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p384

Struct FieldElement

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pub struct FieldElement(/* private fields */);
Available on crate features arithmetic and expose-field only.
Expand description

Element of the secp384r1 base field used for curve coordinates.

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impl FieldElement

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pub const ZERO: Self

Zero element.

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pub const ONE: Self

Multiplicative identity.

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pub fn from_bytes(repr: &FieldBytes) -> CtOption<Self>

Create a FieldElement from a canonical big-endian representation.

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pub fn from_slice(slice: &[u8]) -> Option<Self>

Decode FieldElement from a big endian byte slice.

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pub fn from_uint(uint: U384) -> CtOption<Self>

Decode FieldElement from U384 converting it into Montgomery form:

w * R^2 * R^-1 mod p = wR mod p
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pub const fn from_u64(w: u64) -> Self

Convert a u64 into a FieldElement.

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pub fn to_bytes(self) -> FieldBytes

Returns the big-endian encoding of this FieldElement.

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pub fn is_odd(&self) -> Choice

Determine if this FieldElement is odd in the SEC1 sense: self mod 2 == 1.

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If odd, return Choice(1). Otherwise, return Choice(0).

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pub fn is_even(&self) -> Choice

Determine if this FieldElement is even in the SEC1 sense: self mod 2 == 0.

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If even, return Choice(1). Otherwise, return Choice(0).

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pub fn is_zero(&self) -> Choice

Determine if this FieldElement is zero.

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If zero, return Choice(1). Otherwise, return Choice(0).

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pub const fn pow_vartime(&self, exp: &[u64]) -> Self

Returns self^exp, where exp is a little-endian integer exponent.

This operation is variable time with respect to the exponent.

If the exponent is fixed, this operation is constant time.

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pub const fn shr(&self, shift: u32) -> Self

Right shifts the FieldElement.

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pub const fn shr_vartime(&self, shift: u32) -> Self

Right shifts the FieldElement.

Note: not constant-time with respect to the shift parameter.

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impl FieldElement

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pub const fn to_canonical(self) -> U384

Translate FieldElement out of the Montgomery domain, returning a U384 in canonical form.

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

Add elements.

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pub const fn double(&self) -> Self

Double element (add it to itself).

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

Subtract elements.

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

Multiply elements.

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pub const fn neg(&self) -> Self

Negate element.

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pub const fn square(&self) -> Self

Compute modular square.

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

Compute FieldElement inversion: 1 / self.

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impl FieldElement

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

Returns the square root of self mod p, or None if no square root exists.

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impl Add<&FieldElement> for &FieldElement

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type Output = FieldElement

The resulting type after applying the + operator.
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fn add(self, rhs: &FieldElement) -> FieldElement

Performs the + operation. Read more
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impl Add<&FieldElement> for FieldElement

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type Output = FieldElement

The resulting type after applying the + operator.
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fn add(self, rhs: &FieldElement) -> FieldElement

Performs the + operation. Read more
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impl Add for FieldElement

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type Output = FieldElement

The resulting type after applying the + operator.
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fn add(self, rhs: FieldElement) -> FieldElement

Performs the + operation. Read more
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impl AddAssign<&FieldElement> for FieldElement

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

Performs the += operation. Read more
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impl AddAssign for FieldElement

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fn add_assign(&mut self, other: FieldElement)

Performs the += operation. Read more
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impl Clone for FieldElement

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fn clone(&self) -> FieldElement

Returns a copy of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl ConditionallySelectable for FieldElement

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

Select a or b according to choice. Read more
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fn conditional_assign(&mut self, other: &Self, choice: Choice)

Conditionally assign other to self, according to choice. Read more
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fn conditional_swap(a: &mut Self, b: &mut Self, choice: Choice)

Conditionally swap self and other if choice == 1; otherwise, reassign both unto themselves. Read more
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impl ConstantTimeEq for FieldElement

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

Determine if two items are equal. Read more
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fn ct_ne(&self, other: &Self) -> Choice

Determine if two items are NOT equal. Read more
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impl ConstantTimeGreater for FieldElement

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

Determine whether self > other. Read more
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impl ConstantTimeLess for FieldElement

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

Determine whether self < other. Read more
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impl Debug for FieldElement

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

Formats the value using the given formatter. Read more
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impl Default for FieldElement

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fn default() -> Self

Returns the “default value” for a type. Read more
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impl Field for FieldElement

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const ZERO: Self = Self::ZERO

The zero element of the field, the additive identity.
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const ONE: Self = Self::ONE

The one element of the field, the multiplicative identity.
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fn try_from_rng<R: TryRngCore + ?Sized>(rng: &mut R) -> Result<Self, R::Error>

Returns an element chosen uniformly at random using a user-provided RNG.
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fn is_zero(&self) -> Choice

Returns true iff this element is zero.
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fn square(&self) -> Self

