Struct snarkvm_circuit::Group

pub struct Group<E>where
    E: Environment,{ /* private fields */ }

Implementations

impl<E> Group<E>where
    E: Environment,

pub fn from_x_coordinate(x: Field<E>) -> Group<E>

Initializes an affine group element from a given x-coordinate field element. For safety, the resulting point is always enforced to be on the curve with constraints.

impl<E> Group<E>where
    E: Environment,

pub fn from_xy_coordinates(x: Field<E>, y: Field<E>) -> Group<E>

Initializes an affine group element from a given x- and y-coordinate field element. For safety, the resulting point is always enforced to be on the curve and in the subgroup.

impl<E> Group<E>where
    E: Environment,

pub fn mul_by_cofactor(&self) -> Group<E>

Returns the product of the group element and the cofactor.

impl<E> Group<E>where
    E: Environment,

pub fn to_x_coordinate(&self) -> Field<E>

Returns the x-coordinate of the group element.

impl<E> Group<E>where
    E: Environment,

pub fn to_y_coordinate(&self) -> Field<E>

Returns the y-coordinate of the group element.

impl<E> Group<E>where
    E: Environment,

pub fn enforce_on_curve(&self)

Checks (x, y) is on the curve.

Ensure ax^2 + y^2 = 1 + dx^2y^2 by checking that y^2 * (dx^2 - 1) = (ax^2 - 1)

Trait Implementations

impl<E> Add<&Group<E>> for &Group<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the + operator.

fn add(self, other: &Group<E>) -> <&Group<E> as Add<&Group<E>>>::Output

Performs the + operation.

impl<E> Add<&Group<E>> for Group<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the + operator.

fn add(self, other: &Group<E>) -> <Group<E> as Add<&Group<E>>>::Output

Performs the + operation.

impl<E> Add<Group<E>> for Group<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the + operator.

fn add(self, other: Group<E>) -> <Group<E> as Add<Group<E>>>::Output

Performs the + operation.

impl<E> AddAssign<&Group<E>> for Group<E>where
    E: Environment,

fn add_assign(&mut self, other: &Group<E>)

Performs the += operation.

impl<E> AddAssign<Group<E>> for Group<E>where
    E: Environment,

fn add_assign(&mut self, other: Group<E>)

Performs the += operation.

impl<E> Clone for Group<E>where
    E: Clone + Environment,

fn clone(&self) -> Group<E>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<E> Debug for Group<E>where
    E: Environment,

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

Formats the value using the given formatter.

impl<E> Display for Group<E>where
    E: Environment,

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

Formats the value using the given formatter.

impl<E> Double for Group<E>where
    E: Environment,

type Output = Group<E>

fn double(&self) -> <Group<E> as Double>::Output

impl<E> Eject for Group<E>where
    E: Environment,

fn eject_mode(&self) -> Mode

Ejects the mode of the group element.

fn eject_value(&self) -> <Group<E> as Eject>::Primitive

Ejects the group as a constant group element.

type Primitive = Group<<E as Environment>::Network>

fn eject(&self) -> (Mode, Self::Primitive)

Ejects the mode and primitive value of the circuit type.

fn is_constant(&self) -> bool

Returns true if the circuit is a constant.

fn is_public(&self) -> bool

Returns true if the circuit is a public.

fn is_private(&self) -> bool

Returns true if the circuit is a private.

impl<E> Equal<Group<E>> for Group<E>where
    E: Environment,

fn is_equal(&self, other: &Group<E>) -> <Group<E> as Equal<Group<E>>>::Output

Returns true if self and other are equal.

This method costs 8 constraints.

fn is_not_equal(&self, other: &Group<E>) -> <Group<E> as Equal<Group<E>>>::Output

Returns true if self and other are not equal.

This method constructs a boolean that indicates if self and other are not equal to each other.

