# Paillier

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Efficient pure-Rust library for the [Paillier](https://en.wikipedia.org/wiki/Paillier_cryptosystem) partially homomorphic encryption scheme, offering also packed encoding for encrypting several values together as well as several zero-knowledge proofs related to typical use-cases.
Supports several underlying arbitrary precision libraries: [GMP](https://github.com/ZenGo-X/rust-gmp) and [num-bigint](https://github.com/rust-num/num-bigint).

Several companies have invested resources in the development of this library, including [Snips](https://snips.ai/) who implemented the [original version](https://github.com/snipsco/rust-paillier) for use in their privacy-preserving analytics system, and [KZen networks](https://github.com/KZen-networks) who contributed with implementations of many zero-knowledge proofs. See [contributions](#contributions) below for more details.

**Important**: while we have followed recommendations regarding the scheme itself, some parts of this library have not yet been hardened against non-cryptographic attacks such as side-channel attacks.


```rust
extern crate paillier;
use paillier::*;

fn main() {

  // generate a fresh keypair and extract encryption and decryption keys
  let (ek, dk) = Paillier::keypair().keys();

  // encrypt four values
  let c1 = Paillier::encrypt(&ek, 10);
  let c2 = Paillier::encrypt(&ek, 20);
  let c3 = Paillier::encrypt(&ek, 30);
  let c4 = Paillier::encrypt(&ek, 40);

  // add all of them together
  let c = Paillier::add(&ek,
    &Paillier::add(&ek, &c1, &c2),
    &Paillier::add(&ek, &c3, &c4)
  );

  // multiply the sum by 2
  let d = Paillier::mul(&ek, &c, 2);

  // decrypt final result
  let m: u64 = Paillier::decrypt(&dk, &d);
  println!("decrypted total sum is {}", m);

}
```

# Installation

```toml
[dependencies.paillier]
package = "kzen-paillier"
version = "0.2"
```

## Underlying arithmetic

The choice of underlying arithmetic library may be changed using features
`curv/rust-gmp-kzen` (default) and `curv/num-bigint`. GMP generally offers
better performance, but requires GMP shared library to be installed on the
system. `nim-bigint` is pure Rust implementation of big integer and doesn't
require any external dependencies.

Only performance is affected by choosing one of arithmetic implementation.
All functionality remains the same.

In order to build on `num-bigint` instead, put into Cargo.toml:

```toml
[dependencies.paillier]
package = "kzen-paillier"
version = "0.2"
default-features = false
features = ["curv/num-bigint"]
```

# Usage

## Key generation

Key generation feature `keygen` is included by default but if unneeded may safely be excluded to avoid extra dependencies.

```rust
extern crate paillier;
use paillier::*;

fn main() {

  // generate a fresh keypair and extract encryption and decryption keys
  let (ek, dk) = Paillier::keypair().keys();

  ...

}
```

# Benchmarks

Several benches are included, testing both the underlying arithmetic libraries as well as the operations of the scheme. All may be run using
```
cargo bench
```
and including either several arithmetic libraries and key generation as discussed [above](#building).

# License

Forked from [`snipsco/rust-paillier`](https://github.com/snipsco/rust-paillier) with additional functionality. Licensed under either of

 * Apache License, Version 2.0 ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0)
 * MIT license ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)

at your option.

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.


# Contributions

Several people have had a significant impact in the development of this library (in alphabetical order):
- [Gary Benattar](https://github.com/gbenattar) (KZen networks)
- [Mario Cornejo](https://github.com/mcornejo) (while at Snips)
- [Mathieu Poumeyrol](https://github.com/kali) (Snips)
- [Omer Shlomovits](https://github.com/omershlo) (KZen networks)

and several companies have invested resources:
- [Snips](https://github.com/snipsco) sponsored implementation of the original version
- [KZen networks](https://github.com/KZen-networks) sponsored extension of many zero-knowledge proofs

## Reported uses

- [Snips](https://github.com/snipsco): privacy-preserving analytics
- [KZen networks](https://github.com/KZen-networks): multi-party signatures