Struct snarkvm_fields::Fp12

pub struct Fp12<P: Fp12Parameters> {
    pub c0: Fp6<P::Fp6Params>,
    pub c1: Fp6<P::Fp6Params>,
}

An element of Fp12, represented by c0 + c1 * v

Fields

c0: Fp6<P::Fp6Params>

c1: Fp6<P::Fp6Params>

Implementations

impl<P: Fp12Parameters> Fp12<P>

pub fn new(c0: Fp6<P::Fp6Params>, c1: Fp6<P::Fp6Params>) -> Self

pub fn mul_by_fp(
    &mut self,
    element: &<<P::Fp6Params as Fp6Parameters>::Fp2Params as Fp2Parameters>::Fp
)

pub fn conjugate(&mut self)

pub fn mul_by_034(
    &mut self,
    c0: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
    c3: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
    c4: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>
)

pub fn mul_by_014(
    &mut self,
    c0: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
    c1: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
    c4: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>
)

pub fn cyclotomic_square(&self) -> Self

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

Trait Implementations

impl<P: Fp12Parameters> Add<&&Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, P: Fp12Parameters> Add<&'a Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, P: Fp12Parameters> Add<&'a mut Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the + operator.

fn add(self, other: &'a mut Self) -> Self

Performs the + operation.

impl<P: Fp12Parameters> Add<Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<P: Fp12Parameters> AddAssign<&&Fp12<P>> for Fp12<P>

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

Performs the += operation.

impl<'a, P: Fp12Parameters> AddAssign<&'a Fp12<P>> for Fp12<P>

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

Performs the += operation.

impl<'a, P: Fp12Parameters> AddAssign<&'a mut Fp12<P>> for Fp12<P>

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

Performs the += operation.

impl<P: Fp12Parameters> AddAssign<Fp12<P>> for Fp12<P>

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<P: Fp12Parameters> CanonicalDeserialize for Fp12<P>

fn deserialize_with_mode<R: Read>(
    reader: R,
    compress: Compress,
    validate: Validate
) -> Result<Self, SerializationError>

fn deserialize_compressed<R>(reader: R) -> Result<Self, SerializationError>where
    R: Read,

fn deserialize_compressed_unchecked<R>(
    reader: R
) -> Result<Self, SerializationError>where
    R: Read,

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

fn deserialize_uncompressed_unchecked<R>(
    reader: R
) -> Result<Self, SerializationError>where
    R: Read,

impl<P: Fp12Parameters> CanonicalDeserializeWithFlags for Fp12<P>

fn deserialize_with_flags<R: Read, F: Flags>(
    reader: R
) -> Result<(Self, F), SerializationError>

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

impl<P: Fp12Parameters> CanonicalSerialize for Fp12<P>

fn serialize_with_mode<W: Write>(
    &self,
    writer: W,
    _compress: Compress
) -> Result<(), SerializationError>

fn serialized_size(&self, compress: Compress) -> usize

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

fn compressed_size(&self) -> usize

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

fn uncompressed_size(&self) -> usize

impl<P: Fp12Parameters> CanonicalSerializeWithFlags for Fp12<P>

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

Serializes self and flags into writer.

fn serialized_size_with_flags<F: Flags>(&self) -> usize

Serializes self and flags into writer.

impl<P: Fp12Parameters> Clone for Fp12<P>where
    P: Fp12Parameters,

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<P: Fp12Parameters> Debug for Fp12<P>where
    P: Fp12Parameters,

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

Formats the value using the given formatter.

impl<P: Fp12Parameters> Default for Fp12<P>where
    P: Fp12Parameters,

fn default() -> Self

Returns the “default value” for a type.

impl<'de, P: Fp12Parameters> Deserialize<'de> for Fp12<P>

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>where
    __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<P: Fp12Parameters> Display for Fp12<P>

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

Formats the value using the given formatter.

impl<P: Fp12Parameters> Distribution<Fp12<P>> for Standard

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Fp12<P>

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<P: Fp12Parameters> Div<&&Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the / operator.

fn div(self, other: &&Self) -> Self

Performs the / operation.

impl<'a, P: Fp12Parameters> Div<&'a Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the / operator.

fn div(self, other: &Self) -> Self

Performs the / operation.

impl<'a, P: Fp12Parameters> Div<&'a mut Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the / operator.

fn div(self, other: &'a mut Self) -> Self

Performs the / operation.

impl<P: Fp12Parameters> Div<Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<P: Fp12Parameters> DivAssign<&&Fp12<P>> for Fp12<P>

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

Performs the /= operation.

impl<'a, P: Fp12Parameters> DivAssign<&'a Fp12<P>> for Fp12<P>

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

Performs the /= operation.

impl<'a, P: Fp12Parameters> DivAssign<&'a mut Fp12<P>> for Fp12<P>

fn div_assign(&mut self, other: &'a mut Self)

Performs the /= operation.

impl<P: Fp12Parameters> DivAssign<Fp12<P>> for Fp12<P>

fn div_assign(&mut self, other: Self)

Performs the /= operation.

impl<P: Fp12Parameters> Field for Fp12<P>

type BasePrimeField = <Fp6<<P as Fp12Parameters>::Fp6Params> as Field>::BasePrimeField

fn from_base_prime_field(other: Self::BasePrimeField) -> Self

Constructs an element of Self from an element of the base prime field.

