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use super::{CheckError, CiphertextNoiseDegree, LookupTable, ServerKey};
use crate::core_crypto::prelude::container::Container;
use crate::shortint::ciphertext::{Degree, MaxDegree, NoiseLevel};
use crate::shortint::server_key::add::unchecked_add_assign;
use crate::shortint::{Ciphertext, MessageModulus};
use std::cmp::Ordering;
#[must_use]
pub struct BivariateLookupTable<C: Container<Element = u64>> {
// A bivariate lookup table is an univariate loolookup table
// where the message space is shared to encode
// 2 values
pub acc: LookupTable<C>,
// By how much we shift the lhs in the LUT
pub ct_right_modulus: MessageModulus,
}
pub type BivariateLookupTableOwned = BivariateLookupTable<Vec<u64>>;
pub type BivariateLookupTableMutView<'a> = BivariateLookupTable<&'a mut [u64]>;
pub type BivariateLookupTableView<'a> = BivariateLookupTable<&'a [u64]>;
impl<C: Container<Element = u64>> BivariateLookupTable<C> {
pub fn is_bivariate_pbs_possible(
&self,
server_key: &ServerKey,
lhs: CiphertextNoiseDegree,
rhs: CiphertextNoiseDegree,
) -> Result<(), CheckError> {
ciphertexts_can_be_packed_without_exceeding_space_or_noise(
server_key,
lhs,
rhs,
self.ct_right_modulus.0,
)?;
Ok(())
}
}
/// Returns whether it is possible to pack lhs and rhs into a unique
/// ciphertext without exceeding the max storable value using the formula:
/// `unique_ciphertext = (lhs * factor) + rhs`
fn ciphertexts_can_be_packed_without_exceeding_space_or_noise(
server_key: &ServerKey,
lhs: CiphertextNoiseDegree,
rhs: CiphertextNoiseDegree,
factor: usize,
) -> Result<(), CheckError> {
let final_degree = (lhs.degree * factor) + rhs.degree;
let max_degree =
MaxDegree::from_msg_carry_modulus(server_key.message_modulus, server_key.carry_modulus);
max_degree.validate(final_degree)?;
server_key
.max_noise_level
.validate(lhs.noise_level * factor + rhs.noise_level)?;
if rhs.degree.get() >= factor {
return Err(CheckError::UnscaledScaledOverlap {
unscaled_degree: rhs.degree,
scale: factor as u8,
});
}
Ok(())
}
impl ServerKey {
/// Generates a bivariate accumulator
pub fn generate_lookup_table_bivariate_with_factor<F>(
&self,
f: F,
left_message_scaling: MessageModulus,
) -> BivariateLookupTableOwned
where
F: Fn(u64, u64) -> u64,
{
// Depending on the factor used, rhs and / or lhs may have carries
// (degree >= message_modulus) which is why we need to apply the message_modulus
// to clear them
let factor_u64 = left_message_scaling.0 as u64;
let message_modulus = self.message_modulus.0 as u64;
let wrapped_f = |input: u64| -> u64 {
let lhs = (input / factor_u64) % message_modulus;
let rhs = (input % factor_u64) % message_modulus;
f(lhs, rhs)
};
let accumulator = self.generate_lookup_table(wrapped_f);
BivariateLookupTable {
acc: accumulator,
ct_right_modulus: left_message_scaling,
}
}
/// Constructs the lookup table for a given bivariate function as input.
///
/// # Example
///
/// ```rust
/// use tfhe::shortint::gen_keys;
/// use tfhe::shortint::parameters::PARAM_MESSAGE_2_CARRY_2_KS_PBS;
///
/// // Generate the client key and the server key:
/// let (cks, sks) = gen_keys(PARAM_MESSAGE_2_CARRY_2_KS_PBS);
///
/// let msg_1 = 3;
/// let msg_2 = 2;
///
/// let ct1 = cks.encrypt(msg_1);
/// let ct2 = cks.encrypt(msg_2);
///
/// let f = |x, y| (x + y) % 4;
///
/// let acc = sks.generate_lookup_table_bivariate(f);
/// acc.is_bivariate_pbs_possible(&sks, ct1.noise_degree(), ct2.noise_degree())
/// .unwrap();
/// let ct_res = sks.apply_lookup_table_bivariate(&ct1, &ct2, &acc);
///
/// let dec = cks.decrypt(&ct_res);
/// assert_eq!(dec, f(msg_1, msg_2));
/// ```
pub fn generate_lookup_table_bivariate<F>(&self, f: F) -> BivariateLookupTableOwned
where
F: Fn(u64, u64) -> u64,
{
self.generate_lookup_table_bivariate_with_factor(f, self.message_modulus)
}
/// Compute a keyswitch and programmable bootstrap.
