Struct curve25519_dalek::backend::serial::u32::field::FieldElement2625

pub struct FieldElement2625(_);

Available on curve25519_dalek_bits="32" only.

A FieldElement2625 represents an element of the field \( \mathbb Z / (2^{255} - 19)\).

In the 32-bit implementation, a FieldElement is represented in radix \(2^{25.5}\) as ten u32s. This means that a field element \(x\) is represented as $$ x = \sum_{i=0}^9 x_i 2^{\lceil i \frac {51} 2 \rceil} = x_0 + x_1 2^{26} + x_2 2^{51} + x_3 2^{77} + \cdots + x_9 2^{230}; $$ the coefficients are alternately bounded by \(2^{25}\) and \(2^{26}\). The limbs are allowed to grow between reductions up to \(2^{25+b}\) or \(2^{26+b}\), where \(b = 1.75\).

Note

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

The backend-specific type FieldElement2625 should not be used outside of the curve25519_dalek::field module.

Implementations

impl FieldElement2625

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).

pub fn is_zero(&self) -> Choice

Determine if this FieldElement is zero.

Return

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

pub fn batch_invert(inputs: &mut [FieldElement2625])

Available on crate feature alloc only.

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

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

pub fn invert(&self) -> FieldElement2625

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.

pub fn sqrt_ratio_i( u: &FieldElement2625, v: &FieldElement2625 ) -> (Choice, FieldElement2625)

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).

pub fn invsqrt(&self) -> (Choice, FieldElement2625)

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;

impl FieldElement2625

pub const ZERO: FieldElement2625 = _

The scalar \( 0 \).

pub const ONE: FieldElement2625 = _

The scalar \( 1 \).

pub const MINUS_ONE: FieldElement2625 = _

The scalar \( -1 \).

pub fn negate(&mut self)

Invert the sign of this field element

pub fn pow2k(&self, k: u32) -> FieldElement2625

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

pub fn from_bytes(data: &[u8; 32]) -> FieldElement2625

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

Warning

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.

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

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

pub fn square(&self) -> FieldElement2625

Compute self^2.

pub fn square2(&self) -> FieldElement2625

Compute 2*self^2.

Trait Implementations

impl<'a, 'b> Add<&'b FieldElement2625> for &'a FieldElement2625

type Output = FieldElement2625

The resulting type after applying the + operator.

fn add(self, _rhs: &'b FieldElement2625) -> FieldElement2625

Performs the + operation.

impl<'b> AddAssign<&'b FieldElement2625> for FieldElement2625

fn add_assign(&mut self, _rhs: &'b FieldElement2625)

Performs the += operation.

impl Clone for FieldElement2625

fn clone(&self) -> FieldElement2625

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for FieldElement2625

fn conditional_select( a: &FieldElement2625, b: &FieldElement2625, choice: Choice ) -> FieldElement2625

Select a or b according to choice.

fn conditional_assign(&mut self, other: &FieldElement2625, choice: Choice)

Conditionally assign other to self, according to choice.

fn conditional_swap( a: &mut FieldElement2625, b: &mut FieldElement2625, choice: Choice )

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

impl ConstantTimeEq for FieldElement2625

fn ct_eq(&self, other: &FieldElement2625) -> Choice

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

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

Determine if two items are NOT equal.

impl Debug for FieldElement2625

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

Formats the value using the given formatter.

impl<'a, 'b> Mul<&'b FieldElement2625> for &'a FieldElement2625

type Output = FieldElement2625

The resulting type after applying the * operator.

fn mul(self, _rhs: &'b FieldElement2625) -> FieldElement2625

Performs the * operation.

impl<'b> MulAssign<&'b FieldElement2625> for FieldElement2625

fn mul_assign(&mut self, _rhs: &'b FieldElement2625)

Performs the *= operation.

impl<'a> Neg for &'a FieldElement2625

type Output = FieldElement2625

The resulting type after applying the - operator.

fn neg(self) -> FieldElement2625

Performs the unary - operation.

impl PartialEq<FieldElement2625> for FieldElement2625

fn eq(&self, other: &FieldElement2625) -> bool

This method tests for self and other values to be equal, and is used by ==.

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

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<'a, 'b> Sub<&'b FieldElement2625> for &'a FieldElement2625

type Output = FieldElement2625

The resulting type after applying the - operator.

fn sub(self, _rhs: &'b FieldElement2625) -> FieldElement2625

Performs the - operation.

impl<'b> SubAssign<&'b FieldElement2625> for FieldElement2625

fn sub_assign(&mut self, _rhs: &'b FieldElement2625)

Performs the -= operation.

impl Zeroize for FieldElement2625

Available on crate feature zeroize only.

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.

impl Copy for FieldElement2625

impl Eq for FieldElement2625