps",

    # Generated via pip-compile requirements.in

    requirements_lock = "@org_openmined_psi//private_set_intersection/python:requirements.txt",

)



load("@pip_deps//:requirements.bzl", "install_deps")



install_deps()



load("@build_bazel_rules_nodejs//:index.bzl", "node_repositories", "npm_install")



node_repositories()



npm_install(

    name = "npm",

    package_json = "//:package.json",

    package_lock_json = "//:package-lock.json",

)



load("@emsdk//:emscripten_deps.bzl", emsdk_emscripten_deps = "emscripten_deps")



emsdk_emscripten_deps()

```



A full description of the protocol can be found in the documentation of the

[PsiClient](private_set_intersection/cpp/psi_client.h) class. The corresponding

server class is [PsiServer](private_set_intersection/cpp/psi_server.h). An

example of how to interleave the different phases of the protocol can be found

in [psi_server_test.cpp](private_set_intersection/cpp/psi_server_test.cpp).



## Changes



See [CHANGES.md](CHANGES.md).



## Contributing



Pull requests are welcome. For major changes, please open an issue first to

discuss what you would like to change.



Please make sure to update tests as appropriate.



## Contributors



See [CONTRIBUTORS.md](CONTRIBUTORS.md).



## License



[Apache License 2.0](https://choosealicense.com/licenses/apache-2.0/)