Squares this element.
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fn double(&self) -> Self

Doubles this element.
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fn invert(&self) -> CtOption<Self>

Computes the multiplicative inverse of this element, failing if the element is zero.
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fn sqrt(&self) -> CtOption<Self>

Returns the square root of the field element, if it is quadratic residue. Read more
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fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self)

Computes: Read more
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fn random<R>(rng: &mut R) -> Self
where R: RngCore + ?Sized,

Returns an element chosen uniformly at random using a user-provided RNG.
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fn is_zero_vartime(&self) -> bool

Returns true iff this element is zero. Read more
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fn cube(&self) -> Self

Cubes this element.
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fn sqrt_alt(&self) -> (Choice, Self)

Equivalent to Self::sqrt_ratio(self, one()). Read more
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fn pow<S>(&self, exp: S) -> Self
where S: AsRef<[u64]>,

Exponentiates self by exp, where exp is a little-endian order integer exponent. Read more
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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. Read more
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impl From<&FieldElement> for FieldBytes

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fn from(fe: &FieldElement) -> Self

Converts to this type from the input type.
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impl From<&FieldElement> for U384

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fn from(fe: &FieldElement) -> U384

Converts to this type from the input type.
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impl From<FieldElement> for FieldBytes

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fn from(fe: FieldElement) -> Self

Converts to this type from the input type.
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impl From<FieldElement> for U384

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fn from(fe: FieldElement) -> U384

Converts to this type from the input type.
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impl From<u128> for FieldElement

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fn from(n: u128) -> FieldElement

Converts to this type from the input type.
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impl From<u32> for FieldElement

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fn from(n: u32) -> FieldElement

Converts to this type from the input type.
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impl From<u64> for FieldElement

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fn from(n: u64) -> FieldElement

Converts to this type from the input type.
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impl FromOkm for FieldElement

Available on crate feature hash2curve only.
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type Length = UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B1>, B0>, B0>, B0>

The number of bytes needed to convert to a field element.
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fn from_okm(data: &Array<u8, Self::Length>) -> Self

Convert a byte sequence into a field element.
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impl Invert for FieldElement

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type Output = CtOption<FieldElement>

Output of the inversion.
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fn invert(&self) -> CtOption<Self>

Computes the inverse.
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fn invert_vartime(&self) -> Self::Output

Computes the inverse in variable-time.
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impl Mul<&FieldElement> for &FieldElement

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type Output = FieldElement

The resulting type after applying the * operator.
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fn mul(self, rhs: &FieldElement) -> FieldElement

Performs the * operation. Read more
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impl Mul<&FieldElement> for FieldElement

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type Output = FieldElement

The resulting type after applying the * operator.
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fn mul(self, rhs: &FieldElement) -> FieldElement

Performs the * operation. Read more
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impl Mul for FieldElement

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type Output = FieldElement

The resulting type after applying the * operator.
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fn mul(self, rhs: FieldElement) -> FieldElement

Performs the * operation. Read more
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impl MulAssign<&FieldElement> for FieldElement

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

Performs the *= operation. Read more
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impl MulAssign for FieldElement

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fn mul_assign(&mut self, other: FieldElement)

Performs the *= operation. Read more
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impl Neg for &FieldElement

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type Output = FieldElement

The resulting type after applying the - operator.
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fn neg(self) -> FieldElement

Performs the unary - operation. Read more
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impl Neg for FieldElement

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type Output = FieldElement

The resulting type after applying the - operator.
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fn neg(self) -> FieldElement

Performs the unary - operation. Read more
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impl OsswuMap for FieldElement

Available on crate feature hash2curve only.
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const PARAMS: OsswuMapParams<Self>

The OSSWU parameters for mapping the field to affine points. For Weierstrass curves having A==0 or B==0, the parameters should be for isogeny where A≠0 and B≠0.
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fn sqrt_ratio_3mod4(u: Self, v: Self) -> (Choice, Self)

Optimized sqrt_ratio for q = 3 mod 4.
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fn osswu(&self) -> (Self, Self)

Convert this field element into an affine point on the elliptic curve returning (X, Y). For Weierstrass curves having A==0 or B==0 the result is a point on an isogeny.
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impl PartialEq for FieldElement

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

Tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl PrimeField for FieldElement

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const MODULUS: &'static str = "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff"

Modulus of the field written as a string for debugging purposes. Read more
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const NUM_BITS: u32 = 384u32

How many bits are needed to represent an element of this field.
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const CAPACITY: u32 = 383u32

How many bits of information can be reliably stored in the field element. Read more
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const TWO_INV: Self

Inverse of $2$ in the field.
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const MULTIPLICATIVE_GENERATOR: Self

A fixed multiplicative generator of modulus - 1 order. This element must also be a quadratic nonresidue. Read more
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const S: u32 = 1u32

