Struct Fp

pub struct Fp(/* private fields */);

This represents an element of $\mathbb{F}_p$ where

p = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001

is the base field of the Pallas curve.

Implementations

impl Fp

pub const fn zero() -> Fp

Returns zero, the additive identity.

pub const fn one() -> Fp

Returns one, the multiplicative identity.

pub const fn double(&self) -> Fp

Doubles this field element.

pub const fn from_raw(val: [u64; 4]) -> Fp

Converts from an integer represented in little endian into its (congruent) Fp representation.

pub const fn square(&self) -> Fp

Squares this element.

pub const fn mul(&self, rhs: &Fp) -> Fp

Multiplies rhs by self, returning the result.

pub const fn sub(&self, rhs: &Fp) -> Fp

Subtracts rhs from self, returning the result.

pub const fn add(&self, rhs: &Fp) -> Fp

Adds rhs to self, returning the result.

pub const fn neg(&self) -> Fp

Negates self.

Trait Implementations

impl<'a, 'b> Add<&'b Fp> for &'a Fp

type Output = Fp

The resulting type after applying the + operator.

fn add(self, rhs: &'b Fp) -> Fp

Performs the + operation.

impl<'b> Add<&'b Fp> for Fp

type Output = Fp

The resulting type after applying the + operator.

fn add(self, rhs: &'b Fp) -> Fp

Performs the + operation.

impl<'a> Add<Fp> for &'a Fp

type Output = Fp

The resulting type after applying the + operator.

fn add(self, rhs: Fp) -> Fp

Performs the + operation.

impl Add for Fp

type Output = Fp

The resulting type after applying the + operator.

fn add(self, rhs: Fp) -> Fp

Performs the + operation.

impl<'b> AddAssign<&'b Fp> for Fp

fn add_assign(&mut self, rhs: &'b Fp)

Performs the += operation.

impl AddAssign for Fp

fn add_assign(&mut self, rhs: Fp)

Performs the += operation.

impl Clone for Fp

fn clone(&self) -> Fp

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for Fp

fn conditional_select(a: &Fp, b: &Fp, choice: Choice) -> Fp

Select a or b according to choice.

fn conditional_assign(&mut self, other: &Self, choice: Choice)

Conditionally assign other to self, according to choice.

fn conditional_swap(a: &mut Self, b: &mut Self, choice: Choice)

Conditionally swap self and other if choice == 1; otherwise, reassign both unto themselves.

impl ConstantTimeEq for Fp

fn ct_eq(&self, other: &Fp) -> Choice

Determine if two items are equal.

fn ct_ne(&self, other: &Self) -> Choice

Determine if two items are NOT equal.

impl Debug for Fp

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

Formats the value using the given formatter.

impl Default for Fp

fn default() -> Fp

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Fp

fn deserialize<D>(d: D) -> Result<Fp, <D as Deserializer<'de>>::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Field for Fp

fn sqrt(&self) -> CtOption<Fp>

Computes the square root of this element, if it exists.

fn invert(&self) -> CtOption<Fp>

Computes the multiplicative inverse of this element, failing if the element is zero.

const ZERO: Fp = _

The zero element of the field, the additive identity.

const ONE: Fp = _

The one element of the field, the multiplicative identity.

fn random(rng: impl RngCore) -> Fp

Returns an element chosen uniformly at random using a user-provided RNG.

fn double(&self) -> Fp

Doubles this element.

fn square(&self) -> Fp

Squares this element.

fn sqrt_ratio(num: &Fp, div: &Fp) -> (Choice, Fp)

Computes:

fn sqrt_alt(&self) -> (Choice, Fp)

Equivalent to Self::sqrt_ratio(self, one()).

fn pow_vartime<S>(&self, exp: S) -> Fp

where S: AsRef<[u64]>,

Exponentiates self by exp, where exp is a little-endian order integer exponent.

fn is_zero(&self) -> Choice

Returns true iff this element is zero.

fn is_zero_vartime(&self) -> bool

Returns true iff this element is zero.

