Struct snarkvm_wasm::Fp2

pub struct Fp2<P> where
    P: Fp2Parameters,  {
    pub c0: <P as Fp2Parameters>::Fp,
    pub c1: <P as Fp2Parameters>::Fp,
    // some fields omitted
}

Fields

c0: <P as Fp2Parameters>::Fp

c1: <P as Fp2Parameters>::Fp

Implementations

impl<P> Fp2<P> where
    P: Fp2Parameters, 

pub fn new(c0: <P as Fp2Parameters>::Fp, c1: <P as Fp2Parameters>::Fp) -> Fp2<P>

pub fn norm(&self) -> <P as Fp2Parameters>::Fp

Norm of Fp2 over Fp: Norm(a) = a.x^2 - beta * a.y^2

pub fn mul_by_fp(&mut self, element: &<P as Fp2Parameters>::Fp)

Trait Implementations

impl<'a, P> Add<&'a Fp2<P>> for Fp2<P> where
    P: Fp2Parameters, 

type Output = Fp2<P>

The resulting type after applying the + operator.

pub fn add(self, other: &Fp2<P>) -> Fp2<P>

Performs the + operation.

impl<'a, P> AddAssign<&'a Fp2<P>> for Fp2<P> where
    P: Fp2Parameters, 

pub fn add_assign(&mut self, other: &Fp2<P>)

Performs the += operation.

impl<P, F> AllocGadget<Fp2<P>, F> for Fp2Gadget<P, F> where
    P: Fp2Parameters<Fp = F>,
    F: PrimeField, 

pub fn alloc<Fn, T, CS>(
    cs: CS,
    value_gen: Fn
) -> Result<Fp2Gadget<P, F>, SynthesisError> where
    Fn: FnOnce() -> Result<T, SynthesisError>,
    CS: ConstraintSystem<F>,
    T: Borrow<Fp2<P>>, 

pub fn alloc_input<Fn, T, CS>(
    cs: CS,
    value_gen: Fn
) -> Result<Fp2Gadget<P, F>, SynthesisError> where
    Fn: FnOnce() -> Result<T, SynthesisError>,
    CS: ConstraintSystem<F>,
    T: Borrow<Fp2<P>>, 

fn alloc_constant<Fn, T, CS>(_cs: CS, _f: Fn) -> Result<Self, SynthesisError> where
    Fn: FnOnce() -> Result<T, SynthesisError>,
    CS: ConstraintSystem<F>,
    T: Borrow<V>, 

fn alloc_checked<Fn, T, CS>(cs: CS, f: Fn) -> Result<Self, SynthesisError> where
    Fn: FnOnce() -> Result<T, SynthesisError>,
    CS: ConstraintSystem<F>,
    T: Borrow<V>, 

fn alloc_input_checked<Fn, T, CS>(cs: CS, f: Fn) -> Result<Self, SynthesisError> where
    Fn: FnOnce() -> Result<T, SynthesisError>,
    CS: ConstraintSystem<F>,
    T: Borrow<V>, 

impl<P> CanonicalDeserialize for Fp2<P> where
    P: Fp2Parameters, 

pub fn deserialize<R>(reader: &mut R) -> Result<Fp2<P>, SerializationError> where
    R: Read, 

Reads Self from reader.

fn deserialize_uncompressed<R>(
    reader: &mut R
) -> Result<Self, SerializationError> where
    R: Read, 

Reads Self from reader without compression.

impl<P> CanonicalDeserializeWithFlags for Fp2<P> where
    P: Fp2Parameters, 

pub fn deserialize_with_flags<R, F>(
    reader: &mut R
) -> Result<(Fp2<P>, F), SerializationError> where
    R: Read,
    F: Flags, 

Reads Self and Flags from reader. Returns empty flags by default.

impl<P> CanonicalSerialize for Fp2<P> where
    P: Fp2Parameters, 

pub fn serialize<W>(&self, writer: &mut W) -> Result<(), SerializationError> where
    W: Write, 

Serializes self into writer.

pub fn serialized_size(&self) -> usize

fn serialize_uncompressed<W>(
    &self,
    writer: &mut W
) -> Result<(), SerializationError> where
    W: Write, 

Serializes self into writer without compression.

fn uncompressed_size(&self) -> usize

impl<P> CanonicalSerializeWithFlags for Fp2<P> where
    P: Fp2Parameters, 

pub fn serialize_with_flags<W, F>(
    &self,
    writer: &mut W,
    flags: F
) -> Result<(), SerializationError> where
    F: Flags,
    W: Write, 