An integer s satisfying the equation 2^s * t = modulus - 1 with t odd. Read more
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const ROOT_OF_UNITY: Self

The 2^s root of unity. Read more
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const ROOT_OF_UNITY_INV: Self

Inverse of Self::ROOT_OF_UNITY.
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const DELTA: Self

Generator of the t-order multiplicative subgroup. Read more
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type Repr = Array<u8, <NistP384 as Curve>::FieldBytesSize>

The prime field can be converted back and forth into this binary representation.
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fn from_repr(bytes: FieldBytes) -> 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). Read more
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fn to_repr(&self) -> FieldBytes

Converts an element of the prime field into the standard byte representation for this field. Read more
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fn is_odd(&self) -> Choice

Returns true iff this element is odd.
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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. Read more
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fn from_u128(v: u128) -> Self

Obtains a field element congruent to the integer v. Read more
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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). Read more
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fn is_even(&self) -> Choice

Returns true iff this element is even.
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impl<'a> Product<&'a FieldElement> for FieldElement

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

Takes an iterator and generates Self from the elements by multiplying the items.
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impl Product for FieldElement

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

Takes an iterator and generates Self from the elements by multiplying the items.
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impl Sgn0 for FieldElement

Available on crate feature hash2curve only.
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fn sgn0(&self) -> Choice

Return the parity of the field 1 == negative 0 == non-negative
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impl Shr<u32> for &FieldElement

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type Output = &FieldElement

The resulting type after applying the >> operator.
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fn shr(self, rhs: u32) -> Self

Performs the >> operation. Read more
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impl Shr<u32> for FieldElement

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type Output = FieldElement

The resulting type after applying the >> operator.
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fn shr(self, rhs: u32) -> Self

Performs the >> operation. Read more
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impl Shr<usize> for &FieldElement

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type Output = &FieldElement

The resulting type after applying the >> operator.
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fn shr(self, rhs: usize) -> Self

Performs the >> operation. Read more
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impl Shr<usize> for FieldElement

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type Output = FieldElement

The resulting type after applying the >> operator.
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fn shr(self, rhs: usize) -> Self

Performs the >> operation. Read more
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impl ShrAssign<u32> for FieldElement

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fn shr_assign(&mut self, rhs: u32)

Performs the >>= operation. Read more
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impl ShrAssign<usize> for FieldElement

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fn shr_assign(&mut self, rhs: usize)

Performs the >>= operation. Read more
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impl Sub<&FieldElement> for &FieldElement

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type Output = FieldElement

The resulting type after applying the - operator.
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fn sub(self, rhs: &FieldElement) -> FieldElement

Performs the - operation. Read more
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impl Sub<&FieldElement> for FieldElement

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type Output = FieldElement

The resulting type after applying the - operator.
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fn sub(self, rhs: &FieldElement) -> FieldElement

Performs the - operation. Read more
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impl Sub for FieldElement

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type Output = FieldElement

The resulting type after applying the - operator.
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fn sub(self, rhs: FieldElement) -> FieldElement

Performs the - operation. Read more
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impl SubAssign<&FieldElement> for FieldElement

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

Performs the -= operation. Read more
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impl SubAssign for FieldElement

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fn sub_assign(&mut self, other: FieldElement)

Performs the -= operation. Read more
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impl<'a> Sum<&'a FieldElement> for FieldElement

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

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

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

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

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impl DefaultIsZeroes for FieldElement

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impl Eq for FieldElement

Auto Trait Implementations§

Blanket Implementations§

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impl<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> BatchInvert<&[T]> for T
where T: Field,

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type Output = Vec<T>

The output of batch inversion. A container of field elements.
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fn batch_invert(field_elements: &[T]) -> CtOption<Vec<T>>

Invert a batch of field elements.
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impl<'this, T> BatchInvert<&'this mut [T]> for T
where T: Field,

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type Output = &'this mut [T]

The output of batch inversion. A container of field elements.
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fn batch_invert(field_elements: &'this mut [T]) -> CtOption<&'this mut [T]>

Invert a batch of field elements.
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impl<const N: usize, T> BatchInvert<[T; N]> for T
where T: Field,

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type Output = [T; N]

The output of batch inversion. A container of field elements.
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fn batch_invert(field_elements: [T; N]) -> CtOption<[T; N]>

Invert a batch of field elements.
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impl<T> BatchInvert<Vec<T>> for T
where T: Field,

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type Output = Vec<T>

The output of batch inversion. A container of field elements.
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fn batch_invert(field_elements: Vec<T>) -> CtOption<Vec<T>>

Invert a batch of field elements.
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<T> CloneToUninit for T
where T: Clone,

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unsafe fn clone_to_uninit(&self, dest: *mut u8)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dest. Read more
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impl<T> ConditionallyNegatable for T
where T: ConditionallySelectable, &'a T: for<'a> Neg<Output = T>,

