Zero-knowledge proofs

This document explains how to implement the zero-knowledge proofs function for compact public key encryption to verify the encryption process without revealing the encrypted information.

TFHE-rs can generate zero-knowledge proofs to verify that the compact public key encryption process is correct. In other words, TFHE-rs generates the proof without revealing any information other than the already known range of the encrypted message. This technique is derived from Libert’s work.

You can enable this feature using the flag: --features=zk-pok when building TFHE-rs.

Using this feature is straightforward: during encryption, the client generates the proof, and the server validates it before conducting any homomorphic computations. The following example demonstrates how a client can encrypt and prove a ciphertext, and how a server can verify the ciphertext and compute it:

use rand::prelude::*;
use tfhe::prelude::FheDecrypt;
use tfhe::set_server_key;
use tfhe::zk::{CompactPkeCrs, ZkComputeLoad};

pub fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut rng = thread_rng();

    let params =
        tfhe::shortint::parameters::PARAM_MESSAGE_2_CARRY_2_KS_PBS_TUNIFORM_2M64;
    let config = tfhe::ConfigBuilder::with_custom_parameters(params, None);

    let client_key = tfhe::ClientKey::generate(config.clone());
    // This is done in an offline phase and the CRS is shared to all clients and the server
    let crs = CompactPkeCrs::from_config(config.into(), 64).unwrap();
    let public_zk_params = crs.public_params();
    let server_key = tfhe::ServerKey::new(&client_key);
    let public_key = tfhe::CompactPublicKey::try_new(&client_key).unwrap();

    let clear_a = rng.gen::<u64>();
    let clear_b = rng.gen::<u64>();
    
    let proven_compact_list = tfhe::ProvenCompactCiphertextList::builder(&public_key)
        .push(clear_a)
        .push(clear_b)
        .build_with_proof_packed(public_zk_params, ZkComputeLoad::Proof)?;

    // Server side
    let result = {
        set_server_key(server_key);

        // Verify the ciphertexts
        let mut expander = proven_compact_list.verify_and_expand(&public_zk_params, &public_key)?;
        let a: tfhe::FheUint64 = expander.get(0).unwrap()?;
        let b: tfhe::FheUint64 = expander.get(1).unwrap()?;

        a + b
    };

    // Back on the client side
    let a_plus_b: u64 = result.decrypt(&client_key);
    assert_eq!(a_plus_b, clear_a.wrapping_add(clear_b));

    Ok(())
}

Performance can be improved by setting lto="fat" in Cargo.toml

[profile.release]
lto = "fat"

and by building the code for the native CPU architecture and in release mode, e.g. by calling RUSTFLAGS="-C target-cpu=native" cargo run --release.

You can choose a more costly proof with ZkComputeLoad::Proof, which has a faster verification time. Alternatively, you can select ZkComputeLoad::Verify for a faster proof and slower verification.

Using dedicated Compact Public Key parameters

A first example

You can use dedicated parameters for the compact public key encryption to reduce the size of encrypted data and speed up the zero-knowledge proof computation.

This works essentially in the same way as before. Additionally, you need to indicate the dedicated parameters to use:

use rand::prelude::*;
use tfhe::prelude::FheDecrypt;
use tfhe::set_server_key;
use tfhe::zk::{CompactPkeCrs, ZkComputeLoad};

pub fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut rng = thread_rng();

    let params = tfhe::shortint::parameters::PARAM_MESSAGE_2_CARRY_2_KS_PBS_TUNIFORM_2M64;
    // Indicate which parameters to use for the Compact Public Key encryption
    let cpk_params = tfhe::shortint::parameters::compact_public_key_only::PARAM_PKE_MESSAGE_2_CARRY_2_KS_PBS_TUNIFORM_2M64;
    // And parameters allowing to keyswitch/cast to the computation parameters.
    let casting_params = tfhe::shortint::parameters::key_switching::PARAM_KEYSWITCH_MESSAGE_2_CARRY_2_KS_PBS_TUNIFORM_2M64;
    // Enable the dedicated parameters on the config
    let config = tfhe::ConfigBuilder::with_custom_parameters(params, None)
        .use_dedicated_compact_public_key_parameters((cpk_params, casting_params));

    // Then use TFHE-rs as usual
    let client_key = tfhe::ClientKey::generate(config.clone());
    // This is done in an offline phase and the CRS is shared to all clients and the server
    let crs = CompactPkeCrs::from_config(config.into(), 64).unwrap();
    let public_zk_params = crs.public_params();
    let server_key = tfhe::ServerKey::new(&client_key);
    let public_key = tfhe::CompactPublicKey::try_new(&client_key).unwrap();

    let clear_a = rng.gen::<u64>();
    let clear_b = rng.gen::<u64>();

    let proven_compact_list = tfhe::ProvenCompactCiphertextList::builder(&public_key)
        .push(clear_a)
        .push(clear_b)
        .build_with_proof_packed(public_zk_params, ZkComputeLoad::Verify)?;

    // Server side
    let result = {
        set_server_key(server_key);

        // Verify the ciphertexts
        let mut expander = proven_compact_list.verify_and_expand(&public_zk_params, &public_key)?;
        let a: tfhe::FheUint64 = expander.get(0).unwrap()?;
        let b: tfhe::FheUint64 = expander.get(1).unwrap()?;

        a + b
    };

    // Back on the client side
    let a_plus_b: u64 = result.decrypt(&client_key);
    assert_eq!(a_plus_b, clear_a.wrapping_add(clear_b));

    Ok(())
}

Benchmarks

Benchmarks for the proofs have been run on a m6i.4xlarge with 16 cores to simulate an usual client configuration. The verification are done on a hpc7a.96xlarge AWS instances to mimic a powerful server.

Timings in the case where the workload is mainly on the prover, i.e., with the ZkComputeLoad::Proof option.

Inputs	Proving	Verifying
1xFheUint64	2.79s	197ms
10xFheUint64	3.68s	251ms

Timings in the case where the workload is mainly on the verifier, i.e., with the ZkComputeLoad::Verify option.

Inputs	Proving	Verifying
1xFheUint64	730ms	522ms
10xFheUint64	1.08s	682ms