Struct ProjectiveVar

pub struct ProjectiveVar<P: SWCurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>>
where
    for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
{
    pub x: F,
    pub y: F,
    pub z: F,
    /* private fields */
}

An implementation of arithmetic for Short Weierstrass curves that relies on the complete formulae derived in the paper of [Renes, Costello, Batina 2015].

Fields

x: F

The x-coordinate.

y: F

The y-coordinate.

z: F

The z-coordinate.

Implementations

impl<P: SWCurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>> ProjectiveVar<P, F>

where for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,

pub fn new(x: F, y: F, z: F) -> Self

Constructs Self from an (x, y, z) coordinate triple.

pub fn to_affine(&self) -> Result<AffineVar<P, F>, SynthesisError>

Convert this point into affine form.

pub fn new_variable_omit_on_curve_check( cs: impl Into<Namespace<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>>, f: impl FnOnce() -> Result<SWProjective<P>, SynthesisError>, mode: AllocationMode, ) -> Result<Self, SynthesisError>

Allocates a new variable without performing an on-curve check, which is useful if the variable is known to be on the curve (eg., if the point is a constant or is a public input).

Trait Implementations

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Add<&'a ProjectiveVar<P, F>> for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the + operator.

fn add(self, other: &'a ProjectiveVar<P, F>) -> Self::Output

Performs the + operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Add<Projective<P>> for &'a ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the + operator.

fn add(self, other: SWProjective<P>) -> Self::Output

Performs the + operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Add<Projective<P>> for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the + operator.

fn add(self, other: SWProjective<P>) -> Self::Output

Performs the + operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Add<ProjectiveVar<P, F>> for &'a ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the + operator.

fn add(self, other: ProjectiveVar<P, F>) -> Self::Output

Performs the + operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Add for &'a ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the + operator.

fn add(self, other: &'a ProjectiveVar<P, F>) -> Self::Output

Performs the + operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Add for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the + operator.

fn add(self, other: ProjectiveVar<P, F>) -> Self::Output

Performs the + operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> AddAssign<&'a ProjectiveVar<P, F>> for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

fn add_assign(&mut self, other: &'a ProjectiveVar<P, F>)

Performs the += operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> AddAssign<Projective<P>> for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

fn add_assign(&mut self, other: SWProjective<P>)

Performs the += operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> AddAssign for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

fn add_assign(&mut self, other: ProjectiveVar<P, F>)

Performs the += operation.

impl<P, F> AllocVar<Affine<P>, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F>

where P: SWCurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,

fn new_variable<T: Borrow<SWAffine<P>>>( cs: impl Into<Namespace<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>>, f: impl FnOnce() -> Result<T, SynthesisError>, mode: AllocationMode, ) -> Result<Self, SynthesisError>

Allocates a new variable of type Self in the ConstraintSystem cs. The mode of allocation is decided by mode.

fn new_constant( cs: impl Into<Namespace<F>>, t: impl Borrow<V>, ) -> Result<Self, SynthesisError>

Allocates a new constant of type Self in the ConstraintSystem cs.

fn new_input<T: Borrow<V>>( cs: impl Into<Namespace<F>>, f: impl FnOnce() -> Result<T, SynthesisError>, ) -> Result<Self, SynthesisError>

Allocates a new public input of type Self in the ConstraintSystem cs.

fn new_witness<T: Borrow<V>>( cs: impl Into<Namespace<F>>, f: impl FnOnce() -> Result<T, SynthesisError>, ) -> Result<Self, SynthesisError>

Allocates a new private witness of type Self in the ConstraintSystem cs.

fn new_variable_with_inferred_mode<T: Borrow<V>>( cs: impl Into<Namespace<F>>, f: impl FnOnce() -> Result<T, SynthesisError>, ) -> Result<Self, SynthesisError>

Allocates a new constant or private witness of type Self in the ConstraintSystem cs with the allocation mode inferred from cs. A constant is allocated if cs is None, and a private witness is allocated otherwise.

impl<P, F> AllocVar<Projective<P>, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F>

where P: SWCurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,

fn new_variable<T: Borrow<SWProjective<P>>>( cs: impl Into<Namespace<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>>, f: impl FnOnce() -> Result<T, SynthesisError>, mode: AllocationMode, ) -> Result<Self, SynthesisError>

Allocates a new variable of type Self in the ConstraintSystem cs. The mode of allocation is decided by mode.

fn new_constant( cs: impl Into<Namespace<F>>, t: impl Borrow<V>, ) -> Result<Self, SynthesisError>

Allocates a new constant of type Self in the ConstraintSystem cs.