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fn conditional_negate(&mut self, choice: Choice)

Negate self if choice == Choice(1); otherwise, leave it unchanged. Read more
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impl<T> ConstantTimeSelect for T
where T: ConditionallySelectable,

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fn ct_select(a: &T, b: &T, choice: Choice) -> T

Select a or b according to choice. Read more
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fn ct_assign(&mut self, other: &T, choice: Choice)

Conditionally assign other to self, according to choice.
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fn ct_swap(a: &mut T, b: &mut T, choice: Choice)

Conditionally swap self and other if choice == 1; otherwise, reassign both unto themselves.
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impl<T> Conv for T

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fn conv<T>(self) -> T
where Self: Into<T>,

Converts self into T using Into<T>. Read more
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impl<T> FmtForward for T

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fn fmt_binary(self) -> FmtBinary<Self>
where Self: Binary,

Causes self to use its Binary implementation when Debug-formatted.
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fn fmt_display(self) -> FmtDisplay<Self>
where Self: Display,

Causes self to use its Display implementation when Debug-formatted.
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fn fmt_lower_exp(self) -> FmtLowerExp<Self>
where Self: LowerExp,

Causes self to use its LowerExp implementation when Debug-formatted.
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fn fmt_lower_hex(self) -> FmtLowerHex<Self>
where Self: LowerHex,

Causes self to use its LowerHex implementation when Debug-formatted.
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where Self: Octal,

Causes self to use its Octal implementation when Debug-formatted.
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where Self: Pointer,

Causes self to use its Pointer implementation when Debug-formatted.
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where Self: UpperExp,

Causes self to use its UpperExp implementation when Debug-formatted.
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where Self: UpperHex,

Causes self to use its UpperHex implementation when Debug-formatted.
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where &'a Self: for<'a> IntoIterator,

Formats each item in a sequence. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T> Pipe for T
where T: ?Sized,

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fn pipe<R>(self, func: impl FnOnce(Self) -> R) -> R
where Self: Sized,

Pipes by value. This is generally the method you want to use. Read more
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fn pipe_ref<'a, R>(&'a self, func: impl FnOnce(&'a Self) -> R) -> R
where R: 'a,

Borrows self and passes that borrow into the pipe function. Read more
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where R: 'a,

Mutably borrows self and passes that borrow into the pipe function. Read more
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where Self: Borrow<B>, B: 'a + ?Sized, R: 'a,

Borrows self, then passes self.borrow() into the pipe function. Read more
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where Self: AsRef<U>, U: 'a + ?Sized, R: 'a,

Borrows self, then passes self.as_ref() into the pipe function.
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where Self: AsMut<U>, U: 'a + ?Sized, R: 'a,

Mutably borrows self, then passes self.as_mut() into the pipe function.
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where Self: Deref<Target = T>, T: 'a + ?Sized, R: 'a,

Borrows self, then passes self.deref() into the pipe function.
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where Self: DerefMut<Target = T> + Deref, T: 'a + ?Sized, R: 'a,

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type Output = T

Should always be Self
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fn tap(self, func: impl FnOnce(&Self)) -> Self

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Calls .tap() only in debug builds, and is erased in release builds.
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fn tap_deref_dbg<T>(self, func: impl FnOnce(&T)) -> Self
where Self: Deref<Target = T>, T: ?Sized,

Calls .tap_deref() only in debug builds, and is erased in release builds.
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fn tap_deref_mut_dbg<T>(self, func: impl FnOnce(&mut T)) -> Self
where Self: DerefMut<Target = T> + Deref, T: ?Sized,

Calls .tap_deref_mut() only in debug builds, and is erased in release builds.
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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T> TryConv for T

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fn try_conv<T>(self) -> Result<T, Self::Error>
where Self: TryInto<T>,

Attempts to convert self into T using TryInto<T>. Read more
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<Z> Zeroize for Z
where Z: DefaultIsZeroes,

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fn zeroize(&mut self)

Zero out this object from memory using Rust intrinsics which ensure the zeroization operation is not “optimized away” by the compiler.
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impl<T, Rhs, Output> GroupOps<Rhs, Output> for T
where T: Add<Rhs, Output = Output> + Sub<Rhs, Output = Output> + AddAssign<Rhs> + SubAssign<Rhs>,

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impl<T, Rhs, Output> GroupOpsOwned<Rhs, Output> for T
where T: for<'r> GroupOps<&'r Rhs, Output>,

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impl<T, Rhs, Output> ScalarMul<Rhs, Output> for T
where T: Mul<Rhs, Output = Output> + MulAssign<Rhs>,

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impl<T, Rhs, Output> ScalarMulOwned<Rhs, Output> for T
where T: for<'r> ScalarMul<&'r Rhs, Output>,