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

Returns the characteristic of the field.

fn double(&self) -> Self

Returns self + self.

fn from_random_bytes_with_flags<F: Flags>(bytes: &[u8]) -> Option<(Self, F)>

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.

fn from_random_bytes(bytes: &[u8]) -> Option<Self>

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.

fn double_in_place(&mut self)

Doubles self in place.

fn frobenius_map(&mut self, power: usize)

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

fn square(&self) -> Self

Returns self * self.

fn square_in_place(&mut self) -> &mut Self

Squares self in place.

fn inverse(&self) -> Option<Self>

Computes the multiplicative inverse of self if self is nonzero.

fn inverse_in_place(&mut self) -> Option<&mut Self>

Sets self to self’s inverse if it exists. Otherwise it is a no-op.

fn half() -> Self

Returns the constant 2^{-1}.

fn sum_of_products<'a>(
    a: impl Iterator<Item = &'a Self> + Clone,
    b: impl Iterator<Item = &'a Self> + Clone
) -> Self

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

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

impl<P: Fp12Parameters> From<u128> for Fp12<P>

fn from(other: u128) -> Self

Converts to this type from the input type.

impl<P: Fp12Parameters> From<u16> for Fp12<P>

fn from(other: u16) -> Self

Converts to this type from the input type.

impl<P: Fp12Parameters> From<u32> for Fp12<P>

fn from(other: u32) -> Self

Converts to this type from the input type.

impl<P: Fp12Parameters> From<u64> for Fp12<P>

fn from(other: u64) -> Self

Converts to this type from the input type.

impl<P: Fp12Parameters> From<u8> for Fp12<P>

fn from(other: u8) -> Self

Converts to this type from the input type.

impl<P: Fp12Parameters> FromBytes for Fp12<P>

fn read_le<R: Read>(reader: R) -> IoResult<Self>

Reads Self from reader as little-endian bytes.

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

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

impl<P: Fp12Parameters> Hash for Fp12<P>where
    P: Fp12Parameters,

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,
    Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<P: Fp12Parameters> Mul<&&Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the * operator.

fn mul(self, other: &&Self) -> Self

Performs the * operation.

impl<'a, P: Fp12Parameters> Mul<&'a Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the * operator.

fn mul(self, other: &Self) -> Self

Performs the * operation.

impl<'a, P: Fp12Parameters> Mul<&'a mut Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the * operator.

fn mul(self, other: &'a mut Self) -> Self

Performs the * operation.

impl<P: Fp12Parameters> Mul<Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<P: Fp12Parameters> MulAssign<&&Fp12<P>> for Fp12<P>

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

Performs the *= operation.

impl<'a, P: Fp12Parameters> MulAssign<&'a Fp12<P>> for Fp12<P>

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

Performs the *= operation.

impl<'a, P: Fp12Parameters> MulAssign<&'a mut Fp12<P>> for Fp12<P>

fn mul_assign(&mut self, other: &'a mut Self)

Performs the *= operation.

impl<P: Fp12Parameters> MulAssign<Fp12<P>> for Fp12<P>

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl<P: Fp12Parameters> Neg for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<P: Fp12Parameters> One for Fp12<P>

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

impl<P: Fp12Parameters> Ord for Fp12<P>

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

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

Compares and returns the maximum of two values.

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

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Selfwhere
    Self: Sized + PartialOrd<Self>,

Restrict a value to a certain interval.

impl<P: Fp12Parameters> PartialEq<Fp12<P>> for Fp12<P>where
    P: Fp12Parameters,

fn eq(&self, other: &Self) -> bool

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

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

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

impl<P: Fp12Parameters> PartialOrd<Fp12<P>> for Fp12<P>

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

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

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

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

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

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

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

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

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<'a, P: Fp12Parameters> Product<&'a Fp12<P>> for Fp12<P>

fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<P: Fp12Parameters> Product<Fp12<P>> for Fp12<P>

fn product<I: Iterator<Item = Self>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<P: Fp12Parameters> Serialize for Fp12<P>

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

Serialize this value into the given Serde serializer.

impl<P: Fp12Parameters> Sub<&&Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, P: Fp12Parameters> Sub<&'a Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, P: Fp12Parameters> Sub<&'a mut Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the - operator.

fn sub(self, other: &'a mut Self) -> Self

Performs the - operation.

impl<P: Fp12Parameters> Sub<Fp12<P>> for Fp12<P>

type Output = Fp12<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<P: Fp12Parameters> SubAssign<&&Fp12<P>> for Fp12<P>

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

Performs the -= operation.

impl<'a, P: Fp12Parameters> SubAssign<&'a Fp12<P>> for Fp12<P>

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

Performs the -= operation.

impl<'a, P: Fp12Parameters> SubAssign<&'a mut Fp12<P>> for Fp12<P>

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

Performs the -= operation.

impl<P: Fp12Parameters> SubAssign<Fp12<P>> for Fp12<P>

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<'a, P: Fp12Parameters> Sum<&'a Fp12<P>> for Fp12<P>

fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<P: Fp12Parameters> Sum<Fp12<P>> for Fp12<P>

fn sum<I: Iterator<Item = Self>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<P: Fp12Parameters> ToBits for Fp12<P>

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.

impl<P: Fp12Parameters> ToBytes for Fp12<P>

fn write_le<W: Write>(&self, writer: W) -> IoResult<()>

Writes self into writer as little-endian bytes.

fn to_bytes_le(&self) -> Result<Vec<u8, Global>, Error>where
    Self: Sized,

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

impl<P: Fp12Parameters> Valid for Fp12<P>

fn check(&self) -> Result<(), SerializationError>

fn batch_check<'a>(
    _batch: impl Iterator<Item = &'a Self>
) -> Result<(), SerializationError>where
    Self: 'a,

impl<P: Fp12Parameters> Zero for Fp12<P>

fn zero() -> Self

fn is_zero(&self) -> bool

impl<P: Fp12Parameters> Copy for Fp12<P>where
    P: Fp12Parameters,

impl<P: Fp12Parameters> Eq for Fp12<P>where
    P: Fp12Parameters,