Struct oberon::inner_types::elliptic_curve::bigint::modular::constant_mod::Residue

pub struct Residue<MOD, const LIMBS: usize>where
    MOD: ResidueParams<LIMBS>,{ /* private fields */ }

Expand description

A residue mod MOD, represented using LIMBS limbs. The modulus of this residue is constant, so it cannot be set at runtime.

Implementations§

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impl<MOD, const LIMBS: usize> Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

pub const fn add(&self, rhs: &Residue<MOD, LIMBS>) -> Residue<MOD, LIMBS>

Adds rhs.

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impl<MOD, const LIMBS: usize> Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

pub const fn invert(&self) -> (Residue<MOD, LIMBS>, CtChoice)

Computes the residue self^-1 representing the multiplicative inverse of self. I.e. self * self^-1 = 1. If the number was invertible, the second element of the tuple is the truthy value, otherwise it is the falsy value (in which case the first element’s value is unspecified).

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impl<MOD, const LIMBS: usize> Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

pub const fn mul(&self, rhs: &Residue<MOD, LIMBS>) -> Residue<MOD, LIMBS>

Multiplies by rhs.

pub const fn square(&self) -> Residue<MOD, LIMBS>

Computes the (reduced) square of a residue.

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impl<MOD, const LIMBS: usize> Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

pub const fn neg(&self) -> Residue<MOD, LIMBS>

Negates the number.

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impl<MOD, const LIMBS: usize> Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

pub const fn pow(&self, exponent: &Uint<LIMBS>) -> Residue<MOD, LIMBS>

Raises to the exponent power.

pub const fn pow_bounded_exp( &self, exponent: &Uint<LIMBS>, exponent_bits: usize ) -> Residue<MOD, LIMBS>

Raises to the exponent power, with exponent_bits representing the number of (least significant) bits to take into account for the exponent.

NOTE: exponent_bits may be leaked in the time pattern.

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impl<MOD, const LIMBS: usize> Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

pub const fn sub(&self, rhs: &Residue<MOD, LIMBS>) -> Residue<MOD, LIMBS>

Subtracts rhs.

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impl<MOD, const LIMBS: usize> Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

pub const ZERO: Residue<MOD, LIMBS> = Self{ montgomery_form: Uint<LIMBS>::ZERO, phantom: PhantomData,}

The representation of 0 mod MOD.

pub const ONE: Residue<MOD, LIMBS> = Self{ montgomery_form: MOD::R, phantom: PhantomData,}

The representation of 1 mod MOD.

pub const fn new(integer: &Uint<LIMBS>) -> Residue<MOD, LIMBS>

Instantiates a new Residue that represents this integer mod MOD.

pub const fn retrieve(&self) -> Uint<LIMBS>

Retrieves the integer currently encoded in this Residue, guaranteed to be reduced.

pub fn div_by_2(&self) -> Residue<MOD, LIMBS>

Performs the modular division by 2, that is for given x returns y such that y * 2 = x mod p. This means:

if x is even, returns x / 2,
if x is odd, returns (x + p) / 2 (since the modulus p in Montgomery form is always odd, this divides entirely).

Trait Implementations§

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impl<MOD, const LIMBS: usize> Add<&Residue<MOD, LIMBS>> for &Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

The resulting type after applying the + operator.

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fn add(self, rhs: &Residue<MOD, LIMBS>) -> Residue<MOD, LIMBS>

Performs the + operation. Read more

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impl<MOD, const LIMBS: usize> Add<&Residue<MOD, LIMBS>> for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

The resulting type after applying the + operator.

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fn add(self, rhs: &Residue<MOD, LIMBS>) -> Residue<MOD, LIMBS>

Performs the + operation. Read more

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impl<MOD, const LIMBS: usize> Add<Residue<MOD, LIMBS>> for &Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

The resulting type after applying the + operator.

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fn add(self, rhs: Residue<MOD, LIMBS>) -> Residue<MOD, LIMBS>

Performs the + operation. Read more

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impl<MOD, const LIMBS: usize> Add<Residue<MOD, LIMBS>> for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

The resulting type after applying the + operator.

