TFHE-rs includes two main types to represent encrypted data:
FheUint: this is the homomorphic equivalent of Rust unsigned integers u8, u16, ...
FheInt: this is the homomorphic equivalent of Rust (signed) integers i8, i16, ...
In the same manner as many programming languages, the number of bits used to represent the data must be chosen when declaring a variable. For instance:
// 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)?;
Operation list
The table below contains an overview of the available operations in TFHE-rs. The notation Enc (for Encypted) either refers to FheInt or FheUint, for any size between 1 and 256-bits.
More details, and further examples, are given in the following sections.
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
✔️
✔️
Lower than
lt
✔️
✔️
Lower or equal than
le
✔️
✔️
Equal
eq
✔️
✔️
Cast (into dest type)
cast_into
✔️
✖️
Cast (from src type)
cast_from
✔️
✖️
Ternary operator
if_then_else
✔️
✖️
Integer
In TFHE-rs, integers are used to encrypt all messages which are larger than 4 bits. All supported operations are listed below.
Arithmetic operations.
Homomorphic integer types support arithmetic operations.
For division by 0, the convention is to return modulus - 1. For instance, for FheUint8, the modulus is 28=256, so a division by 0 will return an encryption of 255. For the remainder operator, the convention is to return the first input without any modification. For instance, if ct1 = FheUint8(63) and ct2 = FheUint8(0) then ct1 % ct2 will return FheUint8(63).
A simple example of how to use these operations:
use tfhe::prelude::*;use tfhe::{generate_keys, set_server_key, ConfigBuilder, FheInt8, FheUint8};fnmain() ->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;letmut a =FheUint8::try_encrypt(clear_a, &keys)?;letmut b =FheUint8::try_encrypt(clear_b, &keys)?;letmut c =FheUint8::try_encrypt(clear_c, &keys)?;letmut 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) asu8);assert_eq!(dec_b, (((clear_b + clear_c).wrapping_sub(76_u64)) %256_u64) asu8);assert_eq!(dec_d, (clear_d -13) asi8);Ok(())}
Bitwise operations.
Homomorphic integer types support some bitwise operations.
use tfhe::prelude::*;use tfhe::{generate_keys, set_server_key, ConfigBuilder, FheUint8};fnmain() ->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;letmut a =FheUint8::try_encrypt(clear_a, &keys)?;letmut 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 operationsassert_eq!(dec_a, clear_b);assert_eq!(dec_b, clear_a);Ok(())}
Comparisons.
Homomorphic integers support comparison operations.
Due to some Rust limitations, it is not possible to overload the comparison symbols because of the inner definition of the operations. This is because Rust expects to have a Boolean as an output, whereas a ciphertext is returned when using homomorphic types.
You will need to use different methods instead of using symbols for the comparisons. These methods follow the same naming conventions as the two standard Rust traits:
Homomorphic integers support the min/max operations.
name
symbol
type
Min
min
Binary
Max
max
Binary
A simple example of how to use these operations:
use tfhe::prelude::*;use tfhe::{generate_keys, set_server_key, ConfigBuilder, FheUint8};fnmain() ->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;letmut a =FheUint8::try_encrypt(clear_a, &keys)?;letmut 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 operator.
The ternary conditional operator allows computing conditional instructions of the form if cond { choice_if } else { choice_else }.
name
symbol
type
Ternary operator
if_then_else
Ternary
The syntax is encrypted_condition.if_then_else(encrypted_choice_if, encrypted_choice_else). The encrypted_condition should be an encryption of 0 or 1 in order to be valid.
use tfhe::prelude::*;use tfhe::{generate_keys, set_server_key, ConfigBuilder, FheInt32};fnmain() ->Result<(), Box<dyn std::error::Error>> {// Basic configuration to use homomorphic integerslet config =ConfigBuilder::default().build();// Key generationlet (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 i32let 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 > -45let 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.
Casting between integer types is possible via the cast_from associated function or the cast_into method.
use tfhe::prelude::*;use tfhe::{generate_keys, set_server_key, ConfigBuilder, FheInt16, FheUint8, FheUint32, FheUint16};fnmain() ->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);// Downcastinglet a:FheUint8= a.cast_into();let da:u8= a.decrypt(&client_key);assert_eq!(da, clear asu8);// Upcastinglet a:FheUint32= a.cast_into();let da:u32= a.decrypt(&client_key);assert_eq!(da, (clear asu8) asu32); } {let clear =12_837u16;let a =FheUint16::encrypt(clear, &client_key);// Upcastinglet a =FheUint32::cast_from(a);let da:u32= a.decrypt(&client_key);assert_eq!(da, clear asu32);// Downcastinglet a =FheUint8::cast_from(a);let da:u8= a.decrypt(&client_key);assert_eq!(da, (clear asu32) asu8); } {let clear =12_837i16;let a =FheInt16::encrypt(clear, &client_key);// Casting from FheInt16 to FheUint16let a =FheUint16::cast_from(a);let da:u16= a.decrypt(&client_key);assert_eq!(da, clear asu16); }Ok(())}
Boolean Operations
Native homomorphic Booleans support common Boolean operations.