Struct Group

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

Implementations

impl<E: Environment> Group<E>

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

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.

pub fn from_x_coordinate_flagged(x: Field<E>) -> (Self, Boolean<E>)

Initializes an affine group element from a given x-coordinate field element. Additionally, returns an error flag. If the error flag is set, there is no group element with the given x-coordinate. If the error flag is set, the returned point is (0, 0).

impl<E: Environment> Group<E>

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

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: Environment> Group<E>

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

Returns the product of the group element and the cofactor.

impl<E: Environment> Group<E>

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

Returns the x-coordinate of the group element.

impl<E: Environment> Group<E>

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

Returns the y-coordinate of the group element.

impl<E: Environment> Group<E>

pub fn enforce_double(&self, double: &Group<E>)

Enforce that double = 2 * self.

impl<E: Environment> Group<E>

pub fn generator() -> Self

Returns the generator of the prime-order subgroup.

impl<E: Environment> Group<E>

pub fn enforce_on_curve(&self)

Enforces that self is on the curve.

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

impl<E: Environment> Group<E>

pub fn enforce_in_group(&self)

Enforces that self is on the curve and in the largest prime-order subgroup.

pub fn is_in_group(&self) -> Boolean<E>

Returns a Boolean indicating if self is in the largest prime-order subgroup, assuming that self is on the curve.

Trait Implementations

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

type Output = Group<E>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Group<E>

The resulting type after applying the + operator.

fn add(self, other: &Self) -> Self::Output

Performs the + operation.

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

type Output = Group<E>

The resulting type after applying the + operator.

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

Performs the + operation.

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

fn add_assign(&mut self, other: &Self)

Performs the += operation.

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

fn add_assign(&mut self, other: Self)

Performs the += operation.

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

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: Environment> Debug for Group<E>

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

Formats the value using the given formatter.

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

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

Formats the value using the given formatter.

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

type Output = Group<E>

fn double(&self) -> Self::Output

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

fn eject_mode(&self) -> Mode

Ejects the mode of the group element.

fn eject_value(&self) -> Self::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: Environment> Equal for Group<E>

fn is_equal(&self, other: &Self) -> Self::Output

Returns true if self and other are equal.

This method costs 8 constraints.

fn is_not_equal(&self, other: &Self) -> Self::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: Environment> From<&Group<E>> for LinearCombination<E::BaseField>

fn from(group: &Group<E>) -> Self

Converts to this type from the input type.

impl<E: Environment> From<Group<E>> for LinearCombination<E::BaseField>

fn from(group: Group<E>) -> Self

Converts to this type from the input type.

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

fn from_bits_le(bits_le: &[Self::Boolean]) -> Self

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: &[Self::Boolean]) -> Self

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: Environment> FromStr for Group<E>

fn from_str(string: &str) -> Result<Self>

Parses a string into a group circuit.

type Err = Error

The associated error which can be returned from parsing.

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

fn new(mode: Mode, group: Self::Primitive) -> Self

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) -> Self

where Self: Sized,

Initializes a constant of the given primitive value.

impl<E: Environment> Metrics<dyn Add<Group<E>, Output = Group<E>>> for Group<E>

type Case = (Mode, Mode)

fn count(case: &Self::Case) -> Count

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

impl<E: Environment> Metrics<dyn Neg<Output = Group<E>>> for Group<E>

type Case = Mode

fn count(_case: &Self::Case) -> Count

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

impl<E: Environment> Metrics<dyn Sub<Group<E>, Output = Group<E>>> for Group<E>

type Case = (Mode, Mode)

fn count(case: &Self::Case) -> Count

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

impl<E: Environment> Metrics<dyn Ternary<Boolean = Boolean<E>, Output = Group<E>>> for Group<E>

type Case = (Mode, Mode, Mode)

fn count(case: &Self::Case) -> Count

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

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

type Output = Group<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Group<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: &Group<E>) -> Self::Output

Performs the * operation.

