Struct FieldElement 

#[repr(align(16))]
pub struct FieldElement([u8; 16]);

An element in POLYVAL’s field.

This type represents an element of the binary field GF(2^128) modulo the irreducible polynomial x^128 + x^127 + x^126 + x^121 + 1 as described in RFC8452 §3.

Arithmetic in POLYVAL’s field has the following properties:

• All arithmetic operations are performed modulo the polynomial above.
• Addition is equivalent to the XOR operation applied to the two field elements
• Multiplication is carryless

Tuple Fields

0: [u8; 16]

Implementations

impl FieldElement

unsafe fn from_m128i(reg: __m128i) -> Self

unsafe fn to_m128i(self) -> __m128i

impl FieldElement

pub(crate) fn karatsuba_mul(self, rhs: Self) -> Product

Compute the unreduced 256-bit carryless product of two 128-bit field elements.

Uses a Karatsuba decomposition in which the 128x128 multiplication is reduced to three 64x64 multiplications together with a bit-reversal trick to efficiently recover the high half.

fn to_u64x2(self) -> (u64, u64)

Splits into (lo, hi).

impl FieldElement

pub fn mulx(self) -> Self

The mulX_POLYVAL() function as defined in RFC 8452 Appendix A.

Performs a doubling (a.k.a. “multiply by x”) over GF(2^128). This is useful for implementing GHASH in terms of POLYVAL.

impl FieldElement

pub fn reverse(self) -> Self

Reverse this field element at a byte-level of granularity.

This is useful when implementing GHASH in terms of POLYVAL.

Trait Implementations

impl Add for FieldElement

fn add(self, rhs: Self) -> Self::Output

Adds two POLYVAL field elements.

In POLYVAL’s field, addition is the equivalent operation to XOR.

type Output = FieldElement

The resulting type after applying the + operator.

impl Clone for FieldElement

fn clone(&self) -> FieldElement

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for FieldElement

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

Formats the value using the given formatter.

impl Default for FieldElement

fn default() -> FieldElement

Returns the “default value” for a type.

impl From<&Array<u8, <Polyval as BlockSizeUser>::BlockSize>> for FieldElement

fn from(block: &Block) -> Self

Converts to this type from the input type.

impl From<&FieldElement> for Block

fn from(fe: &FieldElement) -> Self

Converts to this type from the input type.

impl From<[u8; 16]> for FieldElement

fn from(bytes: [u8; 16]) -> Self

Converts to this type from the input type.

impl From<Array<u8, <Polyval as BlockSizeUser>::BlockSize>> for FieldElement

fn from(block: Block) -> Self

Converts to this type from the input type.

impl From<FieldElement> for [u8; 16]

fn from(fe: FieldElement) -> [u8; 16]

Converts to this type from the input type.

impl From<FieldElement> for Block

fn from(fe: FieldElement) -> Self

Converts to this type from the input type.

impl From<FieldElement> for u128

fn from(fe: FieldElement) -> Self

Converts to this type from the input type.

impl From<u128> for FieldElement

fn from(x: u128) -> Self

Converts to this type from the input type.

impl Mul for FieldElement

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

Perform carryless multiplication within POLYVAL’s field modulo its polynomial.

type Output = FieldElement

The resulting type after applying the * operator.

impl MulAssign for FieldElement

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl Copy for FieldElement