Types & Operations

This document explains the encryption types and operations supported by TFHE-rs.

Types

TFHE-rs supports two main types of encrypted data:

• FheUint: homomorphic equivalent of Rust unsigned integers u8, u16, ...

• FheInt: homomorphic equivalent of Rust signed integers i8, i16, ...

Integer

TFHE-rs uses integers to encrypt all messages which are larger than 4 bits.

Similar to Rust integers, you need to specify the bit size of data when declaring a variable:

    // let clear_a: u64 = 7;
let mut a = FheUint64::try_encrypt(clear_a, &keys)?;

// let clear_b: i8 = 3;
let mut b = FheInt8::try_encrypt(clear_b, &keys)?;

// let clear_c: u128 = 2;
let mut c = FheUint128::try_encrypt(clear_c, &keys)?;

Operations

TFHE-rs supports various operations on encrypted integers (Enc) of any size between 1 and 256 bits. These operations can also work between encrypted integers and clear integers (Int).

 name symbol Enc/Enc Enc/ Int Neg - Add + Sub - Mul * Div / Rem % Not ! BitAnd & BitOr | BitXor ^ Shr >> Shl << Min min Max max Greater than gt Greater or equal than ge Less than lt Less or equal than le Equal eq Cast (into dest type) cast_into Cast (from src type) cast_from Ternary operator if_then_else

Arithmetic operations

Homomorphic integer types (FheUint and FheInt) support the following arithmetic operations:

namesymboltype

-

Unary

+

Binary

-

Binary

*

Binary

/

Binary

%

Binary

Specifications for operations with zero:

• Division by zero: returns modulus - 1.

• Example: for FheUint8 (modulus = $2^8=256$), dividing by zero returns an ecryption of 255.

• Remainder operator: returns the first input unchanged.

• Example: if ct1 = FheUint8(63) and ct2 = FheUint8(0), then ct1 % ct2 returns FheUint8(63).

The following example shows how to perform arithmetic operations:

use tfhe::prelude::*;
use tfhe::{generate_keys, set_server_key, ConfigBuilder, FheInt8, FheUint8};

fn main() -> Result<(), Box<dyn std::error::Error>> {
let config = ConfigBuilder::default().build();
let (keys, server_keys) = generate_keys(config);
set_server_key(server_keys);

let clear_a = 15_u64;
let clear_b = 27_u64;
let clear_c = 43_u64;
let clear_d = -87_i64;

let mut a = FheUint8::try_encrypt(clear_a, &keys)?;
let mut b = FheUint8::try_encrypt(clear_b, &keys)?;
let mut c = FheUint8::try_encrypt(clear_c, &keys)?;
let mut d = FheInt8::try_encrypt(clear_d, &keys)?;

a = a * &b;     // Clear equivalent computations: 15 * 27 mod 256 = 149
b = &b + &c;    // Clear equivalent computations: 27 + 43 mod 256 = 70
b = b - 76u8;   // Clear equivalent computations: 70 - 76 mod 256 = 250
d = d - 13i8;   // Clear equivalent computations: -87 - 13 = 100 in [-128, 128[

let dec_a: u8 = a.decrypt(&keys);
let dec_b: u8 = b.decrypt(&keys);
let dec_d: i8 = d.decrypt(&keys);

assert_eq!(dec_a, ((clear_a * clear_b) % 256_u64) as u8);
assert_eq!(dec_b, (((clear_b  + clear_c).wrapping_sub(76_u64)) % 256_u64) as u8);
assert_eq!(dec_d, (clear_d - 13) as i8);

Ok(())
}

Bitwise operations

Homomorphic integer types support the following bitwise operations:

namesymboltype

!

Unary

&

Binary

|

Binary

^

Binary

>>

Binary

<<

Binary

rotate_right

Binary

rotate_left

Binary

The following example shows how to perform bitwise operations:

use tfhe::prelude::*;
use tfhe::{generate_keys, set_server_key, ConfigBuilder, FheUint8};

fn main() -> Result<(), Box<dyn std::error::Error>> {
let config = ConfigBuilder::default().build();
let (keys, server_keys) = generate_keys(config);
set_server_key(server_keys);

let clear_a = 164;
let clear_b = 212;

let mut a = FheUint8::try_encrypt(clear_a, &keys)?;
let mut b = FheUint8::try_encrypt(clear_b, &keys)?;

a = a ^ &b;
b = b ^ &a;
a = a ^ &b;

let dec_a: u8 = a.decrypt(&keys);
let dec_b: u8 = b.decrypt(&keys);

// We homomorphically swapped values using bitwise operations
assert_eq!(dec_a, clear_b);
assert_eq!(dec_b, clear_a);

Ok(())
}

Comparison operations

Homomorphic integers support comparison operations. However, due to Rust's limitations, you cannot overload comparison symbols. This is because Rust requires Boolean outputs from such operations, but homomorphic types return ciphertexts. Therefore, you should use the following methods, which conform to the naming conventions of Rust’s standard traits:

