Struct Rijndael8b 

pub struct Rijndael8b(/* private fields */);

The binary field GF(2^8) modulo x^8 + x^4 + x^3 + x + 1.

Bit i stores the coefficient of x^i, and every byte is a distinct field element.

This is the modulus the byte-wise field instructions are defined for.

That is what makes it worth carrying beside the tower’s own byte field.

Arithmetic here is table-free: nothing indexes a table by an operand.

Implementations

impl Rijndael8b

pub const fn frobenius_map(power_log: usize) -> ByteMatrix

The map raising every element to the power 2^k, for k the argument.

The orbit closes after eight steps, so the argument is taken modulo that.

pub fn frobenius_orbit(self) -> [Self; 8]

This element raised to 2^k, for every k below the field’s degree.

These are the element’s conjugates with multiplicity, so a subfield element repeats.

impl Rijndael8b

pub const fn from_byte(byte: u8) -> Self

Construct a field element from its byte representation.

Every byte is a valid element.

pub const fn to_byte(self) -> u8

The byte representation of this element.

pub const fn invert_or_zero(self) -> Self

The inverse of this element, with zero sent to zero.

The chain runs whatever the operand is, so its cost says nothing about the value.

pub const fn scaling_matrix(self) -> ByteMatrix

Multiplication by this element, as a map ready for the byte-wise engine.

Scaling is F_2-linear, so a fixed factor is a matrix like any other.

Trait Implementations

impl Add for Rijndael8b

type Output = Rijndael8b

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<Gf2> for Rijndael8b

type Output = Rijndael8b

The resulting type after applying the + operator.

fn add(self, rhs: Gf2) -> Self

Performs the + operation.

impl<const N: usize> Add<PackedRijndael8b<N>> for Rijndael8b

type Output = PackedRijndael8b<N>

The resulting type after applying the + operator.

fn add(self, rhs: PackedRijndael8b<N>) -> Self::Output

Performs the + operation.

impl<const N: usize> Add<Rijndael8b> for PackedRijndael8b<N>

type Output = PackedRijndael8b<N>

The resulting type after applying the + operator.

fn add(self, rhs: Rijndael8b) -> Self

Performs the + operation.

impl Add<Rijndael8b> for Gf2

type Output = Rijndael8b

The resulting type after applying the + operator.

fn add(self, rhs: Rijndael8b) -> Self::Output

Performs the + operation.

impl<T: Into<Self>> AddAssign<T> for Rijndael8b

fn add_assign(&mut self, rhs: T)

Performs the += operation.

impl Algebra<Gf2> for Rijndael8b

fn quadratic_extension_square(a: &[Self; 2], w: F) -> [Self; 2]

Square a[0] + a[1] X modulo X^2 - w.

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl<const N: usize> Algebra<Rijndael8b> for PackedRijndael8b<N>

fn quadratic_extension_square(a: &[Self; 2], w: F) -> [Self; 2]

Square a[0] + a[1] X modulo X^2 - w.

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl Clone for Rijndael8b

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Rijndael8b

impl Debug for Rijndael8b

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

Formats the value using the given formatter.

impl Default for Rijndael8b

fn default() -> Self

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Rijndael8b

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for Rijndael8b

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

Formats the value using the given formatter.

impl Distribution<Rijndael8b> for StandardUniform

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Rijndael8b

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> Iter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> Map<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Map sampled values to type S

impl Div for Rijndael8b

type Output = Rijndael8b

The resulting type after applying the / operator.

fn div(self, rhs: Rijndael8b) -> Self

Performs the / operation.

impl<const N: usize> Div<Rijndael8b> for PackedRijndael8b<N>

type Output = PackedRijndael8b<N>

The resulting type after applying the / operator.

fn div(self, rhs: Rijndael8b) -> Self

Performs the / operation.

impl DivAssign for Rijndael8b

fn div_assign(&mut self, rhs: Rijndael8b)

Performs the /= operation.

impl<const N: usize> DivAssign<Rijndael8b> for PackedRijndael8b<N>

fn div_assign(&mut self, rhs: Rijndael8b)

Performs the /= operation.

impl Eq for Rijndael8b

impl Field for Rijndael8b

fn bits() -> usize

An element of GF(2^n) is exactly n bits wide.

fn interpolation_node(i: usize) -> Self

The enumeration by bit pattern.

The coordinates of the returned element over GF(2) are the bits of the index.

