Struct test_dalek_docs::backend::serial::u64::field::FieldElement51

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pub struct FieldElement51(_);

Expand description

A FieldElement51 represents an element of the field \( \mathbb Z / (2^{255} - 19)\).

In the 64-bit implementation, a FieldElement is represented in radix \(2^{51}\) as five u64s; the coefficients are allowed to grow up to \(2^{54}\) between reductions modulo \(p\).

Note

The curve25519_dalek::field module provides a type alias curve25519_dalek::field::FieldElement to either FieldElement51 or FieldElement2625.

The backend-specific type FieldElement51 should not be used outside of the curve25519_dalek::field module.

Implementations

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impl FieldElement51

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pub fn is_negative(&self) -> Choice

Determine if this FieldElement is negative, in the sense used in the ed25519 paper: x is negative if the low bit is set.

Return

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

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pub fn is_zero(&self) -> Choice

Determine if this FieldElement is zero.

Return

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

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pub fn batch_invert(inputs: &mut [FieldElement51])

Given a slice of public FieldElements, replace each with its inverse.

When an input FieldElement is zero, its value is unchanged.

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pub fn invert(&self) -> FieldElement51

Given a nonzero field element, compute its inverse.

The inverse is computed as self^(p-2), since x^(p-2)x = x^(p-1) = 1 (mod p).

This function returns zero on input zero.

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pub fn sqrt_ratio_i(
u: &FieldElement51,
v: &FieldElement51
) -> (Choice, FieldElement51)

Given FieldElements u and v, compute either sqrt(u/v) or sqrt(i*u/v) in constant time.

This function always returns the nonnegative square root.

Return

(Choice(1), +sqrt(u/v)) if v is nonzero and u/v is square;
(Choice(1), zero) if u is zero;
(Choice(0), zero) if v is zero and u is nonzero;
(Choice(0), +sqrt(i*u/v)) if u/v is nonsquare (so i*u/v is square).

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pub fn invsqrt(&self) -> (Choice, FieldElement51)

Attempt to compute sqrt(1/self) in constant time.

Convenience wrapper around sqrt_ratio_i.

This function always returns the nonnegative square root.

Return

(Choice(1), +sqrt(1/self)) if self is a nonzero square;
(Choice(0), zero) if self is zero;
(Choice(0), +sqrt(i/self)) if self is a nonzero nonsquare;

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impl FieldElement51

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pub fn negate(&mut self)

Invert the sign of this field element

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pub fn zero() -> FieldElement51

Construct zero.

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pub fn one() -> FieldElement51

Construct one.

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pub fn minus_one() -> FieldElement51

Construct -1.

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pub fn from_bytes(bytes: &[u8; 32]) -> FieldElement51

Load a FieldElement51 from the low 255 bits of a 256-bit input.

This function does not check that the input used the canonical representative. It masks the high bit, but it will happily decode 2^255 - 18 to 1. Applications that require a canonical encoding of every field element should decode, re-encode to the canonical encoding, and check that the input was canonical.

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

Serialize this FieldElement51 to a 32-byte array. The encoding is canonical.

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pub fn pow2k(&self, k: u32) -> FieldElement51

Given k > 0, return self^(2^k).

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pub fn square(&self) -> FieldElement51

Returns the square of this field element.

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pub fn square2(&self) -> FieldElement51

Returns 2 times the square of this field element.

Trait Implementations

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impl<'a, 'b> Add<&'b FieldElement51> for &'a FieldElement51

type Output = FieldElement51

The resulting type after applying the + operator.

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fn add(self, _rhs: &'b FieldElement51) -> FieldElement51

Performs the + operation. Read more

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impl<'b> AddAssign<&'b FieldElement51> for FieldElement51

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fn add_assign(&mut self, _rhs: &'b FieldElement51)

Performs the += operation. Read more

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impl Clone for FieldElement51

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fn clone(&self) -> FieldElement51

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 FieldElement51

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fn conditional_select(
    a: &FieldElement51,
    b: &FieldElement51,
    choice: Choice
) -> FieldElement51

Select a or b according to choice. Read more

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fn conditional_swap(
    a: &mut FieldElement51,
    b: &mut FieldElement51,
    choice: Choice
)

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

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fn conditional_assign(&mut self, other: &FieldElement51, choice: Choice)

Conditionally assign other to self, according to choice. Read more

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impl ConstantTimeEq for FieldElement51

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fn ct_eq(&self, other: &FieldElement51) -> Choice

Test equality between two FieldElements. Since the internal representation is not canonical, the field elements are normalized to wire format before comparison.

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