///
/// # Example
///
/// ```rust
/// use tfhe::shortint::gen_keys;
/// use tfhe::shortint::parameters::PARAM_MESSAGE_2_CARRY_2_KS_PBS;
///
/// // Generate the client key and the server key:
/// let (cks, sks) = gen_keys(PARAM_MESSAGE_2_CARRY_2_KS_PBS);
///
/// let msg: u64 = 3;
/// let msg2: u64 = 2;
/// let ct1 = cks.encrypt(msg);
/// let ct2 = cks.encrypt(msg2);
/// let modulus = cks.parameters.message_modulus().0 as u64;
///
/// // Generate the lookup table for the function f: x, y -> (x * y * x) mod 4
/// let acc = sks.generate_lookup_table_bivariate(|x, y| x * y * x % modulus);
/// let ct_res = sks.unchecked_apply_lookup_table_bivariate(&ct1, &ct2, &acc);
///
/// let dec = cks.decrypt(&ct_res);
/// assert_eq!(dec, (msg * msg2 * msg) % modulus);
/// ```
pub fn unchecked_apply_lookup_table_bivariate(
&self,
ct_left: &Ciphertext,
ct_right: &Ciphertext,
acc: &BivariateLookupTableOwned,
) -> Ciphertext {
let mut ct_res = ct_left.clone();
self.unchecked_apply_lookup_table_bivariate_assign(&mut ct_res, ct_right, acc);
ct_res
}
pub fn unchecked_apply_lookup_table_bivariate_assign(
&self,
ct_left: &mut Ciphertext,
ct_right: &Ciphertext,
acc: &BivariateLookupTableOwned,
) {
let modulus = (ct_right.degree.get() + 1) as u64;
assert!(modulus <= acc.ct_right_modulus.0 as u64);
self.unchecked_scalar_mul_assign(ct_left, acc.ct_right_modulus.0 as u8);
unchecked_add_assign(ct_left, ct_right);
// Compute the PBS
self.apply_lookup_table_assign(ct_left, &acc.acc);
}
/// Compute a keyswitch and programmable bootstrap.
///
/// # Example
///
/// ```rust
/// use tfhe::shortint::gen_keys;
/// use tfhe::shortint::parameters::PARAM_MESSAGE_2_CARRY_2_KS_PBS;
///
/// // Generate the client key and the server key:
/// let (cks, sks) = gen_keys(PARAM_MESSAGE_2_CARRY_2_KS_PBS);
///
/// let msg: u64 = 3;
/// let msg2: u64 = 2;
/// let ct1 = cks.encrypt(msg);
/// let ct2 = cks.encrypt(msg2);
/// let modulus = cks.parameters.message_modulus().0 as u64;
///
/// // Generate the lookup table for the function f: x, y -> (x * y * x) mod 4
/// let acc = sks.generate_lookup_table_bivariate(|x, y| x * y * x % modulus);
/// let ct_res = sks.apply_lookup_table_bivariate(&ct1, &ct2, &acc);
///
/// let dec = cks.decrypt(&ct_res);
/// assert_eq!(dec, (msg * msg2 * msg) % modulus);
/// ```
pub fn apply_lookup_table_bivariate(
&self,
ct_left: &Ciphertext,
ct_right: &Ciphertext,
acc: &BivariateLookupTableOwned,
) -> Ciphertext {
let ct_left_clean;
let ct_right_clean;
let (ct_left, ct_right) = if self
.is_functional_bivariate_pbs_possible(ct_left.noise_degree(), ct_right.noise_degree())
.is_err()
{
// After the message_extract, we'll have ct_left, ct_right in [0, message_modulus[
// so the factor has to be message_modulus
assert_eq!(ct_right.message_modulus.0, acc.ct_right_modulus.0);
ct_left_clean = self.message_extract(ct_left);
ct_right_clean = self.message_extract(ct_right);
(&ct_left_clean, &ct_right_clean)
} else {
(ct_left, ct_right)
};
self.is_functional_bivariate_pbs_possible(ct_left.noise_degree(), ct_right.noise_degree())
.unwrap();
self.unchecked_apply_lookup_table_bivariate(ct_left, ct_right, acc)
}
pub fn apply_lookup_table_bivariate_assign(
&self,
ct_left: &mut Ciphertext,
ct_right: &mut Ciphertext,
acc: &BivariateLookupTableOwned,
) {
if self
.is_functional_bivariate_pbs_possible(ct_left.noise_degree(), ct_right.noise_degree())
.is_err()
{
// After the message_extract, we'll have ct_left, ct_right in [0, message_modulus[
// so the factor has to be message_modulus
assert_eq!(ct_right.message_modulus.0, acc.ct_right_modulus.0);
self.message_extract_assign(ct_left);
self.message_extract_assign(ct_right);
}
self.is_functional_bivariate_pbs_possible(ct_left.noise_degree(), ct_right.noise_degree())
.unwrap();
self.unchecked_apply_lookup_table_bivariate_assign(ct_left, ct_right, acc);
}
/// Generic programmable bootstrap where messages are concatenated into one ciphertext to
/// evaluate a bivariate function. This is used to apply many binary operations (comparisons,
/// multiplications, division).
