Struct AffineVar

pub struct AffineVar<P: TECurveConfig, 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,
    /* private fields */
}

An implementation of arithmetic for Twisted Edwards curves that relies on the complete formulae for the affine model, as outlined in the EFD.

Fields

x: F

The x-coordinate.

y: F

The y-coordinate.

Implementations

impl<P: TECurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>> AffineVar<P, F>

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

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

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

pub fn new_variable_omit_on_curve_check<T: Into<TEAffine<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 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).

impl<P, F> AffineVar<P, F>

where P: TECurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField> + ThreeBitCondNegLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,

pub fn precomputed_base_3_bit_signed_digit_scalar_mul<J>( bases: &[impl Borrow<[TEProjective<P>]>], scalars: &[impl Borrow<[J]>], ) -> Result<Self, SynthesisError>

where J: Borrow<[Boolean<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>]>,

Compute a scalar multiplication of bases with respect to scalars, where the elements of scalars are length-three slices of bits, and which such that the first two bits are use to select one of the bases, while the third bit is used to conditionally negate the selection.

Trait Implementations

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Add<&'a AffineVar<P, F>> for AffineVar<P, F>

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

type Output = AffineVar<P, F>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Add<AffineVar<P, F>> for &'a AffineVar<P, F>

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

type Output = AffineVar<P, F>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Add<Projective<P>> for &'a AffineVar<P, F>

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

type Output = AffineVar<P, F>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Add<Projective<P>> for AffineVar<P, F>

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

type Output = AffineVar<P, F>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Add for &'a AffineVar<P, F>

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

type Output = AffineVar<P, F>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Add for AffineVar<P, F>

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

type Output = AffineVar<P, F>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> AddAssign<&'a AffineVar<P, F>> for AffineVar<P, F>

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

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

Performs the += operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> AddAssign<Projective<P>> for AffineVar<P, F>

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

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

Performs the += operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> AddAssign for AffineVar<P, F>

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

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

Performs the += operation.

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

where P: TECurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,

fn new_variable<Point: Borrow<TEAffine<P>>>( cs: impl Into<Namespace<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>>, f: impl FnOnce() -> Result<Point, 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 AffineVar<P, F>

where P: TECurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,

fn new_variable<Point: Borrow<TEProjective<P>>>( cs: impl Into<Namespace<<<P as CurveConfig>::BaseField as Field>::BasePrimeField>>, f: impl FnOnce() -> Result<Point, 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: TECurveConfig, F> Clone for AffineVar<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 AffineVar<P, F>

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

where P: TECurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, 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 constant(g: TEProjective<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<TEProjective<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_base_multiples: I, ) -> Result<(), SynthesisError>

where I: Iterator<Item = (B, &'a TEProjective<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 scalar_mul_le<'a>( &self, bits: impl Iterator<Item = &'a Boolean<ConstraintF>>, ) -> Result<Self, SynthesisError>

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

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: TECurveConfig, F> Debug for AffineVar<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 AffineVar<P, F>

where P: TECurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>, for<'b> &'b F: FieldOpsBounds<'b, 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> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Mul<&'a EmulatedFpVar<<P as CurveConfig>::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>> for &'a AffineVar<P, F>

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

type Output = AffineVar<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> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Mul<&'a EmulatedFpVar<<P as CurveConfig>::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>> for AffineVar<P, F>

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

type Output = AffineVar<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> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Mul<EmulatedFpVar<<P as CurveConfig>::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>> for &'a AffineVar<P, F>

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

type Output = AffineVar<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> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Mul<EmulatedFpVar<<P as CurveConfig>::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>> for AffineVar<P, F>

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

type Output = AffineVar<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> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> MulAssign<&'a EmulatedFpVar<<P as CurveConfig>::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>> for AffineVar<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> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> MulAssign<EmulatedFpVar<<P as CurveConfig>::ScalarField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField>> for AffineVar<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> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Sub<&'a AffineVar<P, F>> for AffineVar<P, F>

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

type Output = AffineVar<P, F>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Sub<AffineVar<P, F>> for &'a AffineVar<P, F>

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

type Output = AffineVar<P, F>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Sub<Projective<P>> for &'a AffineVar<P, F>

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

type Output = AffineVar<P, F>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Sub<Projective<P>> for AffineVar<P, F>

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

type Output = AffineVar<P, F>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Sub for &'a AffineVar<P, F>

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

type Output = AffineVar<P, F>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> Sub for AffineVar<P, F>

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

type Output = AffineVar<P, F>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> SubAssign<&'a AffineVar<P, F>> for AffineVar<P, F>

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

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

Performs the -= operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> SubAssign<Projective<P>> for AffineVar<P, F>

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

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

Performs the -= operation.

impl<F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, P: TECurveConfig> SubAssign for AffineVar<P, F>

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

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

Performs the -= operation.

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

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

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

where P: TECurveConfig, 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>, AffineVar<P, F>> for &'a AffineVar<P, F>

where P: TECurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,

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

where P: TECurveConfig, F: FieldVar<P::BaseField, <<P as CurveConfig>::BaseField as Field>::BasePrimeField> + TwoBitLookupGadget<<<P as CurveConfig>::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>, for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,