Struct curve25519_dalek::field::FieldElement32

pub struct FieldElement32(_);

A FieldElement32 represents an element of the field GF(2²⁵⁵ - 19).

In the 32-bit implementation, a FieldElement32 is represented in radix 2^25.5 as ten i32s, so that an element t, entries t[0],...,t[9], represents the integer t[0]+2²⁶ t[1]+2⁵¹ t[2]+2⁷⁷ t[3]+2¹⁰² t[4]+...+2²³⁰ t[9].

The coefficients t[i] are allowed to grow between multiplications.

XXX document by how much

Warning

You almost certainly do not want to use FieldElement32 directly. Consider using curve25519_dalek::field::FieldElement, which will automatically select between FieldElement32 and FieldElement64 depending on whether curve25519-dalek was compiled with --features="nightly".

This implementation, FieldElement32, is intended for platforms that can multiply 32-bit inputs to produce 64-bit outputs, and is not preferred for use on x86_64, since the 64-bit implementation is both much simpler and much faster. However, the FieldElement64 implementation requires Rust's u128, which is not yet stable.

Methods

impl FieldElement32

fn negate(&mut self)

Invert the sign of this field element

fn zero() -> FieldElement32

Construct zero.

fn one() -> FieldElement32

Construct one.

fn minus_one() -> FieldElement32

Construct -1.

fn from_bytes(data: &[u8; 32]) -> FieldElement32

Load a FieldElement64 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 2²⁵⁵ - 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.

XXX the above applies to the 64-bit implementation; check that it applies here too.

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

Serialize this FieldElement64 to a 32-byte array. The encoding is canonical.

fn square(&self) -> FieldElement32

Calculates h = f*f. Can overlap h with f.

XXX limbs: better to talk about headroom?

Preconditions

• |f[i]| bounded by 1.1*2^26, 1.1*2^25, 1.1*2^26, 1.1*2^25, etc.

Postconditions

• |h[i]| bounded by 1.1*2^25, 1.1*2^24, 1.1*2^25, 1.1*2^24, etc.

fn square2(&self) -> FieldElement32

Square this field element and multiply the result by 2.

XXX explain why square2 exists vs square (overflow)

Preconditions

• |f[i]| bounded by 1.65*2^26, 1.65*2^25, 1.65*2^26, 1.65*2^25, etc.

Postconditions

• |h[i]| bounded by 1.01*2^25, 1.01*2^24, 1.01*2^25, 1.01*2^24, etc.

Notes

See fe_mul.c in ref10 implementation for discussion of implementation strategy.

Trait Implementations

impl Copy for FieldElement32

impl Clone for FieldElement32

fn clone(&self) -> FieldElement32

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for FieldElement32

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

Formats the value using the given formatter.

impl<'b> AddAssign<&'b FieldElement32> for FieldElement32

fn add_assign(&mut self, _rhs: &'b FieldElement32)

Performs the += operation.

impl<'a, 'b> Add<&'b FieldElement32> for &'a FieldElement32

type Output = FieldElement32

The resulting type after applying the + operator.

fn add(self, _rhs: &'b FieldElement32) -> FieldElement32

Performs the + operation.

impl<'b> SubAssign<&'b FieldElement32> for FieldElement32

fn sub_assign(&mut self, _rhs: &'b FieldElement32)

Performs the -= operation.

impl<'a, 'b> Sub<&'b FieldElement32> for &'a FieldElement32

type Output = FieldElement32

The resulting type after applying the - operator.

fn sub(self, _rhs: &'b FieldElement32) -> FieldElement32

Performs the - operation.

impl<'b> MulAssign<&'b FieldElement32> for FieldElement32

fn mul_assign(&mut self, _rhs: &'b FieldElement32)

Performs the *= operation.

impl<'a, 'b> Mul<&'b FieldElement32> for &'a FieldElement32

type Output = FieldElement32

The resulting type after applying the * operator.

fn mul(self, _rhs: &'b FieldElement32) -> FieldElement32

Performs the * operation.

impl<'a> Neg for &'a FieldElement32

type Output = FieldElement32

The resulting type after applying the - operator.

fn neg(self) -> FieldElement32

Performs the unary - operation.

impl ConditionallyAssignable for FieldElement32

fn conditional_assign(&mut self, f: &FieldElement32, choice: u8)

Conditionally assign other to self in constant time.