README.md

rust-elgamal

Simple interface for ElGamal and Homomorphic-ElGamal cryptosystems.

Usage

use curv::arithmetic::traits::Modulo;
use curv::arithmetic::traits::Samplable;
use curv::BigInt;
use elgamal::{
    rfc7919_groups::SupportedGroups, ElGamal, ElGamalKeyPair, ElGamalPP, ElGamalPrivateKey,
    ElGamalPublicKey,ExponentElGamal,ElGamalCiphertext,
};

fn main() {

    // choose suitable field parameter, https://tools.ietf.org/html/rfc7919
    let group_id = SupportedGroups::FFDHE2048;

    let alice_pp = ElGamalPP::generate_from_rfc7919(group_id);

    // create a public, secret keypair
    let alice_key_pair = ElGamalKeyPair::generate(&alice_pp);


    // basic en/decryption roundtrip
    let message = BigInt::from(13);
    let cipher = ElGamal::encrypt(&message, &alice_key_pair.pk).unwrap();
    let message_tag = ElGamal::decrypt(&cipher, &alice_key_pair.sk).unwrap();
    println!("basic encryption: message: {}, decrypted: {}", message, message_tag);


    // homomorphic multiplication
    let factor_1 = BigInt::from(13);
    let factor_2 = BigInt::from(9);

    let cipher = ElGamal::encrypt(&factor_1, &alice_key_pair.pk).unwrap();
    let constant_cipher = ElGamal::encrypt(&factor_2, &alice_key_pair.pk).unwrap();

    // homomorphic multiplication in cipher space
    let product_cipher = ElGamal::mul(&cipher, &constant_cipher).unwrap();

    // decrypt homomorphic product
    let product_tag = ElGamal::decrypt(&product_cipher, &alice_key_pair.sk).unwrap();
    println!(" factor1: {} * factor 2: {} = {}; decrypted homomorphic product: {}", factor_1, factor_2, &factor_1 * &factor_2, product_tag);


    // homomorphic (pow) addition
    // note to self: we now have (g^r, g^m * h^r) instead of (g^r, m * h^r)
    // data set:
    let data = vec![BigInt::from(1),BigInt::from(10), BigInt::from(100)];
    let randomness = vec![BigInt::sample_below(&alice_pp.q), BigInt::sample_below(&alice_pp.q), BigInt::sample_below(&alice_pp.q)];

    // encrypt each data point 
    let mut ciphers: Vec<ElGamalCiphertext> = Vec::new();
    for (idx, number) in data.iter().enumerate() {
        let c = ExponentElGamal::encrypt_from_predefined_randomness(&number, &alice_key_pair.pk, &randomness[idx]).unwrap();
        ciphers.push(c);
    }

    // finally, we add the data
    let n = ciphers.len();
    let mut addition_cipher: ElGamalCiphertext = ExponentElGamal::add(&ciphers[0], &ciphers[1]).unwrap();
    for idx in 2..n {
        addition_cipher = ExponentElGamal::add(&ciphers[idx], &addition_cipher).unwrap();
    }

    // and now we decrypt and due to the exponentiation we end up with g^m
    let c_tag =  ExponentElGamal::decrypt_exp(&addition_cipher, &alice_key_pair.sk).unwrap();

    // and we're super inefficiently brute-forcing g^i mod p to validate the raw sum
    for i in 0..1_000_000 {
        let res = BigInt::mod_pow(&alice_key_pair.pk.pp.g, &BigInt::from(i), &alice_key_pair.pk.pp.p);
        if res.eq(&c_tag) {
            println!("result: {}", i);
            break;
        }
    }

}

Tests

Several tests are included:

cargo test --lib

Please note that the test for generate_safe is not part of the default test run due to the potentially long runtime. To run the expensive tests:

cargo test --lib  -- --ignored

Benches

Benchmarks are also included:

cargo bench

The benchmarks are created bycriterion.rs and the default reports include pretty cool plots, which are best with gnuplot installed, e.g., brew install gnuplot. The benchmark reports can found in ../target/criterion/report and open index.html should do.

To run the benches without plots, or with any of the other criterion.rs options, use

cargo bench --bench elgamal_benches -- --noplot

See benches/examples for a full results set.

Contact

Feel free to reach out or join ZenGo X Telegram for discussions on code and research.