fn new_input<T: Borrow<V>>( cs: impl Into<Namespace<F>>, f: impl FnOnce() -> Result<T, SynthesisError>, ) -> Result<Self, SynthesisError>

Allocates a new public input of type Self in the ConstraintSystem cs.

fn new_witness<T: Borrow<V>>( cs: impl Into<Namespace<F>>, f: impl FnOnce() -> Result<T, SynthesisError>, ) -> Result<Self, SynthesisError>

Allocates a new private witness of type Self in the ConstraintSystem cs.

fn new_variable_with_inferred_mode<T: Borrow<V>>( cs: impl Into<Namespace<F>>, f: impl FnOnce() -> Result<T, SynthesisError>, ) -> Result<Self, SynthesisError>

Allocates a new constant or private witness of type Self in the ConstraintSystem cs with the allocation mode inferred from cs. A constant is allocated if cs is None, and a private witness is allocated otherwise.

impl<P: SWCurveConfig, F> Clone for ProjectiveVar<P, F>

where for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>, F: Clone + FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, PhantomData<P>: Clone,

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<P, F> CondSelectGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F>

where P: SWCurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,

fn conditionally_select( cond: &Boolean<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>, true_value: &Self, false_value: &Self, ) -> Result<Self, SynthesisError>

If cond == &Boolean::TRUE, then this returns true_value; else, returns false_value.

fn conditionally_select_power_of_two_vector( position: &[Boolean<ConstraintF>], values: &[Self], ) -> Result<Self, SynthesisError>

Returns an element of values whose index in represented by position. position is an array of boolean that represents an unsigned integer in big endian order.

impl<P, F> CurveVar<Projective<P>, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F>

where P: SWCurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,

fn enforce_prime_order(&self) -> Result<(), SynthesisError>

Enforce that self is in the prime-order subgroup.

Does so by multiplying by the prime order, and checking that the result is unchanged.

fn scalar_mul_le<'a>( &self, bits: impl Iterator<Item = &'a Boolean<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>>, ) -> Result<Self, SynthesisError>

Computes bits * self, where bits is a little-endian Boolean representation of a scalar.

fn constant(g: SWProjective<P>) -> Self

Returns a constant with value v.

fn zero() -> Self

Returns the constant F::zero(). This is the identity of the group.

fn is_zero( &self, ) -> Result<Boolean<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>, SynthesisError>

Returns a Boolean representing whether self == Self::zero().

fn new_variable_omit_prime_order_check( cs: impl Into<Namespace<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>>, f: impl FnOnce() -> Result<SWProjective<P>, SynthesisError>, mode: AllocationMode, ) -> Result<Self, SynthesisError>

Allocates a variable in the subgroup without checking if it’s in the prime-order subgroup.

fn double_in_place(&mut self) -> Result<(), SynthesisError>

Sets self = self + self.

fn negate(&self) -> Result<Self, SynthesisError>

Coputes -self.

fn precomputed_base_scalar_mul_le<'a, I, B>( &mut self, scalar_bits_with_bases: I, ) -> Result<(), SynthesisError>

where I: Iterator<Item = (B, &'a SWProjective<P>)>, B: Borrow<Boolean<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>>,

Computes a I * self in place, where I is a Boolean little-endian representation of the scalar.

fn double(&self) -> Result<Self, SynthesisError>

Computes self + self.

fn precomputed_base_multiscalar_mul_le<'a, T, I, B>( bases: &[B], scalars: I, ) -> Result<Self, SynthesisError>

where T: 'a + ToBitsGadget<ConstraintF> + ?Sized, I: Iterator<Item = &'a T>, B: Borrow<[C]>,

Computes Σⱼ(scalarⱼ * baseⱼ) for all j, where scalarⱼ is a Boolean little-endian representation of the j-th scalar.

impl<P: SWCurveConfig, F> Debug for ProjectiveVar<P, F>

where for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>, F: Debug + FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>,

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

Formats the value using the given formatter.

impl<P, F> EqGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F>

where P: SWCurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,

fn is_eq( &self, other: &Self, ) -> Result<Boolean<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>, SynthesisError>

Output a Boolean value representing whether self.value() == other.value().

fn conditional_enforce_equal( &self, other: &Self, condition: &Boolean<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>, ) -> Result<(), SynthesisError>

If should_enforce == true, enforce that self and other are equal; else, enforce a vacuously true statement.

fn conditional_enforce_not_equal( &self, other: &Self, condition: &Boolean<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>, ) -> Result<(), SynthesisError>

If should_enforce == true, enforce that self and other are not equal; else, enforce a vacuously true statement.

fn is_neq(&self, other: &Self) -> Result<Boolean<F>, SynthesisError>

Output a Boolean value representing whether self.value() != other.value().

