Parmesan

Parallel ARithMEticS on tfhe ENcrypted data

Parmesan implements selected parallel algorithms for multi-digit arithmetics over TFHE ciphertexts. Namely:

addition/subtraction,
scalar multiplication (i.e., multiplication by a known integer),
multiplication,
squaring,
signum,
maximum of two numbers,
rounding, and
evaluation of a simple neural network.

Disclaimer: Parmesan is currently an experimental library, which serves as a proof-of-concept for parallelizable arithmetics over encrypted data. Hence neither correct functionality nor any level of code quality is guaranteed.

The Short Story

In the standard integer representation, parallel addition is not possible due to the carry, which can propagate all the way from the LSB to the MSB. However, using, e.g., an alphabet {-1,0,1} for base-2 integer representation, a parallel addition algorithm does exist. Other operations like (scalar) multiplication and squaring benefit from the fast addition, too.

The Long Story

See our full paper (also at eprint).

Use `parmesan`

Add a dependency to your Cargo.toml file in your Rust project.

[dependencies]
parmesan = { version = "^0.0.20-alpha", features = ["measure"] }
colored = "^2.0.0"

For the best performance, compile with

$ RUSTFLAGS="-C target-cpu=native" cargo build --release

Example

use std::error::Error;

use colored::Colorize;

use parmesan::params;
use parmesan::userovo::*;
use parmesan::ParmesanUserovo;
use parmesan::ParmesanCloudovo;
use parmesan::arithmetics::ParmArithmetics;

pub fn main() -> Result<(), Box<dyn Error>> {

    // =================================
    //  Initialization
    // ---------------------------------
    //  Global Scope
    let par = &params::PAR_CNCR_V0_2__M2_C3;

    // ---------------------------------
    //  Userovo Scope
    let pu = ParmesanUserovo::new(par)?;
    let pub_k = pu.export_pub_keys();
    // ---------------------------------
    //  Cloudovo Scope
    let pc = ParmesanCloudovo::new(par, &pub_k);

    // =================================
    //  U: Encryption
    let a: Vec<i32> = vec![1,0,1,-1,-1,0,-1,1,1,-1,1,1,1,-1,-1,0,0,1,1,0,0,0,0,-1,0,0,0,0,0,-1,0,0,];
    let b: Vec<i32> = vec![-1,0,0,-1,1,1,-1,1,-1,0,0,1,0,1,1,0,0,0,-1,0,0,1,0,0,-1,0,-1,-1,-1,1,1,0,];
    let ca = pu.encrypt_vec(&a)?;
    let cb = pu.encrypt_vec(&b)?;
    // convert to actual numbers
    let a_val = encryption::convert_from_vec(&a)?;
    let b_val = encryption::convert_from_vec(&b)?;
    // print plain inputs
    println!("\nInputs:\n");
    println!("a   = {:12}", a_val);
    println!("b   = {:12}", b_val);

    // =================================
    //  C: Evaluation
    let c_add_a_b = ParmArithmetics::add(&pc, &ca, &cb);

    // =================================
    //  U: Decryption
    let add_a_b = pu.decrypt(&c_add_a_b)?;

    let mut summary_text = format!("\nResults:\n");
    summary_text = format!("{}\nAddition:", summary_text);
    summary_text = format!("{}\na + b         = {:12} :: {} (exp. {})", summary_text,
                            add_a_b,
                            if add_a_b == a_val + b_val {String::from("PASS").bold().green()} else {String::from("FAIL").bold().red()},
                            a_val + b_val
    );

    println!("{}", summary_text);

    println!("\nDemo END\n");

    Ok(())
}

License

Parmesan is licensed under AGPLv3.

Acknowledgments

Partially supported by EURECOM.

parmesan 0.0.20-alpha-2