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.

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 fast addition, too.

The Long Story

See our full paper.

Use parmesan

Add a dependency to your Cargo.toml file in your Rust project. (Currently only from git or locally.)

```toml [dependencies] parmesan = { git = "https://gitlab.fit.cvut.cz/klemsjak/parmesan" } colored = "^2.0.0"

or:

parmesan = { path = "../parmesan" } colored = "^2.0.0" ```

For the best performance, we recommend to compile with the RUSTFLAGS="-C target-cpu=native" cargo build --release command.

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::PARM80__PI_5__D_22;   // or params from Concrete v0.2: CONCR__M_2__C_3
// ---------------------------------
//  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(&a)?;
let b_val = encryption::convert(&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.