fn enforce_equal(&self, other: &Self) -> Result<(), SynthesisError>

Enforce that self and other are equal.

fn enforce_not_equal(&self, other: &Self) -> Result<(), SynthesisError>

Enforce that self and other are not equal.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Mul<&'a EmulatedFpVar<<P as CurveConfig>::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>> for &'a ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the * operator.

fn mul( self, other: &'a EmulatedFpVar<P::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, ) -> Self::Output

Performs the * operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Mul<&'a EmulatedFpVar<<P as CurveConfig>::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>> for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the * operator.

fn mul( self, other: &'a EmulatedFpVar<P::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, ) -> Self::Output

Performs the * operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Mul<EmulatedFpVar<<P as CurveConfig>::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>> for &'a ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the * operator.

fn mul( self, other: EmulatedFpVar<P::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, ) -> Self::Output

Performs the * operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Mul<EmulatedFpVar<<P as CurveConfig>::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>> for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the * operator.

fn mul( self, other: EmulatedFpVar<P::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, ) -> Self::Output

Performs the * operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> MulAssign<&'a EmulatedFpVar<<P as CurveConfig>::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>> for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

fn mul_assign( &mut self, other: &'a EmulatedFpVar<P::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, )

Performs the *= operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> MulAssign<EmulatedFpVar<<P as CurveConfig>::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>> for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

fn mul_assign( &mut self, other: EmulatedFpVar<P::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, )

Performs the *= operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Sub<&'a ProjectiveVar<P, F>> for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the - operator.

fn sub(self, other: &'a ProjectiveVar<P, F>) -> Self::Output

Performs the - operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Sub<Projective<P>> for &'a ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the - operator.

fn sub(self, other: SWProjective<P>) -> Self::Output

Performs the - operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Sub<Projective<P>> for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the - operator.

fn sub(self, other: SWProjective<P>) -> Self::Output

Performs the - operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Sub<ProjectiveVar<P, F>> for &'a ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the - operator.

fn sub(self, other: ProjectiveVar<P, F>) -> Self::Output

Performs the - operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Sub for &'a ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the - operator.

fn sub(self, other: &'a ProjectiveVar<P, F>) -> Self::Output

Performs the - operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> Sub for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

type Output = ProjectiveVar<P, F>

The resulting type after applying the - operator.

fn sub(self, other: ProjectiveVar<P, F>) -> Self::Output

Performs the - operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> SubAssign<&'a ProjectiveVar<P, F>> for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

fn sub_assign(&mut self, other: &'a ProjectiveVar<P, F>)

Performs the -= operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> SubAssign<Projective<P>> for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

fn sub_assign(&mut self, other: SWProjective<P>)

Performs the -= operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, P: SWCurveConfig> SubAssign for ProjectiveVar<P, F>

where for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

fn sub_assign(&mut self, other: ProjectiveVar<P, F>)

Performs the -= operation.

impl<P, F> ToBitsGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F>

where P: SWCurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,

fn to_bits_le( &self, ) -> Result<Vec<Boolean<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>>, SynthesisError>

Outputs the canonical little-endian bit-wise representation of self.

fn to_non_unique_bits_le( &self, ) -> Result<Vec<Boolean<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>>, SynthesisError>

Outputs a possibly non-unique little-endian bit-wise representation of self.

fn to_bits_be(&self) -> Result<Vec<Boolean<F>>, SynthesisError>

Outputs the canonical big-endian bit-wise representation of self.

fn to_non_unique_bits_be(&self) -> Result<Vec<Boolean<F>>, SynthesisError>

Outputs a possibly non-unique big-endian bit-wise representation of self.

impl<P, F> ToBytesGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F>

where P: SWCurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,

fn to_bytes_le( &self, ) -> Result<Vec<UInt8<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>>, SynthesisError>

Outputs a canonical, little-endian, byte decomposition of self.

fn to_non_unique_bytes_le( &self, ) -> Result<Vec<UInt8<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>>, SynthesisError>

Outputs a possibly non-unique byte decomposition of self.

impl<P, F> ToConstraintFieldGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F>

where P: SWCurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + ToConstraintFieldGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>, for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,

fn to_constraint_field( &self, ) -> Result<Vec<FpVar<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>>, SynthesisError>

Converts self to FpVar<ConstraintF> variables.

impl<'a, P, F> GroupOpsBounds<'a, Projective<P>, ProjectiveVar<P, F>> for &'a ProjectiveVar<P, F>

where P: SWCurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

impl<'a, P, F> GroupOpsBounds<'a, Projective<P>, ProjectiveVar<P, F>> for ProjectiveVar<P, F>

where P: SWCurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,