Struct ScalarField 

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

Implementations

impl ScalarField

pub fn from_le_bytes_checked(bytes: [u8; 32]) -> Option<Self>

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

Trait Implementations

impl<'r> Add<&'r ScalarField> for ScalarField

type Output = ScalarField

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add for ScalarField

type Output = ScalarField

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'r> AddAssign<&'r ScalarField> for ScalarField

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

Performs the += operation.

impl AddAssign for ScalarField

fn add_assign(&mut self, other: ScalarField)

Performs the += operation.

impl Clone for ScalarField

fn clone(&self) -> ScalarField

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for ScalarField

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

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 ScalarField

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

Determine if two items are equal.

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

Determine if two items are NOT equal.

impl Debug for ScalarField

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

Formats the value using the given formatter.

impl Default for ScalarField

fn default() -> ScalarField

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for ScalarField

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Field for ScalarField

fn random(rng: impl RngCore) -> Self

Computes a uniformly random element using rejection sampling.

const ZERO: Self

The zero element of the field, the additive identity.

const ONE: Self = R

The one element of the field, the multiplicative identity.

fn is_zero_vartime(&self) -> bool

Returns true iff this element is zero.

fn double(&self) -> Self

Doubles this element.

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

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

fn square(&self) -> Self

Squares this element.

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

Computes:

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

Returns the square root of the field element, if it is quadratic residue.

fn is_zero(&self) -> Choice

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.

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

where S: AsRef<[u64]>,

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

impl From<&BigInt> for ScalarField

fn from(number: &BigInt) -> Self

Converts to this type from the input type.

impl From<&BigUint> for ScalarField

fn from(number: &BigUint) -> Self

Converts to this type from the input type.

impl From<&Number> for ScalarField

fn from(number: &Number) -> Self

Converts to this type from the input type.

impl From<Number> for ScalarField

fn from(number: Number) -> Self

Converts to this type from the input type.

impl From<Scalar> for ScalarField

fn from(value: Scalar) -> Self

Converts to this type from the input type.

impl From<bool> for ScalarField

fn from(value: bool) -> Self

Converts to this type from the input type.

impl From<f64> for ScalarField

fn from(value: f64) -> Self

Converts to this type from the input type.

impl From<i32> for ScalarField

fn from(value: i32) -> Self

Converts to this type from the input type.

impl From<u64> for ScalarField

fn from(val: u64) -> ScalarField

Converts to this type from the input type.

impl FromF25519<BaseField> for ScalarField

fn from_F25519(value: BaseField) -> Vec<ScalarField>

Injectively map a BaseField element into a Vec of ScalarField elements.

impl FromLeBytes for ScalarField

fn from_le_bytes(bytes: [u8; 32]) -> Self

impl Hash for ScalarField

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<'r> Mul<&'r ScalarField> for ScalarField

type Output = ScalarField

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<AffineEdwardsPoint<BaseField>> for ScalarField

type Output = AffineEdwardsPoint<BaseField>

The resulting type after applying the * operator.

fn mul(self, rhs: AffineEdwardsPoint<BaseField>) -> Self::Output

Performs the * operation.

impl Mul<Point<Dalek>> for ScalarField

type Output = Point<Dalek>

The resulting type after applying the * operator.

fn mul(self, rhs: CurvePoint) -> Self::Output

Performs the * operation.

impl Mul<ProjectiveEdwardsPoint<BaseField>> for ScalarField

type Output = ProjectiveEdwardsPoint<BaseField>

The resulting type after applying the * operator.

fn mul(self, rhs: ProjectiveEdwardsPoint<BaseField>) -> Self::Output

Performs the * operation.

impl Mul for ScalarField

type Output = ScalarField

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'r> MulAssign<&'r ScalarField> for ScalarField

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

Performs the *= operation.

impl MulAssign for ScalarField

fn mul_assign(&mut self, other: ScalarField)

Performs the *= operation.

impl MxeRescueKey for ScalarField

fn mxe_rescue_key(i: usize) -> Self

impl MxeX25519PrivateKey for ScalarField

fn mxe_x25519_private_key() -> Self

impl Neg for ScalarField

type Output = ScalarField

The resulting type after applying the - operator.

fn neg(self) -> ScalarField

Performs the unary - operation.

impl Ord for ScalarField

Elements are ordered lexicographically.