pub fn unchecked_evaluate_bivariate_function<F>(
&self,
ct_left: &Ciphertext,
ct_right: &Ciphertext,
f: F,
) -> Ciphertext
where
F: Fn(u64, u64) -> u64,
{
let mut ct_res = ct_left.clone();
self.unchecked_evaluate_bivariate_function_assign(&mut ct_res, ct_right, f);
ct_res
}
pub fn unchecked_evaluate_bivariate_function_assign<F>(
&self,
ct_left: &mut Ciphertext,
ct_right: &Ciphertext,
f: F,
) where
F: Fn(u64, u64) -> u64,
{
// Generate the lookup _table for the function
let factor = MessageModulus(ct_right.degree.get() + 1);
let lookup_table = self.generate_lookup_table_bivariate_with_factor(f, factor);
self.unchecked_apply_lookup_table_bivariate_assign(ct_left, ct_right, &lookup_table);
}
/// Verify if a functional bivariate pbs can be applied on ct_left and ct_right.
pub fn is_functional_bivariate_pbs_possible(
&self,
ct1: CiphertextNoiseDegree,
ct2: CiphertextNoiseDegree,
) -> Result<(), CheckError> {
ciphertexts_can_be_packed_without_exceeding_space_or_noise(
self,
ct1,
ct2,
ct2.degree.get() + 1,
)?;
Ok(())
}
pub fn smart_evaluate_bivariate_function_assign<F>(
&self,
ct_left: &mut Ciphertext,
ct_right: &mut Ciphertext,
f: F,
) where
F: Fn(u64, u64) -> u64,
{
*ct_left = self.smart_evaluate_bivariate_function(ct_left, ct_right, f);
}
pub fn smart_evaluate_bivariate_function<F>(
&self,
ct_left: &mut Ciphertext,
ct_right: &mut Ciphertext,
f: F,
) -> Ciphertext
where
F: Fn(u64, u64) -> u64,
{
let ScalingOperation {
order,
scaled_behavior,
unscaled_bootstrapped,
scale,
} = self
.get_best_bivariate_scaling(ct_left, ct_right)
.expect("Current parameters can't be used to make a bivariate function evaluation");
let (ct_to_scale, unscaled_ct) = match order {
Order::ScaleLeft => (ct_left, ct_right),
Order::ScaleRight => (ct_right, ct_left),
};
if unscaled_bootstrapped {
self.message_extract_assign(unscaled_ct);
}
let scaled = match scaled_behavior {
ScaledBehavior::Scaled => self.unchecked_scalar_mul(ct_to_scale, scale),
ScaledBehavior::BootstrappedThenScaled => {
self.message_extract_assign(ct_to_scale);
self.unchecked_scalar_mul(ct_to_scale, scale)
}
ScaledBehavior::ScaledInBootstrap => {
let lookup_table = self
.generate_lookup_table(|a| (a % self.message_modulus.0 as u64) * scale as u64);
self.apply_lookup_table(ct_to_scale, &lookup_table)
}
};
let temp = self.unchecked_add(&scaled, unscaled_ct);
let lookup_table = match order {
Order::ScaleLeft => {
self.generate_lookup_table_bivariate_with_factor(f, MessageModulus(scale as usize))
}
Order::ScaleRight => self.generate_lookup_table_bivariate_with_factor(
|rhs: u64, lhs: u64| f(lhs, rhs),
MessageModulus(scale as usize),
),
};
self.apply_lookup_table(&temp, &lookup_table.acc)
}
/// To apply a bivariate function to two inputs, we must have both their messages on the same
/// ciphertexts To do that, we add a shift of an input 1 to the other input 2
/// But we must ensure that:
/// - The carry of the input 2 does not overlap with input 1 message
/// - The padding bit is clean
/// - The noise is not too high
/// We have multiple possibilities:
/// - choose which input to shift
/// - bootstrap the unscaled input (less noise and allows for a smaller scale as not carry
/// overlapping is possible) or not
/// - do not bootstrap the scaled input (cheaper), scale it in a bootstrap (least noise) or
/// bootstrap it then scale it (the input is cleaner for other operations)
/// This function choose the solution with the smallest cost and in case of equality, with the
/// most cleaned inputs
fn get_best_bivariate_scaling(