Supported operations:

namesymboltype

eq

Binary

ne

Binary

gt

Binary

ge

Binary

lt

Binary

le

Binary

The following example shows how to perform comparison operations:

use tfhe::prelude::*;
use tfhe::{generate_keys, set_server_key, ConfigBuilder, FheInt8};

fn main() -> Result<(), Box<dyn std::error::Error>> {
let config = ConfigBuilder::default().build();
let (keys, server_keys) = generate_keys(config);
set_server_key(server_keys);

let clear_a: i8 = -121;
let clear_b: i8 = 87;

let mut a = FheInt8::try_encrypt(clear_a, &keys)?;
let mut b = FheInt8::try_encrypt(clear_b, &keys)?;

let greater = a.gt(&b);
let greater_or_equal = a.ge(&b);
let lower = a.lt(&b);
let lower_or_equal = a.le(&b);
let equal = a.eq(&b);

let dec_gt = greater.decrypt(&keys);
let dec_ge = greater_or_equal.decrypt(&keys);
let dec_lt = lower.decrypt(&keys);
let dec_le = lower_or_equal.decrypt(&keys);
let dec_eq = equal.decrypt(&keys);

assert_eq!(dec_gt, clear_a > clear_b);
assert_eq!(dec_ge, clear_a >= clear_b);
assert_eq!(dec_lt, clear_a < clear_b);
assert_eq!(dec_le, clear_a <= clear_b);
assert_eq!(dec_eq, clear_a == clear_b);

Ok(())
}

Min/Max operations

Homomorphic integers support the min/max operations:

namesymboltype

Min

min

Binary

Max

max

Binary

The following example shows how to perform min/max operations:

use tfhe::prelude::*;
use tfhe::{generate_keys, set_server_key, ConfigBuilder, FheUint8};

fn main() -> Result<(), Box<dyn std::error::Error>> {
let config = ConfigBuilder::default().build();
let (keys, server_keys) = generate_keys(config);
set_server_key(server_keys);

let clear_a:u8 = 164;
let clear_b:u8 = 212;

let mut a = FheUint8::try_encrypt(clear_a, &keys)?;
let mut b = FheUint8::try_encrypt(clear_b, &keys)?;

let min = a.min(&b);
let max = a.max(&b);

let dec_min : u8 = min.decrypt(&keys);
let dec_max : u8 = max.decrypt(&keys);

assert_eq!(dec_min, u8::min(clear_a, clear_b));
assert_eq!(dec_max, u8::max(clear_a, clear_b));

Ok(())
}

Ternary conditional operations

The ternary conditional operator execute conditional instructions in the form if cond { choice_if } else { choice_else }.

namesymboltype

Ternary operator

if_then_else

Ternary

The syntax is encrypted_condition.if_then_else(encrypted_choice_if, encrypted_choice_else). The valid encrypted_condition must be an encryption of 0 or 1.

The following example shows how to perform ternary conditional operations:

use tfhe::prelude::*;
use tfhe::{generate_keys, set_server_key, ConfigBuilder, FheInt32};

fn main() -> Result<(), Box<dyn std::error::Error>> {
// Basic configuration to use homomorphic integers
let config = ConfigBuilder::default().build();

// Key generation
let (client_key, server_keys) = generate_keys(config);

let clear_a = 32i32;
let clear_b = -45i32;

// Encrypting the input data using the (private) client_key
// FheInt32: Encrypted equivalent to i32
let encrypted_a = FheInt32::try_encrypt(clear_a, &client_key)?;
let encrypted_b = FheInt32::try_encrypt(clear_b, &client_key)?;

// On the server side:
set_server_key(server_keys);

// Clear equivalent computations: 32 > -45
let encrypted_comp = &encrypted_a.gt(&encrypted_b);
let clear_res = encrypted_comp.decrypt(&client_key);
assert_eq!(clear_res, clear_a > clear_b);

// encrypted_comp is a FheBool, thus it encrypts a boolean value.
// This acts as a condition on which the
// if_then_else function can be applied on.
// Clear equivalent computations:
// if 32 > -45 {result = 32} else {result = -45}
let encrypted_res = &encrypted_comp.if_then_else(&encrypted_a, &encrypted_b);

let clear_res: i32 = encrypted_res.decrypt(&client_key);
assert_eq!(clear_res, clear_a);

Ok(())
}

Casting operations

You can cast between integer types using either the cast_from associated function or the cast_into method.

The following example shows how to perform casting operations:

use tfhe::prelude::*;
use tfhe::{generate_keys, set_server_key, ConfigBuilder, FheInt16, FheUint8, FheUint32, FheUint16};

fn main() -> Result<(), Box<dyn std::error::Error>> {
let config = ConfigBuilder::default().build();
let (client_key, server_key) = generate_keys(config);

// Casting requires server_key to set
// (encryptions/decryptions do not need server_key to be set)
set_server_key(server_key);

{
let clear = 12_837u16;
let a = FheUint16::encrypt(clear, &client_key);

// Downcasting
let a: FheUint8 = a.cast_into();
let da: u8 = a.decrypt(&client_key);
assert_eq!(da, clear as u8);

// Upcasting
let a: FheUint32 = a.cast_into();
let da: u32 = a.decrypt(&client_key);
assert_eq!(da, (clear as u8) as u32);
}

{
let clear = 12_837u16;
let a = FheUint16::encrypt(clear, &client_key);

// Upcasting
let a = FheUint32::cast_from(a);
let da: u32 = a.decrypt(&client_key);
assert_eq!(da, clear as u32);

// Downcasting
let a = FheUint8::cast_from(a);
let da: u8 = a.decrypt(&client_key);
assert_eq!(da, (clear as u32) as u8);
}

{
let clear = 12_837i16;
let a = FheInt16::encrypt(clear, &client_key);

// Casting from FheInt16 to FheUint16
let a = FheUint16::cast_from(a);
let da: u16 = a.decrypt(&client_key);
assert_eq!(da, clear as u16);
}

Ok(())
}

Boolean Operations

Native homomorphic Booleans support the following common Boolean operations:

namesymboltype

&

Binary

|

Binary

^

Binary

!

Unary

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