fn cmp(&self, other: &ScalarField) -> 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 ScalarField

fn eq(&self, other: &ScalarField) -> 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 ScalarField

fn partial_cmp(&self, other: &ScalarField) -> 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 ScalarField

const MODULUS: &'static str = MODULUS_STR

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

const NUM_BITS: u32 = MODULUS_BITS

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

const CAPACITY: u32

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

const TWO_INV: Self = TWO_INV

Inverse of $2$ in the field.

const MULTIPLICATIVE_GENERATOR: Self = GENERATOR

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

const S: u32 = S

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

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.

type Repr = ScalarFieldRepr

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

fn from_repr(r: ScalarFieldRepr) -> CtOption<ScalarField>

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 from_repr_vartime(r: ScalarFieldRepr) -> Option<ScalarField>

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) -> ScalarFieldRepr

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_u128(v: u128) -> Self

Obtains a field element congruent to the integer v.

fn is_even(&self) -> Choice

Returns true iff this element is even.

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

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

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

impl Serialize for ScalarField

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

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl Shr<usize> for ScalarField

type Output = ScalarField

The resulting type after applying the >> operator.

fn shr(self, rhs: usize) -> Self::Output

Performs the >> operation.

impl<'r> Sub<&'r ScalarField> for ScalarField

type Output = ScalarField

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub for ScalarField

type Output = ScalarField

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'r> SubAssign<&'r ScalarField> for ScalarField

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

Performs the -= operation.

impl SubAssign for ScalarField

fn sub_assign(&mut self, other: ScalarField)

Performs the -= operation.

impl<T: Borrow<ScalarField>> Sum<T> for ScalarField

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

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

impl UsedField for ScalarField

fn modulus() -> Number

The prime number p such that the field is F_p.

fn get_alpha() -> Number

The smallest prime such that it does not divide p-1.

fn get_alpha_inverse() -> Number

The smallest positive integer n such that alpha*n = 1 mod (p-1).

fn mds_matrix_and_inverse(width: usize) -> (Matrix<Self>, Matrix<Self>)

An MDS matrix and its inverse.

fn power_of_two(exponent: usize) -> Self

Returns two^exponent.

fn negative_power_of_two(exponent: usize) -> Self

Returns -two^exponent.

fn to_unsigned_number(self) -> Number

fn to_signed_number(self) -> Number

fn is_binary(self) -> bool

Whether a number is binary or not.

fn is_ge_zero(self) -> bool

Whether a number is greater or equal to zero according to the signed order.

fn is_le_zero(self) -> bool

Whether a number is less than or equal to zero according to the signed order.

fn is_gt_zero(self) -> bool

Whether a number is greater than zero according to the signed order.

fn is_lt_zero(self) -> bool

Whether a number is less than zero according to the signed order.

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

Max according to the cyclic order on the smaller interval between the two field elements.

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

Min according to the cyclic order on the smaller interval between the two field elements.

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

Max according to (un)signed order.

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

Min according to (un)signed order.

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

Sort according to the cyclic order on the smaller interval between the two field elements.

fn abs(self) -> Self

Abs according to the signed order.

fn does_mul_overflow(self, other: Self) -> bool

fn does_add_signed_overflow(self, other: Self) -> bool

fn does_add_unsigned_overflow(self, other: Self) -> bool

fn unsigned_bits(self) -> usize

The number of bits of self in unsigned notation.

fn signed_bits(self) -> usize

The number of bits of self in signed notation.

fn unsigned_bit(&self, idx: usize) -> bool

The idx bit of self in unsigned notation.

fn signed_bit(&self, idx: usize) -> bool

The idx bit of self in signed notation.

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

The unsigned Euclidean division. Returns 0 if the divisor is 0.

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

The signed Euclidean division. Returns 0 if the divisor is 0.

fn gen_inclusive_range<R: Rng + ?Sized>( rng: &mut R, min: Self, max: Self, ) -> Self

Generates a field element between min and max, included.

fn from_bin(bin: &str) -> Self

Converts a number in lsb-to-msb binary expansion to the corresponding element in Self.

fn to_bin(&self) -> String

Converts self to its lsb-to-msb binary expansion.

fn as_power_of_two(self) -> Option<usize>

impl Zero for ScalarField

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

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

impl Copy for ScalarField

impl Eq for ScalarField