This method costs 8 constraints.

type Output = Boolean<E>

impl<E> From<&Address<E>> for Group<E>where
    E: Environment,

fn from(value: &Address<E>) -> Group<E>

Returns the affine group element in the address.

impl<E> From<&Group<E>> for Address<E>where
    E: Environment,

fn from(value: &Group<E>) -> Address<E>

Initializes an address from an affine group element.

impl<E> From<&Group<E>> for LinearCombination<<E as Environment>::BaseField>where
    E: Environment,

fn from(group: &Group<E>) -> LinearCombination<<E as Environment>::BaseField>

Converts to this type from the input type.

impl<E> From<Address<E>> for Group<E>where
    E: Environment,

fn from(value: Address<E>) -> Group<E>

Returns the affine group element in the address.

impl<E> From<Group<E>> for Address<E>where
    E: Environment,

fn from(value: Group<E>) -> Address<E>

Initializes an address from an affine group element.

impl<E> From<Group<E>> for LinearCombination<<E as Environment>::BaseField>where
    E: Environment,

fn from(group: Group<E>) -> LinearCombination<<E as Environment>::BaseField>

Converts to this type from the input type.

impl<E> FromBits for Group<E>where
    E: Environment,

fn from_bits_le(bits_le: &[<Group<E> as FromBits>::Boolean]) -> Group<E>

Initializes a new group element from the x-coordinate as a list of little-endian bits without trailing zeros.

fn from_bits_be(bits_be: &[<Group<E> as FromBits>::Boolean]) -> Group<E>

Initializes a new group element from the x-coordinate as a list of big-endian bits without leading zeros.

type Boolean = Boolean<E>

impl<E> FromStr for Group<E>where
    E: Environment,

fn from_str(string: &str) -> Result<Group<E>, Error>

Parses a string into a group circuit.

type Err = Error

The associated error which can be returned from parsing.

impl<E> Inject for Group<E>where
    E: Environment,

fn new(mode: Mode, group: <Group<E> as Inject>::Primitive) -> Group<E>

Initializes a new affine group element.

For safety, the resulting point is always enforced to be on the curve with constraints. regardless of whether the y-coordinate was recovered.

type Primitive = Group<<E as Environment>::Network>

fn constant(value: Self::Primitive) -> Selfwhere
    Self: Sized,

Initializes a constant of the given primitive value.

impl<E> Metrics<dyn Add<Group<E>, Output = Group<E>> + 'static> for Group<E>where
    E: Environment,

type Case = (Mode, Mode)

fn count(
    case: &<Group<E> as Metrics<dyn Add<Group<E>, Output = Group<E>> + 'static>>::Case
) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn Neg<Output = Group<E>> + 'static> for Group<E>where
    E: Environment,

type Case = Mode

fn count(
    _case: &<Group<E> as Metrics<dyn Neg<Output = Group<E>> + 'static>>::Case
) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn Sub<Group<E>, Output = Group<E>> + 'static> for Group<E>where
    E: Environment,

type Case = (Mode, Mode)

fn count(
    case: &<Group<E> as Metrics<dyn Sub<Group<E>, Output = Group<E>> + 'static>>::Case
) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Metrics<dyn Ternary<Output = Group<E>, Boolean = Boolean<E>> + 'static> for Group<E>where
    E: Environment,

type Case = (Mode, Mode, Mode)

fn count(
    case: &<Group<E> as Metrics<dyn Ternary<Output = Group<E>, Boolean = Boolean<E>> + 'static>>::Case
) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.

impl<E> Mul<&[Boolean<E>]> for &Group<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: &[Boolean<E>]) -> <&Group<E> as Mul<&[Boolean<E>]>>::Output

Performs the * operation.

impl<E> Mul<&[Boolean<E>]> for Group<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: &[Boolean<E>]) -> <Group<E> as Mul<&[Boolean<E>]>>::Output

Performs the * operation.

impl<E> Mul<&Group<E>> for &[Boolean<E>]where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: &Group<E>) -> <&[Boolean<E>] as Mul<&Group<E>>>::Output