Panics

Panics if the index does not fit in a byte, which would otherwise alias an earlier node.

const GENERATOR: Self

A generator of this field’s multiplicative group.

type Packing = PackedRijndael8b<{ packed::PACKING_WIDTH }>

fn try_inverse(&self) -> Option<Self>

The multiplicative inverse of this field element, if it exists.

fn try_sqrt(&self) -> Option<Self>

A square root of this field element, if one exists.

fn order() -> BigUint

The number of elements in the field.

const BENEFITS_FROM_LOCKSTEP_EVALUATION: bool = false

Whether evaluating multiple packed vectors of this field in lockstep (to overlap independent dependency chains and hide packed-multiplication latency) is expected to help throughput for this field.

fn is_zero(&self) -> bool

Check if the given field element is equal to the unique additive identity (ZERO).

fn is_one(&self) -> bool

Check if the given field element is equal to the unique multiplicative identity (ONE).

fn inverse(&self) -> Self

The multiplicative inverse of this field element.

fn add_slices(slice_1: &mut [Self], slice_2: &[Self])

Add two slices of field elements together, returning the result in the first slice.

fn batched_columnwise_dot_product<EF, R, I, const N: usize>( acc: &mut [<EF as ExtensionField<Self>>::ExtensionPacking], items: I, )

where EF: ExtensionField<Self>, R: Iterator<Item = Self::Packing>, I: Iterator<Item = (R, [EF; N])>,

Accumulate acc[c * N + j] += scales[j] * row[c] over a stream of packed rows.

impl From<BinaryField8> for Rijndael8b

fn from(x: BinaryField8) -> Self

The same field element, seen in the polynomial basis.

impl From<Gf2> for Rijndael8b

fn from(x: Gf2) -> Self

GF(2) is the prime subfield, embedded as {ZERO, ONE}.

impl<const N: usize> From<Rijndael8b> for PackedRijndael8b<N>

fn from(value: Rijndael8b) -> Self

Converts to this type from the input type.

impl From<Rijndael8b> for BinaryField8

fn from(x: Rijndael8b) -> Self

The same field element, seen in the tower basis.

impl Hash for Rijndael8b

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Mul for Rijndael8b

type Output = Rijndael8b

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Gf2> for Rijndael8b

type Output = Rijndael8b

The resulting type after applying the * operator.

fn mul(self, rhs: Gf2) -> Self

Performs the * operation.

impl<const N: usize> Mul<PackedRijndael8b<N>> for Rijndael8b

type Output = PackedRijndael8b<N>

The resulting type after applying the * operator.

fn mul(self, rhs: PackedRijndael8b<N>) -> Self::Output

Performs the * operation.

impl<const N: usize> Mul<Rijndael8b> for PackedRijndael8b<N>

fn mul(self, rhs: Rijndael8b) -> Self

A broadcast plus the byte-wise product beats tabulating the factor as a map.

Callers holding one factor across a loop should hoist its matrix and sweep with that.

type Output = PackedRijndael8b<N>

The resulting type after applying the * operator.

impl Mul<Rijndael8b> for Gf2

type Output = Rijndael8b

The resulting type after applying the * operator.

fn mul(self, rhs: Rijndael8b) -> Self::Output

Performs the * operation.

impl<T: Into<Self>> MulAssign<T> for Rijndael8b

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl Neg for Rijndael8b

type Output = Rijndael8b

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl Ord for Rijndael8b

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

fn clamp_to<R>(self, range: R) -> Self

where Self: Sized, R: ClampBounds<Self>,

🔬This is a nightly-only experimental API. (clamp_to)

Restrict a value to a certain range.

impl Packable for Rijndael8b

impl PartialEq for Rijndael8b

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

Equality operator ==.

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

Inequality operator !=.

impl PartialOrd for Rijndael8b

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl PrimeCharacteristicRing for Rijndael8b

fn halve(&self) -> Self

Panics

Always panics: 2 is not invertible in characteristic 2.

fn div_2exp_u64(&self, _exp: u64) -> Self

Panics

Always panics: 2 is not invertible in characteristic 2.

fn exp_power_of_2(&self, power_log: usize) -> Self

Raising to 2^k is one tabulated map, whatever the exponent.

const ZERO: Self

The additive identity of the ring.

const ONE: Self

The multiplicative identity of the ring.

const TWO: Self

The element in the ring given by ONE + ONE.

const NEG_ONE: Self

The element in the ring given by -ONE.

type PrimeSubfield = Gf2

The field ℤ/p where the characteristic of this ring is p.

fn from_prime_subfield(f: Self::PrimeSubfield) -> Self

Embed an element of the prime field ℤ/p into the ring R.

fn from_bool(b: bool) -> Self

Return Self::ONE if b is true and Self::ZERO if b is false.

fn double(&self) -> Self

The elementary function double(a) = 2*a.

fn xor(&self, y: &Self) -> Self

Computes the arithmetic generalization of boolean xor.

fn mul_2exp_u64(&self, exp: u64) -> Self

The elementary function mul_2exp_u64(a, exp) = a * 2^{exp}.

fn square(&self) -> Self

The elementary function square(a) = a^2.

fn from_u8(int: u8) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u16(int: u16) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u32(int: u32) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u64(int: u64) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u128(int: u128) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_usize(int: usize) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i8(int: i8) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i16(int: i16) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i32(int: i32) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i64(int: i64) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i128(int: i128) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_isize(int: isize) -> Self

Given an integer r, return the sum of r copies of ONE:

fn cube(&self) -> Self

The elementary function cube(a) = a^3.

fn xor3(&self, y: &Self, z: &Self) -> Self

Computes the arithmetic generalization of a triple xor.

fn andn(&self, y: &Self) -> Self

Computes the arithmetic generalization of andnot.

