Struct Group

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

Implementations

impl<E> Group<E>

where E: Environment,

pub fn from_x_coordinate(x_coordinate: Field<E>) -> Result<Group<E>, Error>

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

impl<E> Group<E>

where E: Environment,

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

Initializes a new group from the (x, y) affine coordinates.

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

Initializes a new group from the (x, y) affine coordinates. Note: The resulting point is not enforced to be on the curve or in the subgroup.

impl<E> Group<E>

where E: Environment,

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

Returns the x-coordinate in the affine coordinates of the group.

impl<E> Group<E>

where E: Environment,

pub fn to_xy_coordinates(&self) -> (Field<E>, Field<E>)

Returns the x-coordinate and y-coordinate in the affine coordinates of the group.

impl<E> Group<E>

where E: Environment,

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

Returns the y-coordinate in the affine coordinates of the group.

impl<E> Group<E>

where E: Environment,

pub const EDWARDS_A: Field<E> = _

The coefficient A for the twisted Edwards curve equation.

pub const EDWARDS_D: Field<E> = _

The coefficient D for the twisted Edwards curve equation.

pub const MONTGOMERY_A: Field<E> = _

The coefficient A for the Montgomery curve equation.

pub const MONTGOMERY_B: Field<E> = _

The coefficient B for the Montgomery curve equation.

pub fn new(group: <E as Environment>::Affine) -> Group<E>

Initializes a new group.

pub fn generator() -> Group<E>

Returns the prime subgroup generator.

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

Returns self * COFACTOR.

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

Returns self / COFACTOR.

Trait Implementations

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

where E: Environment,

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

Returns the sum of self and other.

type Output = Group<E>

The resulting type after applying the + operator.

impl<E> Add for Group<E>

where E: Environment,

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

Returns the sum of self and other.

type Output = Group<E>

The resulting type after applying the + operator.

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

where E: Environment,

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

Adds other to self.

impl<E> AddAssign for Group<E>

where E: Environment,

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

Adds other to self.

impl<E> Clone for Group<E>

where E: Clone + Environment, <E as Environment>::Projective: Clone,

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> Deref for Group<E>

where E: Environment,

type Target = <E as Environment>::Projective

The resulting type after dereferencing.

fn deref(&self) -> &<Group<E> as Deref>::Target

Dereferences the value.

impl<'de, E> Deserialize<'de> for Group<E>

where E: Environment,

fn deserialize<D>( deserializer: D, ) -> Result<Group<E>, <D as Deserializer<'de>>::Error>

where D: Deserializer<'de>,

Deserializes the group from a string or bytes.

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> Distribution<Group<E>> for Standard

where E: Environment,

fn sample<R>(&self, rng: &mut R) -> Group<E>

where R: Rng + ?Sized,

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<E> Double for Group<E>

where E: Environment,

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

Returns the double of self.

type Output = Group<E>

impl<E> Equal for Group<E>

where E: Environment,

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

Returns true if self and other are equal.

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

Returns true if self and other are not equal.

type Output = Boolean<E>

impl<E> FromBits for Group<E>

where E: Environment,

fn from_bits_le(bits_le: &[bool]) -> Result<Group<E>, Error>

Initializes a new group by recovering the x-coordinate of an affine group from a list of little-endian bits.

fn from_bits_be(bits_be: &[bool]) -> Result<Group<E>, Error>

Initializes a new group by recovering the x-coordinate of an affine group from a list of big-endian bits.

impl<E> FromBytes for Group<E>

where E: Environment,

fn read_le<R>(reader: R) -> Result<Group<E>, Error>

where R: Read,

Reads the group from a buffer.

fn from_bytes_le(bytes: &[u8]) -> Result<Self, Error>

where Self: Sized,

Returns Self from a byte array in little-endian order.

impl<E> FromField for Group<E>

where E: Environment,

fn from_field(field: &<Group<E> as FromField>::Field) -> Result<Group<E>, Error>

Initializes a new group by recovering the x-coordinate of an affine group from a field element.

type Field = Field<E>

impl<E> FromFields for Group<E>

where E: Environment,

fn from_fields( fields: &[<Group<E> as FromFields>::Field], ) -> Result<Group<E>, Error>

Initializes a new group by recovering the x-coordinate of an affine group from a field element.

type Field = Field<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.

type Err = Error

The associated error which can be returned from parsing.

impl<E> Hash for Group<E>

where E: Hash + Environment, <E as Environment>::Projective: Hash,

fn hash<__H>(&self, state: &mut __H)

where __H: Hasher,

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

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

where E: Environment,

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

Returns the product of self and other.

type Output = Group<E>

The resulting type after applying the * operator.

