Struct ark_r1cs_std::groups::curves::short_weierstrass::ProjectiveVar

pub struct ProjectiveVar<P: SWModelParameters, F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>> where
    for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,  {
    pub x: F,
    pub y: F,
    pub z: F,
    // some fields omitted
}

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: SWModelParameters, F: FieldVar<P::BaseField, <P::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::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::BaseField as Field>::BasePrimeField>, P: SWModelParameters> Add<&'a 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: Self) -> Self::Output

Performs the + operation.

impl<'a, F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>, P: SWModelParameters> 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::BaseField as Field>::BasePrimeField>, P: SWModelParameters> Add<GroupProjective<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::BaseField as Field>::BasePrimeField>, P: SWModelParameters> Add<GroupProjective<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::BaseField as Field>::BasePrimeField>, P: SWModelParameters> 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<F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>, P: SWModelParameters> Add<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: ProjectiveVar<P, F>) -> Self::Output

Performs the + operation.

impl<'a, F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>, P: SWModelParameters> 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::BaseField as Field>::BasePrimeField>, P: SWModelParameters> AddAssign<GroupProjective<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::BaseField as Field>::BasePrimeField>, P: SWModelParameters> AddAssign<ProjectiveVar<P, F>> 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<GroupAffine<P>, <<P as ModelParameters>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F> where
    P: SWModelParameters,
    F: FieldVar<P::BaseField, <P::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::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.

impl<P, F> AllocVar<GroupProjective<P>, <<P as ModelParameters>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F> where
    P: SWModelParameters,
    F: FieldVar<P::BaseField, <P::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::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.

impl<P: SWModelParameters, F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>> Clone for ProjectiveVar<P, F> where
    for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
    F: 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 ModelParameters>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F> where
    P: SWModelParameters,
    F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
    for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>, 

fn conditionally_select(
    cond: &Boolean<<P::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<GroupProjective<P>, <<P as ModelParameters>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F> where
    P: SWModelParameters,
    F: FieldVar<P::BaseField, <P::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::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::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::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::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: ?Sized, I, B>(
    bases: &[B],
    scalars: I
) -> Result<Self, SynthesisError> where
    T: 'a + ToBitsGadget<ConstraintF>,
    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: SWModelParameters, F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>> Debug for ProjectiveVar<P, F> where
    for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
    F: Debug, 

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

Formats the value using the given formatter.

impl<P, F> EqGadget<<<P as ModelParameters>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F> where
    P: SWModelParameters,
    F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
    for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>, 

fn is_eq(
    &self,
    other: &Self
) -> Result<Boolean<<P::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::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::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<P, F> R1CSVar<<<P as ModelParameters>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F> where
    P: SWModelParameters,
    F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
    for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>, 

type Value = SWProjective<P>

The type of the “native” value that Self represents in the constraint system.

fn cs(&self) -> ConstraintSystemRef<<P::BaseField as Field>::BasePrimeField>

Returns the underlying ConstraintSystemRef.

fn value(&self) -> Result<Self::Value, SynthesisError>

Returns the value that is assigned to self in the underlying ConstraintSystem.

fn is_constant(&self) -> bool

Returns true if self is a circuit-generation-time constant.

impl<'a, F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>, P: SWModelParameters> Sub<&'a 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: Self) -> Self::Output

Performs the - operation.

impl<'a, F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>, P: SWModelParameters> 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::BaseField as Field>::BasePrimeField>, P: SWModelParameters> Sub<GroupProjective<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::BaseField as Field>::BasePrimeField>, P: SWModelParameters> Sub<GroupProjective<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::BaseField as Field>::BasePrimeField>, P: SWModelParameters> 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<F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>, P: SWModelParameters> Sub<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: ProjectiveVar<P, F>) -> Self::Output

Performs the - operation.

impl<'a, F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>, P: SWModelParameters> 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::BaseField as Field>::BasePrimeField>, P: SWModelParameters> SubAssign<GroupProjective<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::BaseField as Field>::BasePrimeField>, P: SWModelParameters> SubAssign<ProjectiveVar<P, F>> 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 ModelParameters>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F> where
    P: SWModelParameters,
    F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
    for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>, 

fn to_bits_le(
    &self
) -> Result<Vec<Boolean<<P::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::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 ModelParameters>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F> where
    P: SWModelParameters,
    F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
    for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>, 

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

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

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

Outputs a possibly non-unique byte decomposition of self.

impl<P, F> ToConstraintFieldGadget<<<P as ModelParameters>::BaseField as Field>::BasePrimeField> for ProjectiveVar<P, F> where
    P: SWModelParameters,
    F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
    for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
    F: ToConstraintFieldGadget<<P::BaseField as Field>::BasePrimeField>, 

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

Converts self to FpVar<ConstraintF> variables.

impl<'a, P, F> GroupOpsBounds<'a, GroupProjective<P>, ProjectiveVar<P, F>> for ProjectiveVar<P, F> where
    P: SWModelParameters,
    F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
    for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>, 

impl<'a, P, F> GroupOpsBounds<'a, GroupProjective<P>, ProjectiveVar<P, F>> for &'a ProjectiveVar<P, F> where
    P: SWModelParameters,
    F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
    for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,