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.

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

For the best performance, compile with shell $ RUSTFLAGS="-C target-cpu=native" cargo build --release

Benchmarks

For benchmarks, we implement an experimental tool bench-parmesan, which also compares Parmesan and Concrete v0.2. Results will be published in a paper.

Find preliminary measurements of the processor load on a machine with 2xAMD EPYC 7543 during 32-bit multiplication attached in a file.

Example

```rust 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> {

// =================================
//  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.