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

where E: Environment,

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

Returns the product of self and other.

type Output = Group<E>

The resulting type after applying the * operator.

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

where E: Environment,

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

Returns the product of self and other.

type Output = Group<E>

The resulting type after applying the * operator.

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

where E: Environment,

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

Returns the product of self and other.

type Output = Group<E>

The resulting type after applying the * operator.

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

where E: Environment,

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

Multiplies self by other.

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

where E: Environment,

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

Multiplies self by other.

impl<E> Neg for Group<E>

where E: Environment,

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

Returns the negation of self.

type Output = Group<E>

The resulting type after applying the - operator.

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> PartialEq for Group<E>

where E: PartialEq + Environment, <E as Environment>::Projective: PartialEq,

fn eq(&self, other: &Group<E>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<E> Serialize for Group<E>

where E: Environment,

fn serialize<S>( &self, serializer: S, ) -> Result<<S as Serializer>::Ok, <S as Serializer>::Error>

where S: Serializer,

Serializes the group into a string or as bytes.

impl<E> SizeInBits for Group<E>

where E: Environment,

fn size_in_bits() -> usize

Returns the group size in bits.

impl<E> SizeInBytes for Group<E>

where E: Environment,

fn size_in_bytes() -> usize

Returns the group size in bytes.

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

where E: Environment,

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

Returns the difference of self and other.

type Output = Group<E>

The resulting type after applying the - operator.

impl<E> Sub for Group<E>

where E: Environment,

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

Returns the difference of self and other.

type Output = Group<E>

The resulting type after applying the - operator.

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

where E: Environment,

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

Subtracts other from self.

impl<E> SubAssign for Group<E>

where E: Environment,

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

Subtracts other from self.

impl<'a, E> Sum<&'a Group<E>> for Group<E>

where E: Environment,

fn sum<I>(iter: I) -> Group<E>

where I: Iterator<Item = &'a Group<E>>,

Returns the sum of self and other.

impl<E> Sum for Group<E>

where E: Environment,

fn sum<I>(iter: I) -> Group<E>

where I: Iterator<Item = Group<E>>,

Returns the sum of self and other.

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 write_bits_le(&self, vec: &mut Vec<bool>)

Outputs the little-endian bit representation of self.to_x_coordinate() without trailing zeros.

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

Outputs the big-endian bit representation of self.to_x_coordinate() without leading zeros.

fn to_bits_le(&self) -> Vec<bool>

Returns self as a boolean array in little-endian order.

fn to_bits_be(&self) -> Vec<bool>

Returns self as a boolean array in big-endian order.

fn num_bits() -> Option<usize>

An optional indication of how many bits an object can be represented with.

impl<E> ToBytes for Group<E>

where E: Environment,

fn write_le<W>(&self, writer: W) -> Result<(), Error>

where W: Write,

Writes the group to a buffer.

fn to_bytes_le(&self) -> Result<Vec<u8>, Error>

where Self: Sized,

Returns self as a byte array in little-endian order.

impl<E> ToField for Group<E>

where E: Environment,

fn to_field(&self) -> Result<<Group<E> as ToField>::Field, Error>

Returns the group as a field element.

type Field = Field<E>

impl<E> ToFields for Group<E>

where E: Environment,

fn to_fields(&self) -> Result<Vec<<Group<E> as ToFields>::Field>, Error>

Returns the group as field elements.

type Field = Field<E>

impl<E> TypeName for Group<E>

where E: Environment,

fn type_name() -> &'static str

Returns the type name as a string.

impl<E> Visibility for Group<E>

where E: Environment,

fn size_in_fields(&self) -> Result<u16, Error>

Returns the number of field elements to encode self.

type Boolean = Boolean<E>

impl<E> Zero for Group<E>

where E: Environment,

fn zero() -> Group<E>

Returns the 0 element of the group.

fn is_zero(&self) -> bool

Returns true if the element is zero.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl<E> Copy for Group<E>

where E: Copy + Environment, <E as Environment>::Projective: Copy,

impl<E> Eq for Group<E>

where E: Eq + Environment, <E as Environment>::Projective: Eq,

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

where E: Environment,

impl<E> StructuralPartialEq for Group<E>

where E: Environment,