Serializes self and flags into writer.

impl<P> Clone for Fp2<P> where
    P: Fp2Parameters, 

pub fn clone(&self) -> Fp2<P>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<P> ConstantSerializedSize for Fp2<P> where
    P: Fp2Parameters, 

pub const SERIALIZED_SIZE: usize

pub const UNCOMPRESSED_SIZE: usize

impl<P> Debug for Fp2<P> where
    P: Fp2Parameters, 

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

Formats the value using the given formatter.

impl<P> Default for Fp2<P> where
    P: Fp2Parameters, 

pub fn default() -> Fp2<P>

Returns the “default value” for a type.

impl<'de, P> Deserialize<'de> for Fp2<P> where
    P: Fp2Parameters,
    <P as Fp2Parameters>::Fp: Deserialize<'de>, 

pub fn deserialize<__D>(
    __deserializer: __D
) -> Result<Fp2<P>, <__D as Deserializer<'de>>::Error> where
    __D: Deserializer<'de>, 

Deserialize this value from the given Serde deserializer.

impl<P> Display for Fp2<P> where
    P: Fp2Parameters, 

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

Formats the value using the given formatter.

impl<'a, P> Div<&'a Fp2<P>> for Fp2<P> where
    P: Fp2Parameters, 

type Output = Fp2<P>

The resulting type after applying the / operator.

pub fn div(self, other: &Fp2<P>) -> Fp2<P>

Performs the / operation.

impl<'a, P> DivAssign<&'a Fp2<P>> for Fp2<P> where
    P: Fp2Parameters, 

pub fn div_assign(&mut self, other: &Fp2<P>)

Performs the /= operation.

impl<P> Field for Fp2<P> where
    P: Fp2Parameters, 

pub fn characteristic<'a>() -> &'a [u64]

Returns the characteristic of the field.

pub fn double(&self) -> Fp2<P>

Returns self + self.

pub fn double_in_place(&mut self) -> &mut Fp2<P>

Doubles self in place.

pub fn square(&self) -> Fp2<P>

Returns self * self.

pub fn from_random_bytes_with_flags(bytes: &[u8]) -> Option<(Fp2<P>, u8)>

Returns a field element with an extra sign bit used for group parsing if the set of bytes forms a valid field element, otherwise returns None. This function is primarily intended for sampling random field elements from a hash-function or RNG output.

pub fn from_random_bytes(bytes: &[u8]) -> Option<Fp2<P>>

Returns a field element if the set of bytes forms a valid field element, otherwise returns None. This function is primarily intended for sampling random field elements from a hash-function or RNG output.

pub fn square_in_place(&mut self) -> &mut Fp2<P>

Squares self in place.

pub fn inverse(&self) -> Option<Fp2<P>>

Computes the multiplicative inverse of self if self is nonzero.

pub fn inverse_in_place(&mut self) -> Option<&mut Fp2<P>>

pub fn frobenius_map(&mut self, power: usize)

Exponentiates this element by a power of the base prime modulus via the Frobenius automorphism.

fn pow<S>(&self, exp: S) -> Self where
    S: AsRef<[u64]>, 

Exponentiates this element by a number represented with u64 limbs, least significant limb first.

impl<P, F> FieldGadget<Fp2<P>, F> for Fp2Gadget<P, F> where
    P: Fp2Parameters<Fp = F>,
    F: PrimeField, 

type Variable = (ConstraintVariable<F>, ConstraintVariable<F>)

pub fn get_value(&self) -> Option<Fp2<P>>

pub fn get_variable(
    &self
) -> <Fp2Gadget<P, F> as FieldGadget<Fp2<P>, F>>::Variable

