const_monty_form.rs

//! Implements `ConstMontyForm`s, supporting modular arithmetic with a constant modulus.

mod add;
pub(super) mod inv;
mod lincomb;
mod mul;
mod neg;
mod pow;
mod sub;

use self::inv::ConstMontyFormInverter;
use super::{div_by_2::div_by_2, reduction::montgomery_reduction, Retrieve, SafeGcdInverter};
use crate::{ConstZero, Limb, Odd, PrecomputeInverter, Uint};
use core::{fmt::Debug, marker::PhantomData};
use subtle::{Choice, ConditionallySelectable, ConstantTimeEq};

#[cfg(feature = "rand_core")]
use crate::{rand_core::RngCore, Random, RandomMod};

#[cfg(feature = "serde")]
use {
    crate::Encoding,
    serdect::serde::de::Error,
    serdect::serde::{Deserialize, Deserializer, Serialize, Serializer},
};

/// Macros to remove the boilerplate code when dealing with constant moduli.
#[macro_use]
mod macros;

/// The parameters to efficiently go to and from the Montgomery form for a given odd modulus.
///
/// An easy way to generate these parameters is using the [`impl_modulus!`][`crate::impl_modulus`]
/// macro. These parameters are constant, so they cannot be set at runtime.
///
/// Unfortunately, `LIMBS` must be generic for now until const generics are stabilized.
pub trait ConstMontyParams<const LIMBS: usize>:
    Copy + Debug + Default + Eq + Send + Sync + 'static
{
    /// Number of limbs required to encode the Montgomery form
    const LIMBS: usize;

    /// The constant modulus
    const MODULUS: Odd<Uint<LIMBS>>;
    /// 1 in Montgomery form
    const ONE: Uint<LIMBS>;
    /// `R^2 mod MODULUS`, used to move into Montgomery form
    const R2: Uint<LIMBS>;
    /// `R^3 mod MODULUS`, used to perform a multiplicative inverse
    const R3: Uint<LIMBS>;
    /// The lowest limbs of -(MODULUS^-1) mod R
    // We only need the LSB because during reduction this value is multiplied modulo 2**Limb::BITS.
    const MOD_NEG_INV: Limb;
    /// Leading zeros in the modulus, used to choose optimized algorithms
    const MOD_LEADING_ZEROS: u32;

    /// Precompute a Bernstein-Yang inverter for this modulus.
    ///
    /// Use [`ConstMontyFormInverter::new`] if you need `const fn` access.
    fn precompute_inverter<const UNSAT_LIMBS: usize>() -> ConstMontyFormInverter<Self, LIMBS>
    where
        Odd<Uint<LIMBS>>: PrecomputeInverter<
            Inverter = SafeGcdInverter<LIMBS, UNSAT_LIMBS>,
            Output = Uint<LIMBS>,
        >,
    {
        ConstMontyFormInverter::new()
    }
}

/// An integer in Montgomery form modulo `MOD`, represented using `LIMBS` limbs.
/// The modulus is constant, so it cannot be set at runtime.
///
/// Internally, the value is stored in Montgomery form (multiplied by MOD::ONE) until it is retrieved.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub struct ConstMontyForm<MOD: ConstMontyParams<LIMBS>, const LIMBS: usize> {
    montgomery_form: Uint<LIMBS>,
    phantom: PhantomData<MOD>,
}

#[cfg(feature = "zeroize")]
impl<MOD: ConstMontyParams<LIMBS>, const LIMBS: usize> zeroize::DefaultIsZeroes
    for ConstMontyForm<MOD, LIMBS>
{
}

impl<MOD: ConstMontyParams<LIMBS>, const LIMBS: usize> ConstMontyForm<MOD, LIMBS> {
    /// The representation of 0 mod `MOD`.
    pub const ZERO: Self = Self {
        montgomery_form: Uint::<LIMBS>::ZERO,
        phantom: PhantomData,
    };

    /// The representation of 1 mod `MOD`.
    pub const ONE: Self = Self {
        montgomery_form: MOD::ONE,
        phantom: PhantomData,
    };

    /// Internal helper function to convert to Montgomery form;
    /// this lets us cleanly wrap the constructors.
    const fn from_integer(integer: &Uint<LIMBS>) -> Self {
        let product = integer.split_mul(&MOD::R2);
        let montgomery_form =
            montgomery_reduction::<LIMBS>(&product, &MOD::MODULUS, MOD::MOD_NEG_INV);

        Self {
            montgomery_form,
            phantom: PhantomData,
        }
    }

    /// Instantiates a new [`ConstMontyForm`] that represents this `integer` mod `MOD`.
    pub const fn new(integer: &Uint<LIMBS>) -> Self {
        Self::from_integer(integer)
    }