Performs the * operation.

impl<E> Mul<&Group<E>> for &Scalar<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: &Group<E>) -> <&Scalar<E> as Mul<&Group<E>>>::Output

Performs the * operation.

impl<E, const N: usize> Mul<&Group<E>> for [Boolean<E>; N]where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: &Group<E>) -> <[Boolean<E>; N] as Mul<&Group<E>>>::Output

Performs the * operation.

impl<E> Mul<&Group<E>> for Scalar<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: &Group<E>) -> <Scalar<E> as Mul<&Group<E>>>::Output

Performs the * operation.

impl<E> Mul<&Scalar<E>> for &Group<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: &Scalar<E>) -> <&Group<E> as Mul<&Scalar<E>>>::Output

Performs the * operation.

impl<E> Mul<&Scalar<E>> for Group<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: &Scalar<E>) -> <Group<E> as Mul<&Scalar<E>>>::Output

Performs the * operation.

impl<E, const N: usize> Mul<[Boolean<E>; N]> for &Group<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(
    self,
    other: [Boolean<E>; N]
) -> <&Group<E> as Mul<[Boolean<E>; N]>>::Output

Performs the * operation.

impl<E, const N: usize> Mul<[Boolean<E>; N]> for Group<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(
    self,
    other: [Boolean<E>; N]
) -> <Group<E> as Mul<[Boolean<E>; N]>>::Output

Performs the * operation.

impl<E> Mul<Group<E>> for &[Boolean<E>]where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: Group<E>) -> <&[Boolean<E>] as Mul<Group<E>>>::Output

Performs the * operation.

impl<E> Mul<Group<E>> for &Scalar<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: Group<E>) -> <&Scalar<E> as Mul<Group<E>>>::Output

Performs the * operation.

impl<E, const N: usize> Mul<Group<E>> for [Boolean<E>; N]where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: Group<E>) -> <[Boolean<E>; N] as Mul<Group<E>>>::Output

Performs the * operation.

impl<E> Mul<Group<E>> for Scalar<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: Group<E>) -> <Scalar<E> as Mul<Group<E>>>::Output

Performs the * operation.

impl<E> Mul<Scalar<E>> for &Group<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: Scalar<E>) -> <&Group<E> as Mul<Scalar<E>>>::Output

Performs the * operation.

impl<E> Mul<Scalar<E>> for Group<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: Scalar<E>) -> <Group<E> as Mul<Scalar<E>>>::Output

Performs the * operation.

impl<E> MulAssign<&[Boolean<E>]> for Group<E>where
    E: Environment,

fn mul_assign(&mut self, other: &[Boolean<E>])

Performs the *= operation.

impl<E> MulAssign<&Scalar<E>> for Group<E>where
    E: Environment,

fn mul_assign(&mut self, other: &Scalar<E>)

Performs the *= operation.

impl<E, const N: usize> MulAssign<[Boolean<E>; N]> for Group<E>where
    E: Environment,

fn mul_assign(&mut self, other: [Boolean<E>; N])

Performs the *= operation.

impl<E> MulAssign<Scalar<E>> for Group<E>where
    E: Environment,

fn mul_assign(&mut self, other: Scalar<E>)

Performs the *= operation.

impl<E> Neg for &Group<E>where
    E: Environment,

fn neg(self) -> <&Group<E> as Neg>::Output

Performs the unary - operation.

type Output = Group<E>

The resulting type after applying the - operator.

impl<E> Neg for Group<E>where
    E: Environment,

fn neg(self) -> <Group<E> as Neg>::Output

Performs the unary - operation.

type Output = Group<E>

The resulting type after applying the - operator.