pub fn zero<CS>(cs: CS) -> Result<Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn one<CS>(cs: CS) -> Result<Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn conditionally_add_constant<CS>(
    &self,
    cs: CS,
    bit: &Boolean,
    coeff: Fp2<P>
) -> Result<Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn add<CS>(
    &self,
    cs: CS,
    other: &Fp2Gadget<P, F>
) -> Result<Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn sub<CS>(
    &self,
    cs: CS,
    other: &Fp2Gadget<P, F>
) -> Result<Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn double<CS>(&self, cs: CS) -> Result<Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn double_in_place<CS>(
    &mut self,
    cs: CS
) -> Result<&mut Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn negate<CS>(&self, cs: CS) -> Result<Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn negate_in_place<CS>(
    &mut self,
    cs: CS
) -> Result<&mut Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn mul<CS>(
    &self,
    cs: CS,
    other: &Fp2Gadget<P, F>
) -> Result<Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn square<CS>(&self, cs: CS) -> Result<Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn square_in_place<CS>(
    &mut self,
    cs: CS
) -> Result<&mut Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn inverse<CS>(&self, cs: CS) -> Result<Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn mul_equals<CS>(
    &self,
    cs: CS,
    other: &Fp2Gadget<P, F>,
    result: &Fp2Gadget<P, F>
) -> Result<(), SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn frobenius_map<CS>(
    &self,
    cs: CS,
    power: usize
) -> Result<Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn frobenius_map_in_place<CS>(
    &mut self,
    cs: CS,
    power: usize
) -> Result<&mut Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn add_constant<CS>(
    &self,
    cs: CS,
    other: &Fp2<P>
) -> Result<Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn add_constant_in_place<CS>(
    &mut self,
    cs: CS,
    other: &Fp2<P>
) -> Result<&mut Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn mul_by_constant<CS>(
    &self,
    cs: CS,
    fe: &Fp2<P>
) -> Result<Fp2Gadget<P, F>, SynthesisError> where
    CS: ConstraintSystem<F>, 

pub fn cost_of_mul() -> usize

pub fn cost_of_inv() -> usize

fn add_in_place<CS>(
    &mut self,
    cs: CS,
    other: &Self
) -> Result<&mut Self, SynthesisError> where
    CS: ConstraintSystem<F>, 

fn sub_in_place<CS>(
    &mut self,
    cs: CS,
    other: &Self
) -> Result<&mut Self, SynthesisError> where
    CS: ConstraintSystem<F>, 

fn mul_in_place<CS>(
    &mut self,
    cs: CS,
    other: &Self
) -> Result<&mut Self, SynthesisError> where
    CS: ConstraintSystem<F>, 

fn square_equals<CS>(&self, cs: CS, result: &Self) -> Result<(), SynthesisError> where
    CS: ConstraintSystem<F>, 

fn sub_constant<CS>(&self, cs: CS, fe: &NativeF) -> Result<Self, SynthesisError> where
    CS: ConstraintSystem<F>, 

fn sub_constant_in_place<CS>(
    &mut self,
    cs: CS,
    other: &NativeF
) -> Result<&mut Self, SynthesisError> where
    CS: ConstraintSystem<F>, 

fn mul_by_constant_in_place<CS>(
    &mut self,
    cs: CS,
    other: &NativeF
) -> Result<&mut Self, SynthesisError> where
    CS: ConstraintSystem<F>, 

fn pow<CS>(&self, cs: CS, bits: &[Boolean]) -> Result<Self, SynthesisError> where
    CS: ConstraintSystem<F>, 

Accepts as input a list of bits which, when interpreted in big-endian form, are a scalar.

fn pow_by_constant<CS, S>(&self, cs: CS, exp: S) -> Result<Self, SynthesisError> where
    CS: ConstraintSystem<F>,
    S: AsRef<[u64]>, 

Computes self^S, where S is interpreted as an little-endian u64-decomposition of an integer.

impl<P> From<u128> for Fp2<P> where
    P: Fp2Parameters, 

pub fn from(other: u128) -> Fp2<P>

Performs the conversion.

impl<P> From<u16> for Fp2<P> where
    P: Fp2Parameters, 

pub fn from(other: u16) -> Fp2<P>

Performs the conversion.

impl<P> From<u32> for Fp2<P> where
    P: Fp2Parameters, 

pub fn from(other: u32) -> Fp2<P>

Performs the conversion.

impl<P> From<u64> for Fp2<P> where
    P: Fp2Parameters, 

pub fn from(other: u64) -> Fp2<P>

Performs the conversion.

impl<P> From<u8> for Fp2<P> where
    P: Fp2Parameters, 

pub fn from(other: u8) -> Fp2<P>

Performs the conversion.

impl<P> FromBytes for Fp2<P> where
    P: Fp2Parameters, 

pub fn read<R>(reader: R) -> Result<Fp2<P>, Error> where
    R: Read, 

Reads Self from reader.

impl<P> Hash for Fp2<P> where
    P: Fp2Parameters, 

pub fn hash<__HP>(&self, __state: &mut __HP) where
    __HP: Hasher, 

Feeds this value into the given Hasher.