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

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: &Group<E>) -> Self::Output

Performs the * operation.

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

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: &Group<E>) -> Self::Output

Performs the * operation.

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

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: &Group<E>) -> Self::Output

Performs the * operation.

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

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: &Scalar<E>) -> Self::Output

Performs the * operation.

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

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: &Scalar<E>) -> Self::Output

Performs the * operation.

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

type Output = Group<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Group<E>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: Group<E>) -> Self::Output

Performs the * operation.

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

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: Group<E>) -> Self::Output

Performs the * operation.

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

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: Group<E>) -> Self::Output

Performs the * operation.

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

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: Group<E>) -> Self::Output

Performs the * operation.

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

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: Scalar<E>) -> Self::Output

Performs the * operation.

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

type Output = Group<E>

The resulting type after applying the * operator.

fn mul(self, other: Scalar<E>) -> Self::Output

Performs the * operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

fn neg(self) -> Self::Output

Performs the unary - operation.

type Output = Group<E>

The resulting type after applying the - operator.

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

fn neg(self) -> Self::Output

Performs the unary - operation.

type Output = Group<E>

The resulting type after applying the - operator.

impl<E: Environment> OutputMode<dyn Add<Group<E>, Output = Group<E>>> for Group<E>

type Case = (Mode, Mode)

fn output_mode(case: &Self::Case) -> Mode

Returns the mode of the output.

impl<E: Environment> OutputMode<dyn Neg<Output = Group<E>>> for Group<E>

type Case = Mode

fn output_mode(case: &Self::Case) -> Mode

Returns the mode of the output.

impl<E: Environment> OutputMode<dyn Sub<Group<E>, Output = Group<E>>> for Group<E>

type Case = (Mode, Mode)

fn output_mode(case: &Self::Case) -> Mode

Returns the mode of the output.

impl<E: Environment> OutputMode<dyn Ternary<Boolean = Boolean<E>, Output = Group<E>>> for Group<E>

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

fn output_mode(parameter: &Self::Case) -> Mode

Returns the mode of the output.

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

fn parse(string: &str) -> ParserResult<'_, Self>

Parses a string into a group circuit.

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

type Output = Group<E>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Group<E>

The resulting type after applying the - operator.

fn sub(self, other: &Self) -> Self::Output

Performs the - operation.

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

type Output = Group<E>

The resulting type after applying the - operator.

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

Performs the - operation.

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

fn sub_assign(&mut self, other: &Self)

Performs the -= operation.

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

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

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

fn ternary( condition: &Self::Boolean, first: &Self, second: &Self, ) -> Self::Output

Returns first if condition is true, otherwise returns second.

type Boolean = Boolean<E>

type Output = Group<E>

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

fn write_bits_le(&self, vec: &mut Vec<Self::Boolean>)

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

fn write_bits_be(&self, vec: &mut Vec<Self::Boolean>)

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

type Boolean = Boolean<E>

fn to_bits_le(&self) -> Vec<Self::Boolean>

Returns the little-endian bits of the circuit.

fn to_bits_be(&self) -> Vec<Self::Boolean>

Returns the big-endian bits of the circuit.

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

fn write_bits_le(&self, vec: &mut Vec<Self::Boolean>)

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

fn write_bits_be(&self, vec: &mut Vec<Self::Boolean>)

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

type Boolean = Boolean<E>

fn to_bits_le(&self) -> Vec<Self::Boolean>

Returns the little-endian bits of the circuit.

fn to_bits_be(&self) -> Vec<Self::Boolean>

Returns the big-endian bits of the circuit.

impl<E: Environment> ToField for Group<E>

fn to_field(&self) -> Self::Field

Returns the group as a field element.

type Field = Field<E>

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

fn type_name() -> &'static str

Returns the type name of the circuit as a string.

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

type Boolean = Boolean<E>

fn zero() -> Self

Returns a new zero constant.

fn is_zero(&self) -> Self::Boolean

Returns true if self is zero.

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