&self,
ct_left: &Ciphertext,
ct_right: &Ciphertext,
) -> Option<ScalingOperation> {
let valid = |scaled_noise_degree: CiphertextNoiseDegree,
unscaled_noise_degree: CiphertextNoiseDegree| {
let valid_degree = self
.max_degree
.validate(scaled_noise_degree.degree + unscaled_noise_degree.degree)
.is_ok();
let valid_noise = self
.max_noise_level
.validate(scaled_noise_degree.noise_level + unscaled_noise_degree.noise_level)
.is_ok();
valid_degree && valid_noise
};
[Order::ScaleLeft, Order::ScaleRight]
.into_iter()
.flat_map(move |order| {
let (scaled_ct, unscaled_ct) = match order {
Order::ScaleLeft => (ct_left, ct_right),
Order::ScaleRight => (ct_right, ct_left),
};
[false, true]
.into_iter()
.flat_map(move |unscaled_bootstrapped| {
let unscaled_noise_degree = if unscaled_bootstrapped {
unscaled_ct.noise_degree_if_bootstrapped()
} else {
unscaled_ct.noise_degree()
};
let scale = unscaled_noise_degree.degree.get() as u8 + 1;
[
ScaledBehavior::Scaled,
ScaledBehavior::BootstrappedThenScaled,
ScaledBehavior::ScaledInBootstrap,
]
.into_iter()
.filter_map(move |scaled_behavior| {
let scaled_noise_degree = match scaled_behavior {
ScaledBehavior::Scaled => scaled_ct.noise_degree_if_scaled(scale),
ScaledBehavior::BootstrappedThenScaled => {
scaled_ct.noise_degree_if_bootstrapped_then_scaled(scale)
}
ScaledBehavior::ScaledInBootstrap => {
scaled_ct.noise_degree_if_scaled_in_bootstrap(scale)
}
};
if valid(scaled_noise_degree, unscaled_noise_degree) {
Some(ScalingOperation {
order,
scaled_behavior,
unscaled_bootstrapped,
scale,
})
} else {
None
}
})
})
})
.max_by(
|op1, op2| match op1.number_of_pbs().cmp(&op2.number_of_pbs()) {
// If op1 has less pbs,
// we want it to dominate (Greater) op2 (as we take the max)
Ordering::Less => Ordering::Greater,
Ordering::Greater => Ordering::Less,
// op1 and op2 have as many pbs,
// if op1 has more cleaned inputs, we want it to dominate op2
Ordering::Equal => op1.cleaned_inputs().cmp(&op2.cleaned_inputs()),
},
)
}
}
#[derive(Copy, Clone, Debug)]
enum Order {
ScaleLeft,
ScaleRight,
}
#[derive(Copy, Clone, Debug)]
enum ScaledBehavior {
Scaled,
BootstrappedThenScaled,
ScaledInBootstrap,
}
#[derive(Copy, Clone, Debug)]
struct ScalingOperation {
order: Order,
scaled_behavior: ScaledBehavior,
unscaled_bootstrapped: bool,
scale: u8,
}
impl ScalingOperation {
fn cleaned_inputs(self) -> usize {
let scaled_bootstapped_inplace =
matches!(self.scaled_behavior, ScaledBehavior::BootstrappedThenScaled);
usize::from(self.unscaled_bootstrapped) + usize::from(scaled_bootstapped_inplace)
}
fn number_of_pbs(self) -> usize {
let scaled_bootstapped = matches!(
self.scaled_behavior,
ScaledBehavior::BootstrappedThenScaled | ScaledBehavior::ScaledInBootstrap
);
usize::from(self.unscaled_bootstrapped) + usize::from(scaled_bootstapped)
}
}
impl Ciphertext {
fn noise_degree_if_scaled(&self, scale: u8) -> CiphertextNoiseDegree {
CiphertextNoiseDegree {
noise_level: self.noise_level() * scale as usize,
degree: self.degree * scale as usize,
}
}
fn noise_degree_if_bootstrapped_then_scaled(&self, scale: u8) -> CiphertextNoiseDegree {
let CiphertextNoiseDegree {
noise_level: noise,
degree,
} = self.noise_degree_if_bootstrapped();
CiphertextNoiseDegree {
noise_level: noise * scale as usize,
degree: degree * scale as usize,
}
}
fn noise_degree_if_scaled_in_bootstrap(&self, scale: u8) -> CiphertextNoiseDegree {
CiphertextNoiseDegree {
noise_level: NoiseLevel::NOMINAL,
degree: Degree::new(self.degree.get().min(self.message_modulus.0 - 1)) * scale as usize,
}
}
}