Generic trait bounds

This document serves as a practical reference for implementing generic functions in Rust that use operators across mixed references and values. The following explanations help you to understand the trait bounds necessary to handle such operations.

Operators such as +, *, >>, and so on are tied to traits in std:::ops. For instance, the + operator corresponds to std::ops::Add. When writing a generic function that uses the + operator, you need to specify std::ops::Add as a trait bound.

The trait bound varies slightly depending on whether the left-hand side / right-hand side is an owned value or a reference. The following table shows the different scenarios:

operation	trait bound
T $op T	T: $Op<T, Output=T>
T $op &T	T: for<'a> $Op<&'a T, Output=T>
&T $op T	for<'a> &'a T: $Op<T, Output=T>
&T $op &T	for<'a> &'a T: $Op<&'a T, Output=T>

The for<'a> syntax refers to the Higher-Rank Trait Bounds(HRTB).

Using generic functions allows for clearer input handling, which simplifies the debugging.

Example

use std::ops::{Add, Mul};
use tfhe::prelude::*;
use tfhe::{generate_keys, set_server_key, ConfigBuilder, FheUint32, FheUint64};

pub fn ex1<'a, FheType, ClearType>(ct: &'a FheType, pt: ClearType) -> FheType
    where
        &'a FheType: Add<ClearType, Output = FheType>,
{
    ct + pt
}

pub fn ex2<'a, FheType, ClearType>(a: &'a FheType, b: &'a FheType, pt: ClearType) -> FheType
    where
        &'a FheType: Mul<&'a FheType, Output = FheType>,
        FheType: Add<ClearType, Output = FheType>,
{
    (a * b) + pt
}

pub fn ex3<FheType, ClearType>(a: FheType, b: FheType, pt: ClearType) -> FheType
    where
            for<'a> &'a FheType: Add<&'a FheType, Output = FheType>,
            FheType: Add<FheType, Output = FheType> + Add<ClearType, Output = FheType>,
{
    let tmp = (&a + &b) + (&a + &b);
    tmp + pt
}

pub fn ex4<FheType, ClearType>(a: FheType, b: FheType, pt: ClearType) -> FheType
    where
        FheType: Clone + Add<FheType, Output = FheType> + Add<ClearType, Output = FheType>,
{
    let tmp = (a.clone() + b.clone()) + (a.clone() + b.clone());
    tmp + pt
}

fn main() {
    let config = ConfigBuilder::default()
        .build();

    let (client_key, server_keys) = generate_keys(config);

    set_server_key(server_keys);

    // Use FheUint32
    {
        let clear_a = 46546u32;
        let clear_b = 6469u32;
        let clear_c = 64u32;

        let a = FheUint32::try_encrypt(clear_a, &client_key).unwrap();
        let b = FheUint32::try_encrypt(clear_b, &client_key).unwrap();
        assert_eq!(
            ex1(&clear_a, clear_c),
            ex1(&a, clear_c).decrypt(&client_key)
        );
        assert_eq!(
            ex2(&clear_a, &clear_b, clear_c),
            ex2(&a, &b, clear_c).decrypt(&client_key)
        );
        assert_eq!(
            ex3(clear_a, clear_b, clear_c),
            ex3(a.clone(), b.clone(), clear_c).decrypt(&client_key)
        );
        assert_eq!(
            ex4(clear_a, clear_b, clear_c),
            ex4(a, b, clear_c).decrypt(&client_key)
        );
    }

    // Use FheUint64
    {
        let clear_a = 46544866u64;
        let clear_b = 6469446677u64;
        let clear_c = 647897u64;

        let a = FheUint64::try_encrypt(clear_a, &client_key).unwrap();
        let b = FheUint64::try_encrypt(clear_b, &client_key).unwrap();
        assert_eq!(
            ex1(&clear_a, clear_c),
            ex1(&a, clear_c).decrypt(&client_key)
        );
        assert_eq!(
            ex2(&clear_a, &clear_b, clear_c),
            ex2(&a, &b, clear_c).decrypt(&client_key)
        );
        assert_eq!(
            ex3(clear_a, clear_b, clear_c),
            ex3(a.clone(), b.clone(), clear_c).decrypt(&client_key)
        );
        assert_eq!(
            ex4(clear_a, clear_b, clear_c),
            ex4(a, b, clear_c).decrypt(&client_key)
        );
    }
}