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fn add(self, rhs: Residue<MOD, LIMBS>) -> Residue<MOD, LIMBS>

Performs the + operation. Read more

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impl<MOD, const LIMBS: usize> AddAssign<&Residue<MOD, LIMBS>> for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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fn add_assign(&mut self, rhs: &Residue<MOD, LIMBS>)

Performs the += operation. Read more

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impl<MOD, const LIMBS: usize> AddAssign<Residue<MOD, LIMBS>> for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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fn add_assign(&mut self, rhs: Residue<MOD, LIMBS>)

Performs the += operation. Read more

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impl<MOD, const LIMBS: usize> Clone for Residue<MOD, LIMBS>where MOD: Clone + ResidueParams<LIMBS>,

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fn clone(&self) -> Residue<MOD, LIMBS>

Returns a copy of the value. Read more

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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more

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impl<MOD, const LIMBS: usize> ConditionallySelectable for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS> + Copy,

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fn conditional_select( a: &Residue<MOD, LIMBS>, b: &Residue<MOD, LIMBS>, choice: Choice ) -> Residue<MOD, LIMBS>

Select a or b according to choice. Read more

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fn conditional_assign(&mut self, other: &Self, choice: Choice)

Conditionally assign other to self, according to choice. Read more

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fn conditional_swap(a: &mut Self, b: &mut Self, choice: Choice)

Conditionally swap self and other if choice == 1; otherwise, reassign both unto themselves. Read more

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impl<MOD, const LIMBS: usize> ConstantTimeEq for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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fn ct_eq(&self, other: &Residue<MOD, LIMBS>) -> Choice

Determine if two items are equal. Read more

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fn ct_ne(&self, other: &Self) -> Choice

Determine if two items are NOT equal. Read more

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impl<MOD, const LIMBS: usize> Debug for Residue<MOD, LIMBS>where MOD: Debug + ResidueParams<LIMBS>,

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fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter. Read more

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impl<MOD, const LIMBS: usize> Default for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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fn default() -> Residue<MOD, LIMBS>

Returns the “default value” for a type. Read more

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impl<MOD, const LIMBS: usize> Invert for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = CtOption<Residue<MOD, LIMBS>>

Output of the inversion.

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fn invert(&self) -> <Residue<MOD, LIMBS> as Invert>::Output

Computes the inverse.

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impl<MOD, const LIMBS: usize> Mul<&Residue<MOD, LIMBS>> for &Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

The resulting type after applying the * operator.

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fn mul(self, rhs: &Residue<MOD, LIMBS>) -> Residue<MOD, LIMBS>

Performs the * operation. Read more

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impl<MOD, const LIMBS: usize> Mul<&Residue<MOD, LIMBS>> for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

The resulting type after applying the * operator.

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fn mul(self, rhs: &Residue<MOD, LIMBS>) -> Residue<MOD, LIMBS>

Performs the * operation. Read more

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impl<MOD, const LIMBS: usize> Mul<Residue<MOD, LIMBS>> for &Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

The resulting type after applying the * operator.

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fn mul(self, rhs: Residue<MOD, LIMBS>) -> Residue<MOD, LIMBS>

Performs the * operation. Read more

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impl<MOD, const LIMBS: usize> Mul<Residue<MOD, LIMBS>> for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

The resulting type after applying the * operator.

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fn mul(self, rhs: Residue<MOD, LIMBS>) -> Residue<MOD, LIMBS>

Performs the * operation. Read more

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impl<MOD, const LIMBS: usize> MulAssign<&Residue<MOD, LIMBS>> for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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fn mul_assign(&mut self, rhs: &Residue<MOD, LIMBS>)

Performs the *= operation. Read more

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impl<MOD, const LIMBS: usize> MulAssign<Residue<MOD, LIMBS>> for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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fn mul_assign(&mut self, rhs: Residue<MOD, LIMBS>)

Performs the *= operation. Read more

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impl<MOD, const LIMBS: usize> Neg for &Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

The resulting type after applying the - operator.

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fn neg(self) -> Residue<MOD, LIMBS>

Performs the unary - operation. Read more

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impl<MOD, const LIMBS: usize> Neg for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

The resulting type after applying the - operator.

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fn neg(self) -> Residue<MOD, LIMBS>

Performs the unary - operation. Read more

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impl<MOD, const LIMBS: usize> PartialEq<Residue<MOD, LIMBS>> for Residue<MOD, LIMBS>where MOD: PartialEq<MOD> + ResidueParams<LIMBS>,

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fn eq(&self, other: &Residue<MOD, LIMBS>) -> bool

This method tests for self and other values to be equal, and is used by ==.

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fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

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impl<MOD, const LIMBS: usize> PowBoundedExp<Uint<LIMBS>> for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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fn pow_bounded_exp( &self, exponent: &Uint<LIMBS>, exponent_bits: usize ) -> Residue<MOD, LIMBS>

Raises to the exponent power, with exponent_bits representing the number of (least significant) bits to take into account for the exponent. Read more

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impl<MOD, const LIMBS: usize> Random for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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fn random(rng: &mut impl CryptoRngCore) -> Residue<MOD, LIMBS>

Generate a cryptographically secure random value.