fn bool_check(&self) -> Self

The vanishing polynomial for boolean values: x * (x - 1).

fn exp_u64(&self, power: u64) -> Self

Exponentiation by a u64 power.

fn exp_const_u64<const POWER: u64>(&self) -> Self

Exponentiation by a small constant power.

fn powers(&self) -> Powers<Self>

Construct an iterator which returns powers of self: self^0, self^1, self^2, ....

fn shifted_powers(&self, start: Self) -> Powers<Self>

Construct an iterator which returns powers of self shifted by start: start, start*self^1, start*self^2, ....

fn dot_product<const N: usize>(u: &[Self; N], v: &[Self; N]) -> Self

Compute the dot product of two vectors.

fn sum_array<const N: usize>(input: &[Self]) -> Self

Compute the sum of a slice of elements whose length is a compile time constant.

fn zero_vec(len: usize) -> Vec<Self>

Allocates a vector of zero elements of length len. Many operating systems zero pages before assigning them to a userspace process. In that case, our process should not need to write zeros, which would be redundant. However, the compiler may not always recognize this.

impl Product for Rijndael8b

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

Takes an iterator and generates Self from the elements by multiplying the items.

impl<const N: usize> Product<Rijndael8b> for PackedRijndael8b<N>

fn product<I: Iterator<Item = Rijndael8b>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by multiplying the items.

impl RawDataSerializable for Rijndael8b

const NUM_BYTES: usize = 1

The number of bytes which this field element occupies in memory. Must be equal to the length of self.into_bytes().

fn into_bytes(self) -> impl IntoIterator<Item = u8>

Convert a field element into a collection of bytes.

fn into_byte_stream( input: impl IntoIterator<Item = Self>, ) -> impl IntoIterator<Item = u8>

Convert an iterator of field elements into an iterator of bytes.

fn into_u32_stream( input: impl IntoIterator<Item = Self>, ) -> impl IntoIterator<Item = u32>

Convert an iterator of field elements into an iterator of u32s.

fn into_u64_stream( input: impl IntoIterator<Item = Self>, ) -> impl IntoIterator<Item = u64>

Convert an iterator of field elements into an iterator of u64s.

fn into_parallel_byte_streams<const N: usize>( input: impl IntoIterator<Item = [Self; N]>, ) -> impl IntoIterator<Item = [u8; N]>

Convert an iterator of field element arrays into an iterator of byte arrays.

fn into_parallel_u32_streams<const N: usize>( input: impl IntoIterator<Item = [Self; N]>, ) -> impl IntoIterator<Item = [u32; N]>

Convert an iterator of field element arrays into an iterator of u32 arrays.

fn into_parallel_u64_streams<const N: usize>( input: impl IntoIterator<Item = [Self; N]>, ) -> impl IntoIterator<Item = [u64; N]>

Convert an iterator of field element arrays into an iterator of u64 arrays.

impl Serialize for Rijndael8b

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl StructuralPartialEq for Rijndael8b

impl Sub for Rijndael8b

type Output = Rijndael8b

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<Gf2> for Rijndael8b

type Output = Rijndael8b

The resulting type after applying the - operator.

fn sub(self, rhs: Gf2) -> Self

Performs the - operation.

impl<const N: usize> Sub<PackedRijndael8b<N>> for Rijndael8b

type Output = PackedRijndael8b<N>

The resulting type after applying the - operator.

fn sub(self, rhs: PackedRijndael8b<N>) -> Self::Output

Performs the - operation.

impl<const N: usize> Sub<Rijndael8b> for PackedRijndael8b<N>

type Output = PackedRijndael8b<N>

The resulting type after applying the - operator.

fn sub(self, rhs: Rijndael8b) -> Self

Performs the - operation.

impl Sub<Rijndael8b> for Gf2

type Output = Rijndael8b

The resulting type after applying the - operator.

fn sub(self, rhs: Rijndael8b) -> Self::Output

Performs the - operation.

impl<T: Into<Self>> SubAssign<T> for Rijndael8b

fn sub_assign(&mut self, rhs: T)

Performs the -= operation.

impl Sum for Rijndael8b

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

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

impl<const N: usize> Sum<Rijndael8b> for PackedRijndael8b<N>

fn sum<I: Iterator<Item = Rijndael8b>>(iter: I) -> Self

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

impl TowerLevel for Rijndael8b

fn mul_alpha(self) -> Self

The tower scales by a basis vector, which costs it a shift.

Here the same element is an arbitrary one, so it costs a full product.

fn from_le_byte_iter(bytes: impl Iterator<Item = u8>) -> Self

Panics

Panics if the stream ends before a whole element has been read.

fn cantor_basis(i: usize) -> Self

Panics

Panics if the index is at least the bit width of the field.

const LOG_BITS: usize = 3

The k in GF(2^(2^k)).

type Repr = u8

The backing integer of an element.

fn from_repr(r: Self::Repr) -> Self

Build an element from a bit pattern, discarding the bits above 2^LOG_BITS.

fn to_repr(self) -> Self::Repr

The bit pattern of this element, zero above 2^LOG_BITS.