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

Feeds a slice of this type into the given Hasher.

impl<'a, P> Mul<&'a Fp2<P>> for Fp2<P> where
    P: Fp2Parameters, 

type Output = Fp2<P>

The resulting type after applying the * operator.

pub fn mul(self, other: &Fp2<P>) -> Fp2<P>

Performs the * operation.

impl<'a, P> MulAssign<&'a Fp2<P>> for Fp2<P> where
    P: Fp2Parameters, 

pub fn mul_assign(&mut self, other: &Fp2<P>)

Performs the *= operation.

impl<P> Neg for Fp2<P> where
    P: Fp2Parameters, 

type Output = Fp2<P>

The resulting type after applying the - operator.

#[must_use]

pub fn neg(self) -> Fp2<P>

Performs the unary - operation.

impl<P> One for Fp2<P> where
    P: Fp2Parameters, 

pub fn one() -> Fp2<P>

pub fn is_one(&self) -> bool

impl<P> Ord for Fp2<P> where
    P: Fp2Parameters, 

Fp2 elements are ordered lexicographically.

pub fn cmp(&self, other: &Fp2<P>) -> Ordering

This method returns an Ordering between self and other.

#[must_use]

fn max(self, other: Self) -> Self

Compares and returns the maximum of two values.

#[must_use]

fn min(self, other: Self) -> Self

Compares and returns the minimum of two values.

#[must_use]

fn clamp(self, min: Self, max: Self) -> Self

Restrict a value to a certain interval.

impl<P> PartialEq<Fp2<P>> for Fp2<P> where
    P: Fp2Parameters, 

pub fn eq(&self, other: &Fp2<P>) -> bool

This method tests for self and other values to be equal, and is used by ==.

#[must_use]

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

This method tests for !=.

impl<P> PartialOrd<Fp2<P>> for Fp2<P> where
    P: Fp2Parameters, 

pub fn partial_cmp(&self, other: &Fp2<P>) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

#[must_use]

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

This method tests less than (for self and other) and is used by the < operator.

#[must_use]

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

This method tests less than or equal to (for self and other) and is used by the <= operator.

#[must_use]

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

This method tests greater than (for self and other) and is used by the > operator.

#[must_use]

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

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl<P> Serialize for Fp2<P> where
    P: Fp2Parameters,
    <P as Fp2Parameters>::Fp: Serialize, 

pub fn serialize<__S>(
    &self,
    __serializer: __S
) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error> where
    __S: Serializer, 

Serialize this value into the given Serde serializer.

impl<'a, P> SquareRootField for Fp2<P> where
    P: Fp2Parameters,
    <P as Fp2Parameters>::Fp: SquareRootField, 

pub fn legendre(&self) -> LegendreSymbol

Returns the Legendre symbol.

pub fn sqrt(&self) -> Option<Fp2<P>>

Returns the square root of self, if it exists.

pub fn sqrt_in_place(&mut self) -> Option<&mut Fp2<P>>

Sets self to be the square root of self, if it exists.

impl<'a, P> Sub<&'a Fp2<P>> for Fp2<P> where
    P: Fp2Parameters, 

type Output = Fp2<P>

The resulting type after applying the - operator.

pub fn sub(self, other: &Fp2<P>) -> Fp2<P>

Performs the - operation.

impl<'a, P> SubAssign<&'a Fp2<P>> for Fp2<P> where
    P: Fp2Parameters, 

pub fn sub_assign(&mut self, other: &Fp2<P>)

Performs the -= operation.

impl<P> ToBytes for Fp2<P> where
    P: Fp2Parameters, 

pub fn write<W>(&self, writer: W) -> Result<(), Error> where
    W: Write, 

Serializes self into writer.

impl<P> ToConstraintField<<P as Fp2Parameters>::Fp> for Fp2<P> where
    P: Fp2Parameters, 

pub fn to_field_elements(
    &self
) -> Result<Vec<<P as Fp2Parameters>::Fp, Global>, ConstraintFieldError>

impl<P> Zero for Fp2<P> where
    P: Fp2Parameters, 

pub fn zero() -> Fp2<P>

pub fn is_zero(&self) -> bool

impl<P> Copy for Fp2<P> where
    P: Fp2Parameters, 

impl<P> Eq for Fp2<P> where
    P: Fp2Parameters,