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impl<MOD, const LIMBS: usize> Retrieve for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = Uint<LIMBS>

The original type.

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fn retrieve(&self) -> <Residue<MOD, LIMBS> as Retrieve>::Output

Convert the number back from the optimized representation.

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impl<MOD, const LIMBS: usize> Square for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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fn square(&self) -> Residue<MOD, LIMBS>

Computes the same as self.mul(self), but may be more efficient.

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impl<MOD, const LIMBS: usize> Sub<&Residue<MOD, LIMBS>> for &Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

The resulting type after applying the - operator.

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fn sub(self, rhs: &Residue<MOD, LIMBS>) -> Residue<MOD, LIMBS>

Performs the - operation. Read more

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impl<MOD, const LIMBS: usize> Sub<&Residue<MOD, LIMBS>> for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

The resulting type after applying the - operator.

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fn sub(self, rhs: &Residue<MOD, LIMBS>) -> Residue<MOD, LIMBS>

Performs the - operation. Read more

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impl<MOD, const LIMBS: usize> Sub<Residue<MOD, LIMBS>> for &Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

The resulting type after applying the - operator.

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fn sub(self, rhs: Residue<MOD, LIMBS>) -> Residue<MOD, LIMBS>

Performs the - operation. Read more

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impl<MOD, const LIMBS: usize> Sub<Residue<MOD, LIMBS>> for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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type Output = Residue<MOD, LIMBS>

The resulting type after applying the - operator.

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fn sub(self, rhs: Residue<MOD, LIMBS>) -> Residue<MOD, LIMBS>

Performs the - operation. Read more

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impl<MOD, const LIMBS: usize> SubAssign<&Residue<MOD, LIMBS>> for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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fn sub_assign(&mut self, rhs: &Residue<MOD, LIMBS>)

Performs the -= operation. Read more

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impl<MOD, const LIMBS: usize> SubAssign<Residue<MOD, LIMBS>> for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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fn sub_assign(&mut self, rhs: Residue<MOD, LIMBS>)

Performs the -= operation. Read more

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impl<MOD, const LIMBS: usize> Zero for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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const ZERO: Residue<MOD, LIMBS> = Self::ZERO

The value 0.

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fn is_zero(&self) -> Choice

Determine if this value is equal to zero. Read more

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impl<MOD, const LIMBS: usize> Copy for Residue<MOD, LIMBS>where MOD: Copy + ResidueParams<LIMBS>,

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impl<MOD, const LIMBS: usize> DefaultIsZeroes for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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impl<MOD, const LIMBS: usize> Eq for Residue<MOD, LIMBS>where MOD: Eq + ResidueParams<LIMBS>,

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impl<MOD, const LIMBS: usize> StructuralEq for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

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impl<MOD, const LIMBS: usize> StructuralPartialEq for Residue<MOD, LIMBS>where MOD: ResidueParams<LIMBS>,

Auto Trait Implementations§

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impl<MOD, const LIMBS: usize> RefUnwindSafe for Residue<MOD, LIMBS>where MOD: RefUnwindSafe,

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impl<MOD, const LIMBS: usize> UnwindSafe for Residue<MOD, LIMBS>where MOD: UnwindSafe,

Blanket Implementations§

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impl<T> Any for Twhere T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more

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Immutably borrows from an owned value. Read more

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Mutably borrows from an owned value. Read more

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fn conditional_negate(&mut self, choice: Choice)

Negate self if choice == Choice(1); otherwise, leave it unchanged. Read more

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Converts self into T using Into<T>. Read more

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Causes self to use its Binary implementation when Debug-formatted.

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Causes self to use its Display implementation when Debug-formatted.

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Causes self to use its LowerExp implementation when Debug-formatted.

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Causes self to use its LowerHex implementation when Debug-formatted.

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Causes self to use its Octal implementation when Debug-formatted.

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Causes self to use its UpperExp implementation when Debug-formatted.

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Causes self to use its UpperHex implementation when Debug-formatted.

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Formats each item in a sequence. Read more

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Returns the argument unchanged.

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Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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fn pipe<R>(self, func: impl FnOnce(Self) -> R) -> Rwhere Self: Sized,

Pipes by value. This is generally the method you want to use. Read more

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Borrows self and passes that borrow into the pipe function. Read more

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Mutably borrows self and passes that borrow into the pipe function. Read more

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fn pow(&self, exponent: &Exponent) -> T

Raises to the exponent power.

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impl<T, Rhs, Output> GroupOps<Rhs, Output> for Twhere T: Add<Rhs, Output = Output> + Sub<Rhs, Output = Output> + AddAssign<Rhs> + SubAssign<Rhs>,

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