fn cube(&self) -> Self

Cubes this element.

fn pow<S>(&self, exp: S) -> Self

where S: AsRef<[u64]>,

Exponentiates self by exp, where exp is a little-endian order integer exponent.

impl From<bool> for Fp

fn from(bit: bool) -> Fp

Converts to this type from the input type.

impl From<u64> for Fp

fn from(val: u64) -> Fp

Converts to this type from the input type.

impl FromUniformBytes<64> for Fp

fn from_uniform_bytes(bytes: &[u8; 64]) -> Fp

Converts a 512-bit little endian integer into a Fp by reducing by the modulus.

impl<'a, 'b> Mul<&'b Fp> for &'a Eq

type Output = Eq

The resulting type after applying the * operator.

fn mul(self, other: &'b Fp) -> <&'a Eq as Mul<&'b Fp>>::Output

Performs the * operation.

impl<'a, 'b> Mul<&'b Fp> for &'a EqAffine

type Output = Eq

The resulting type after applying the * operator.

fn mul(self, other: &'b Fp) -> <&'a EqAffine as Mul<&'b Fp>>::Output

Performs the * operation.

impl<'a, 'b> Mul<&'b Fp> for &'a Fp

type Output = Fp

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fp) -> Fp

Performs the * operation.

impl<'b> Mul<&'b Fp> for Eq

type Output = Eq

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fp) -> Eq

Performs the * operation.

impl<'b> Mul<&'b Fp> for EqAffine

type Output = Eq

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fp) -> Eq

Performs the * operation.

impl<'b> Mul<&'b Fp> for Fp

type Output = Fp

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fp) -> Fp

Performs the * operation.

impl<'a> Mul<Fp> for &'a Eq

type Output = Eq

The resulting type after applying the * operator.

fn mul(self, rhs: Fp) -> Eq

Performs the * operation.

impl<'a> Mul<Fp> for &'a EqAffine

type Output = Eq

The resulting type after applying the * operator.

fn mul(self, rhs: Fp) -> Eq

Performs the * operation.

impl<'a> Mul<Fp> for &'a Fp

type Output = Fp

The resulting type after applying the * operator.

fn mul(self, rhs: Fp) -> Fp

Performs the * operation.

impl Mul<Fp> for Eq

type Output = Eq

The resulting type after applying the * operator.

fn mul(self, rhs: Fp) -> Eq

Performs the * operation.

impl Mul<Fp> for EqAffine

type Output = Eq

The resulting type after applying the * operator.

fn mul(self, rhs: Fp) -> Eq

Performs the * operation.

impl Mul for Fp

type Output = Fp

The resulting type after applying the * operator.

fn mul(self, rhs: Fp) -> Fp

Performs the * operation.

impl<'b> MulAssign<&'b Fp> for Eq

fn mul_assign(&mut self, rhs: &'b Fp)

Performs the *= operation.

impl<'b> MulAssign<&'b Fp> for Fp

fn mul_assign(&mut self, rhs: &'b Fp)

Performs the *= operation.

impl MulAssign<Fp> for Eq

fn mul_assign(&mut self, rhs: Fp)

Performs the *= operation.

impl MulAssign for Fp

fn mul_assign(&mut self, rhs: Fp)

Performs the *= operation.

impl<'a> Neg for &'a Fp

type Output = Fp

The resulting type after applying the - operator.

fn neg(self) -> Fp

Performs the unary - operation.

impl Neg for Fp

type Output = Fp

The resulting type after applying the - operator.

fn neg(self) -> Fp

Performs the unary - operation.

impl Ord for Fp

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

This method returns an Ordering between self and other.

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

where Self: Sized,

Compares and returns the maximum of two values.

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

where Self: Sized,

Compares and returns the minimum of two values.

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

where Self: Sized,

Restrict a value to a certain interval.

impl PartialEq for Fp

fn eq(&self, other: &Fp) -> 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 PartialOrd for Fp

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

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

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

Tests less than (for self and other) and is used by the < operator.