impl<E> OutputMode<dyn Add<Group<E>, Output = Group<E>> + 'static> for Group<E>where
    E: Environment,

type Case = (Mode, Mode)

fn output_mode(
    case: &<Group<E> as OutputMode<dyn Add<Group<E>, Output = Group<E>> + 'static>>::Case
) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn Neg<Output = Group<E>> + 'static> for Group<E>where
    E: Environment,

type Case = Mode

fn output_mode(
    case: &<Group<E> as OutputMode<dyn Neg<Output = Group<E>> + 'static>>::Case
) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn Sub<Group<E>, Output = Group<E>> + 'static> for Group<E>where
    E: Environment,

type Case = (Mode, Mode)

fn output_mode(
    case: &<Group<E> as OutputMode<dyn Sub<Group<E>, Output = Group<E>> + 'static>>::Case
) -> Mode

Returns the mode of the output.

impl<E> OutputMode<dyn Ternary<Output = Group<E>, Boolean = Boolean<E>> + 'static> for Group<E>where
    E: Environment,

type Case = (CircuitType<Boolean<E>>, Mode, Mode)

fn output_mode(
    parameter: &<Group<E> as OutputMode<dyn Ternary<Output = Group<E>, Boolean = Boolean<E>> + 'static>>::Case
) -> Mode

Returns the mode of the output.

impl<E> Parser for Group<E>where
    E: Environment,

fn parse(string: &str) -> Result<(&str, Group<E>), Err<VerboseError<&str>>>

Parses a string into a group circuit.

impl<E> Sub<&Group<E>> for &Group<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the - operator.

fn sub(self, other: &Group<E>) -> <&Group<E> as Sub<&Group<E>>>::Output

Performs the - operation.

impl<E> Sub<&Group<E>> for Group<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the - operator.

fn sub(self, other: &Group<E>) -> <Group<E> as Sub<&Group<E>>>::Output

Performs the - operation.

impl<E> Sub<Group<E>> for Group<E>where
    E: Environment,

type Output = Group<E>

The resulting type after applying the - operator.

fn sub(self, other: Group<E>) -> <Group<E> as Sub<Group<E>>>::Output

Performs the - operation.

impl<E> SubAssign<&Group<E>> for Group<E>where
    E: Environment,

fn sub_assign(&mut self, other: &Group<E>)

Performs the -= operation.

impl<E> SubAssign<Group<E>> for Group<E>where
    E: Environment,

fn sub_assign(&mut self, other: Group<E>)

Performs the -= operation.

impl<E> Ternary for Group<E>where
    E: Environment,

fn ternary(
    condition: &<Group<E> as Ternary>::Boolean,
    first: &Group<E>,
    second: &Group<E>
) -> <Group<E> as Ternary>::Output

Returns first if condition is true, otherwise returns second.

type Boolean = Boolean<E>

type Output = Group<E>

impl<E> ToBits for &Group<E>where
    E: Environment,

fn to_bits_le(&self) -> Vec<<&Group<E> as ToBits>::Boolean, Global>

Outputs the little-endian bit representation of self.x without trailing zeros.

fn to_bits_be(&self) -> Vec<<&Group<E> as ToBits>::Boolean, Global>

Outputs the big-endian bit representation of self.x without leading zeros.

type Boolean = Boolean<E>

impl<E> ToBits for Group<E>where
    E: Environment,

fn to_bits_le(&self) -> Vec<<Group<E> as ToBits>::Boolean, Global>

Outputs the little-endian bit representation of self.x without trailing zeros.

fn to_bits_be(&self) -> Vec<<Group<E> as ToBits>::Boolean, Global>

Outputs the big-endian bit representation of self.x without leading zeros.

type Boolean = Boolean<E>

impl<E> TypeName for Group<E>where
    E: Environment,

fn type_name() -> &'static str

Returns the type name of the circuit as a string.

impl<E> Zero for Group<E>where
    E: Environment,

type Boolean = Boolean<E>

fn zero() -> Group<E>

Returns a new zero constant.

fn is_zero(&self) -> <Group<E> as Zero>::Boolean

Returns true if self is zero.

impl<E> GroupTrait<Scalar<E>> for Group<E>where
    E: Environment,