    /// Retrieves the integer currently encoded in this [`ConstMontyForm`], guaranteed to be reduced.
    pub const fn retrieve(&self) -> Uint<LIMBS> {
        montgomery_reduction::<LIMBS>(
            &(self.montgomery_form, Uint::ZERO),
            &MOD::MODULUS,
            MOD::MOD_NEG_INV,
        )
    }

    /// Access the `ConstMontyForm` value in Montgomery form.
    pub const fn as_montgomery(&self) -> &Uint<LIMBS> {
        &self.montgomery_form
    }

    /// Mutably access the `ConstMontyForm` value in Montgomery form.
    pub fn as_montgomery_mut(&mut self) -> &mut Uint<LIMBS> {
        &mut self.montgomery_form
    }

    /// Create a `ConstMontyForm` from a value in Montgomery form.
    pub const fn from_montgomery(integer: Uint<LIMBS>) -> Self {
        Self {
            montgomery_form: integer,
            phantom: PhantomData,
        }
    }

    /// Extract the value from the `ConstMontyForm` in Montgomery form.
    pub const fn to_montgomery(&self) -> Uint<LIMBS> {
        self.montgomery_form
    }

    /// Performs division by 2, that is returns `x` such that `x + x = self`.
    pub const fn div_by_2(&self) -> Self {
        Self {
            montgomery_form: div_by_2(&self.montgomery_form, &MOD::MODULUS),
            phantom: PhantomData,
        }
    }
}

impl<MOD: ConstMontyParams<LIMBS> + Copy, const LIMBS: usize> ConditionallySelectable
    for ConstMontyForm<MOD, LIMBS>
{
    fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
        ConstMontyForm {
            montgomery_form: Uint::conditional_select(
                &a.montgomery_form,
                &b.montgomery_form,
                choice,
            ),
            phantom: PhantomData,
        }
    }
}

impl<MOD: ConstMontyParams<LIMBS>, const LIMBS: usize> ConstantTimeEq
    for ConstMontyForm<MOD, LIMBS>
{
    fn ct_eq(&self, other: &Self) -> Choice {
        ConstantTimeEq::ct_eq(&self.montgomery_form, &other.montgomery_form)
    }
}

impl<MOD: ConstMontyParams<LIMBS>, const LIMBS: usize> Default for ConstMontyForm<MOD, LIMBS> {
    fn default() -> Self {
        Self::ZERO
    }
}

impl<MOD: ConstMontyParams<LIMBS>, const LIMBS: usize> ConstZero for ConstMontyForm<MOD, LIMBS> {
    const ZERO: Self = Self::ZERO;
}

impl<MOD: ConstMontyParams<LIMBS>, const LIMBS: usize> num_traits::Zero
    for ConstMontyForm<MOD, LIMBS>
{
    fn zero() -> Self {
        Self::ZERO
    }

    fn is_zero(&self) -> bool {
        self.ct_eq(&Self::ZERO).into()
    }
}

#[cfg(feature = "rand_core")]
impl<MOD, const LIMBS: usize> Random for ConstMontyForm<MOD, LIMBS>
where
    MOD: ConstMontyParams<LIMBS>,
{
    #[inline]
    fn random(rng: &mut impl RngCore) -> Self {
        Self::new(&Uint::random_mod(rng, MOD::MODULUS.as_nz_ref()))
    }
}

impl<MOD: ConstMontyParams<LIMBS>, const LIMBS: usize> Retrieve for ConstMontyForm<MOD, LIMBS> {
    type Output = Uint<LIMBS>;
    fn retrieve(&self) -> Self::Output {
        self.retrieve()
    }
}

#[cfg(feature = "serde")]
impl<'de, MOD, const LIMBS: usize> Deserialize<'de> for ConstMontyForm<MOD, LIMBS>
where
    MOD: ConstMontyParams<LIMBS>,
    Uint<LIMBS>: Encoding,
{
    fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
    where
        D: Deserializer<'de>,
    {
        Uint::<LIMBS>::deserialize(deserializer).and_then(|montgomery_form| {
            if montgomery_form < MOD::MODULUS.0 {
                Ok(Self {
                    montgomery_form,
                    phantom: PhantomData,
                })
            } else {
                Err(D::Error::custom("montgomery form must be reduced"))
            }
        })
    }
}

#[cfg(feature = "serde")]
impl<MOD, const LIMBS: usize> Serialize for ConstMontyForm<MOD, LIMBS>
where
    MOD: ConstMontyParams<LIMBS>,
    Uint<LIMBS>: Encoding,
{
    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
    where
        S: Serializer,
    {
        self.montgomery_form.serialize(serializer)
    }
}