Trait Field
pub trait Field:
Sized
+ Eq
+ Copy
+ Clone
+ Default
+ Send
+ Sync
+ Debug
+ 'static
+ ConditionallySelectable
+ ConstantTimeEq
+ Neg<Output = Self>
+ Add<Output = Self, Output = Self>
+ Sub<Output = Self, Output = Self>
+ Mul<Output = Self, Output = Self>
+ Sum
+ Product
+ for<'a> Add<&'a Self>
+ for<'a> Sub<&'a Self>
+ for<'a> Mul<&'a Self>
+ for<'a> Sum<&'a Self>
+ for<'a> Product<&'a Self>
+ AddAssign
+ SubAssign
+ MulAssign
+ for<'a> AddAssign<&'a Self>
+ for<'a> SubAssign<&'a Self>
+ for<'a> MulAssign<&'a Self> {
const ZERO: Self;
const ONE: Self;
// Required methods
fn random(rng: impl RngCore) -> Self;
fn square(&self) -> Self;
fn double(&self) -> Self;
fn invert(&self) -> CtOption<Self>;
fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self);
// Provided methods
fn is_zero(&self) -> Choice { ... }
fn is_zero_vartime(&self) -> bool { ... }
fn cube(&self) -> Self { ... }
fn sqrt_alt(&self) -> (Choice, Self) { ... }
fn sqrt(&self) -> CtOption<Self> { ... }
fn pow<S>(&self, exp: S) -> Self
where S: AsRef<[u64]> { ... }
fn pow_vartime<S>(&self, exp: S) -> Self
where S: AsRef<[u64]> { ... }
}
Expand description
This trait represents an element of a field.
Required Associated Constants§
const ZERO: Self
const ZERO: Self
The zero element of the field, the additive identity.
const ONE: Self
const ONE: Self
The one element of the field, the multiplicative identity.
Required Methods§
fn random(rng: impl RngCore) -> Self
fn random(rng: impl RngCore) -> Self
Returns an element chosen uniformly at random using a user-provided RNG.
fn square(&self) -> Self
fn square(&self) -> Self
Squares this element.
fn double(&self) -> Self
fn double(&self) -> Self
Doubles this element.
fn invert(&self) -> CtOption<Self>
fn invert(&self) -> CtOption<Self>
Computes the multiplicative inverse of this element, failing if the element is zero.
fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self)
fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self)
Computes:
- $(\textsf{true}, \sqrt{\textsf{num}/\textsf{div}})$, if $\textsf{num}$ and $\textsf{div}$ are nonzero and $\textsf{num}/\textsf{div}$ is a square in the field;
- $(\textsf{true}, 0)$, if $\textsf{num}$ is zero;
- $(\textsf{false}, 0)$, if $\textsf{num}$ is nonzero and $\textsf{div}$ is zero;
- $(\textsf{false}, \sqrt{G_S \cdot \textsf{num}/\textsf{div}})$, if $\textsf{num}$ and $\textsf{div}$ are nonzero and $\textsf{num}/\textsf{div}$ is a nonsquare in the field;
where $G_S$ is a non-square.
§Warnings
- The choice of root from
sqrt
is unspecified. - The value of $G_S$ is unspecified, and cannot be assumed to have any specific value in a generic context.
Provided Methods§
fn is_zero_vartime(&self) -> bool
fn is_zero_vartime(&self) -> bool
Returns true iff this element is zero.
§Security
This method provides no constant-time guarantees. Implementors of the
Field
trait may optimise this method using non-constant-time logic.
fn cube(&self) -> Self
fn cube(&self) -> Self
Cubes this element.
fn sqrt_alt(&self) -> (Choice, Self)
fn sqrt_alt(&self) -> (Choice, Self)
Equivalent to Self::sqrt_ratio(self, one())
.
The provided method is implemented in terms of Self::sqrt_ratio
.
fn sqrt(&self) -> CtOption<Self>
fn sqrt(&self) -> CtOption<Self>
Returns the square root of the field element, if it is quadratic residue.
The provided method is implemented in terms of Self::sqrt_ratio
.
fn pow<S>(&self, exp: S) -> Self
fn pow<S>(&self, exp: S) -> Self
Exponentiates self
by exp
, where exp
is a little-endian order integer
exponent.
§Guarantees
This operation is constant time with respect to self
, for all exponents with the
same number of digits (exp.as_ref().len()
). It is variable time with respect to
the number of digits in the exponent.
fn pow_vartime<S>(&self, exp: S) -> Self
fn pow_vartime<S>(&self, exp: S) -> Self
Exponentiates self
by exp
, where exp
is a little-endian order integer
exponent.
§Guarantees
This operation is variable time with respect to self
, for all exponent. If
the exponent is fixed, this operation is effectively constant time. However, for
stronger constant-time guarantees, Field::pow
should be used.
Dyn Compatibility§
This trait is not dyn compatible.
In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.
Implementations on Foreign Types§
§impl Field for Fp
impl Field for Fp
§fn invert(&self) -> CtOption<Fp>
fn invert(&self) -> CtOption<Fp>
Computes the multiplicative inverse of this element, failing if the element is zero.
const ZERO: Fp = _
const ONE: Fp = _
fn random(rng: impl RngCore) -> Fp
fn double(&self) -> Fp
fn square(&self) -> Fp
fn sqrt_ratio(num: &Fp, div: &Fp) -> (Choice, Fp)
fn sqrt_alt(&self) -> (Choice, Fp)
fn pow_vartime<S>(&self, exp: S) -> Fp
§impl Field for Fq
impl Field for Fq
§fn invert(&self) -> CtOption<Fq>
fn invert(&self) -> CtOption<Fq>
Computes the multiplicative inverse of this element, failing if the element is zero.