Struct Fp

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

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

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f

is the base field of the secp256k1 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 fn invert(&self) -> CtOption<Self>

Returns the multiplicative inverse of the element. If it is zero, the method fails.

pub fn jacobi(&self) -> i64

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

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

pub fn from_bytes(bytes: &[u8; 32]) -> CtOption<Fp>

Attempts to convert a little-endian byte representation of a scalar into a Fr, failing if the input is not canonical.

pub fn to_bytes(&self) -> [u8; 32]

Converts an element of Fr into a byte representation in little-endian byte order.

impl Fp

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

Adds rhs to self, returning the result.

impl Fp

pub const fn double(&self) -> Fp

Doubles this field element.

pub const fn square(&self) -> Fp

Squares this element.

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

Multiplies rhs by self, returning the result.

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

Subtracts rhs from self, returning the result.

pub const fn neg(&self) -> Self

Negates self.

impl Fp

pub const fn size() -> usize

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: &Self, b: &Self, choice: Choice) -> Self

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: &Self) -> 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

Formats the value using the given formatter.

impl Default for Fp

fn default() -> Self

Returns the “default value” for a type.

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

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

Deserialize this value from the given Serde deserializer.

impl Field for Fp

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

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

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

Returns the multiplicative inverse of the element. If it is zero, the method fails.

const ZERO: Self = _

The zero element of the field, the additive identity.

const ONE: Self = _

The one element of the field, the multiplicative identity.

fn random(rng: impl RngCore) -> Self

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

fn double(&self) -> Self

Doubles this element.

fn square(&self) -> Self

Squares this element.

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

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

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

Computes:

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 sqrt_alt(&self) -> (Choice, Self)

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

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<'a> From<&'a Fp> for [u8; 32]

fn from(value: &'a Fp) -> [u8; 32]

Converts to this type from the input type.

impl From<[u64; 4]> for Fp

fn from(digits: [u64; 4]) -> Self

Converts to this type from the input type.

impl From<Fp> for [u64; 4]

fn from(elt: Fp) -> [u64; 4]

Converts to this type from the input type.

impl From<Fp> for [u8; 32]

fn from(value: Fp) -> [u8; 32]

Converts to this type from the input type.

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]) -> Self

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

impl Hash for Fp

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

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 Legendre for Fp

fn legendre(&self) -> i64

fn ct_quadratic_non_residue(&self) -> Choice

fn ct_quadratic_residue(&self) -> Choice

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<'a, 'b> Mul<&'b Fp> for &'a Secq256k1

type Output = Secq256k1

The resulting type after applying the * operator.

fn mul(self, other: &'b Fp) -> Self::Output

Performs the * operation.

impl<'a, 'b> Mul<&'b Fp> for &'a Secq256k1Affine

type Output = Secq256k1

The resulting type after applying the * operator.

fn mul(self, other: &'b Fp) -> Self::Output

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<'b> Mul<&'b Fp> for Secq256k1

type Output = Secq256k1

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fp) -> Secq256k1

Performs the * operation.

impl<'b> Mul<&'b Fp> for Secq256k1Affine

type Output = Secq256k1

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fp) -> Secq256k1

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<'a> Mul<Fp> for &'a Secq256k1

type Output = Secq256k1

The resulting type after applying the * operator.

fn mul(self, rhs: Fp) -> Secq256k1

Performs the * operation.

impl<'a> Mul<Fp> for &'a Secq256k1Affine

type Output = Secq256k1

The resulting type after applying the * operator.

fn mul(self, rhs: Fp) -> Secq256k1

Performs the * operation.

impl Mul<Fp> for Secq256k1

type Output = Secq256k1

The resulting type after applying the * operator.

fn mul(self, rhs: Fp) -> Secq256k1

Performs the * operation.

impl Mul<Fp> for Secq256k1Affine

type Output = Secq256k1

The resulting type after applying the * operator.

fn mul(self, rhs: Fp) -> Secq256k1

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 Fp

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

Performs the *= operation.

impl<'b> MulAssign<&'b Fp> for Secq256k1

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

Performs the *= operation.

impl MulAssign<Fp> for Secq256k1

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: &Self) -> 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: &Self) -> 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 = MODULUS_STR

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

const MULTIPLICATIVE_GENERATOR: Self = MULTIPLICATIVE_GENERATOR

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

const TWO_INV: Self = TWO_INV

Inverse of $2$ in the field.

const ROOT_OF_UNITY: Self = ROOT_OF_UNITY

The 2^s root of unity.

const ROOT_OF_UNITY_INV: Self = ROOT_OF_UNITY_INV

Inverse of Self::ROOT_OF_UNITY.

const DELTA: Self = DELTA

Generator of the t-order multiplicative subgroup.

const NUM_BITS: u32 = 256u32

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

const CAPACITY: u32 = 255u32

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

const S: u32 = 1u32

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

type Repr = [u8; 32]

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

fn from_repr(repr: Self::Repr) -> CtOption<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 to_repr(&self) -> Self::Repr

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

fn from_u128(v: u128) -> Self

Obtains a field element congruent to the integer v.

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) -> FieldBits<Self::ReprBits>

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

fn char_le_bits() -> FieldBits<Self::ReprBits>

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

impl<T: Borrow<Fp>> Product<T> for Fp

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

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

impl SerdeObject for Fp

fn from_raw_bytes_unchecked(bytes: &[u8]) -> Self

The purpose of unchecked functions is to read the internal memory representation of a type from bytes as quickly as possible. No sanitization checks are performed to ensure the bytes represent a valid object. As such this function should only be used internally as an extension of machine memory. It should not be used to deserialize externally provided data.

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

fn to_raw_bytes(&self) -> Vec<u8>

fn read_raw_unchecked<R: Read>(reader: &mut R) -> Self

The purpose of unchecked functions is to read the internal memory representation of a type from disk as quickly as possible. No sanitization checks are performed to ensure the bytes represent a valid object. This function should only be used internally when some machine state cannot be kept in memory (e.g., between runs) and needs to be reloaded as quickly as possible.

fn read_raw<R: Read>(reader: &mut R) -> Result<Self>

fn write_raw<W: Write>(&self, writer: &mut W) -> Result<()>

impl Serialize for Fp

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

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: Borrow<Fp>> Sum<T> for Fp

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

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

impl WithSmallOrderMulGroup<3> for Fp

const ZETA: Self = ZETA

A field element of small multiplicative order $N$.

impl Copy for Fp

impl Eq for Fp

impl StructuralPartialEq for Fp