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

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

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

Tests greater than (for self and other) and is used by the > operator.

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

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

impl PrimeField for Fp

const MODULUS: &'static str = "0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001"

Modulus of the field written as a string for debugging purposes.

const TWO_INV: Fp = _

Inverse of $2$ in the field.

const NUM_BITS: u32 = 255u32

How many bits are needed to represent an element of this field.

const CAPACITY: u32 = 254u32

How many bits of information can be reliably stored in the field element.

const MULTIPLICATIVE_GENERATOR: Fp = GENERATOR

A fixed multiplicative generator of modulus - 1 order. This element must also be a quadratic nonresidue.

const S: u32 = 32u32

An integer s satisfying the equation 2^s * t = modulus - 1 with t odd.

const ROOT_OF_UNITY: Fp = ROOT_OF_UNITY

The 2^s root of unity.

const ROOT_OF_UNITY_INV: Fp = _

Inverse of Self::ROOT_OF_UNITY.

const DELTA: Fp = DELTA

Generator of the t-order multiplicative subgroup.

type Repr = [u8; 32]

The prime field can be converted back and forth into this binary representation.

fn from_u128(v: u128) -> Fp

Obtains a field element congruent to the integer v.

fn from_repr(repr: <Fp as PrimeField>::Repr) -> CtOption<Fp>

Attempts to convert a byte representation of a field element into an element of this prime field, failing if the input is not canonical (is not smaller than the field’s modulus).

fn to_repr(&self) -> <Fp as PrimeField>::Repr

Converts an element of the prime field into the standard byte representation for this field.

fn is_odd(&self) -> Choice

Returns true iff this element is odd.

fn from_str_vartime(s: &str) -> Option<Self>

Interpret a string of numbers as a (congruent) prime field element. Does not accept unnecessary leading zeroes or a blank string.

fn from_repr_vartime(repr: Self::Repr) -> Option<Self>

Attempts to convert a byte representation of a field element into an element of this prime field, failing if the input is not canonical (is not smaller than the field’s modulus).

fn is_even(&self) -> Choice

Returns true iff this element is even.

impl PrimeFieldBits for Fp

type ReprBits = [u64; 4]

The backing store for a bit representation of a prime field element.

fn to_le_bits(&self) -> BitArray<<Fp as PrimeFieldBits>::ReprBits>

Converts an element of the prime field into a little-endian sequence of bits.

fn char_le_bits() -> BitArray<<Fp as PrimeFieldBits>::ReprBits>

Returns the bits of the field characteristic (the modulus) in little-endian order.

impl<T> Product<T> for Fp

where T: Borrow<Fp>,

fn product<I>(iter: I) -> Fp

where I: Iterator<Item = T>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl Serialize for Fp

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

where S: Serializer,

Serialize this value into the given Serde serializer.

impl<'a, 'b> Sub<&'b Fp> for &'a Fp

type Output = Fp

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Fp) -> Fp

Performs the - operation.

impl<'b> Sub<&'b Fp> for Fp

type Output = Fp

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Fp) -> Fp

Performs the - operation.

impl<'a> Sub<Fp> for &'a Fp

type Output = Fp

The resulting type after applying the - operator.

fn sub(self, rhs: Fp) -> Fp

Performs the - operation.

impl Sub for Fp

type Output = Fp

The resulting type after applying the - operator.

fn sub(self, rhs: Fp) -> Fp

Performs the - operation.

impl<'b> SubAssign<&'b Fp> for Fp

fn sub_assign(&mut self, rhs: &'b Fp)

Performs the -= operation.

impl SubAssign for Fp

fn sub_assign(&mut self, rhs: Fp)

Performs the -= operation.

impl<T> Sum<T> for Fp

where T: Borrow<Fp>,

fn sum<I>(iter: I) -> Fp

where I: Iterator<Item = T>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl WithSmallOrderMulGroup<3> for Fp

const ZETA: Fp = _

A field element of small multiplicative order $N$.

impl Copy for Fp

impl Eq for Fp