Native small homomorphic integer types (e.g., FheUint3 or FheUint4) allow to easily compute various operations. In general, computing over encrypted data is as easy as computing over clear data, since the same operation symbol is used. For instance, the addition between two ciphertexts is done using the symbol + between two FheUint. Similarly, many operations can be computed between a clear value (i.e. a scalar) and a ciphertext.
In Rust native types, any operation is modular. In Rust, u8, computations are done modulus 2^8. The similar idea is applied for FheUintX, where operations are done modulus 2^X. For instance, in the type FheUint3, operations are done modulus 8.
Arithmetic operations
Small homomorphic integer types support all common arithmetic operations, meaning +, -, x, /, mod.
The division operation implements a subtlety: since data is encrypted, it might be possible to compute a division by 0. In this case, the division is tweaked so that dividing by 0 returns 0.
use concrete::prelude::*;use concrete::{generate_keys, set_server_key, ConfigBuilder, FheUint3};fnmain() ->Result<(), Box<dyn std::error::Error>> {let config =ConfigBuilder::all_disabled().enable_default_uint3().build();let (keys, server_keys) =generate_keys(config);set_server_key(server_keys);let clear_a =7;let clear_b =3;letmut a =FheUint3::try_encrypt(clear_a, &keys)?;letmut b =FheUint3::try_encrypt(clear_b, &keys)?; a = a ^&b; b = b ^&a; a = a ^&b;let dec_a = a.decrypt(&keys);let dec_b = b.decrypt(&keys);// We homomorphically swapped values using bitwise operationsassert_eq!(dec_a, clear_b);assert_eq!(dec_b, clear_a);Ok(())}
Comparisons
Small homomorphic integer types support comparison operations.
However, due to some Rust limitations, this is not possible to overload the comparison symbols because of the inner definition of the operations. To be precise, Rust expects to have a boolean as output, whereas a ciphertext encrypted the result is returned when using homomorphic types.
So instead of using symbols for the comparisons, you will need to use the different methods. These methods follow the same naming that the 2 standard Rust trait
Using the shortint types offers the possibility to evaluate bivariate functions, i.e., functions that takes two ciphertexts as input.
In what follows, a simple code example:
use concrete::prelude::*;use concrete::{generate_keys, set_server_key, ConfigBuilder, FheUint2};fnmain() ->Result<(), Box<dyn std::error::Error>> {let config =ConfigBuilder::all_disabled().enable_default_uint2().build();let (keys, server_keys) =generate_keys(config);set_server_key(server_keys);let clear_a =1;let clear_b =3;let a =FheUint2::try_encrypt(clear_a, &keys)?;let b =FheUint2::try_encrypt(clear_b, &keys)?;let c = a.bivariate_function(&b, std::cmp::max);let decrypted = c.decrypt(&keys);assert_eq!(decrypted, std::cmp::max(clear_a, clear_b) asu8);Ok(())}
Integer.
In the same vein, native homomorphic types supports modular operations. At the moment, integers are more limited than shortint, but operations will be added soon.
Arithmetic operations
Homomorphic integer types support arithmetic operations.
use concrete::prelude::*;use concrete::{generate_keys, set_server_key, ConfigBuilder, FheUint8};fnmain() ->Result<(), Box<dyn std::error::Error>> {let config =ConfigBuilder::all_disabled().enable_default_uint8().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(())}
Univariate function evaluations
As for shortints, homomorphic integers support the evaluation of univariate functions.