Struct Goldilocks

pub struct Goldilocks { /* private fields */ }

The prime field known as Goldilocks, defined as F_p where p = 2^64 - 2^32 + 1.

Note that the safety of deriving Serialize and Deserialize relies on the fact that the internal value can be any u64.

Implementations

impl Goldilocks

pub const TWO_ADIC_GENERATORS: [Self; 33]

A list of generators for the two-adic subgroups of the goldilocks field.

These satisfy the properties that TWO_ADIC_GENERATORS[0] = 1 and TWO_ADIC_GENERATORS[i+1]^2 = TWO_ADIC_GENERATORS[i].

Trait Implementations

impl Add for Goldilocks

type Output = Goldilocks

The resulting type after applying the + operator.

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

Performs the + operation.

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

fn add_assign(&mut self, rhs: T)

Performs the += operation.

impl BinomiallyExtendable<2> for Goldilocks

const W: Self

The constant coefficient W in the binomial X^D - W.

const DTH_ROOT: Self

A D-th root of unity derived from W.

const EXT_GENERATOR: [Self; 2]

A generator for the extension field, expressed as a degree-D polynomial.

impl BinomiallyExtendable<5> for Goldilocks

const W: Self

The constant coefficient W in the binomial X^D - W.

const DTH_ROOT: Self

A D-th root of unity derived from W.

const EXT_GENERATOR: [Self; 5]

A generator for the extension field, expressed as a degree-D polynomial.

impl BinomiallyExtendableAlgebra<Goldilocks, 2> for Goldilocks

fn binomial_mul(a: &[Self; D], b: &[Self; D], res: &mut [Self; D], w: F)

Multiplication in the algebra extension ring A<X> / (X^D - W).

fn binomial_add(a: &[Self; D], b: &[Self; D]) -> [Self; D]

Addition of elements in the algebra extension ring A<X> / (X^D - W).

fn binomial_sub(a: &[Self; D], b: &[Self; D]) -> [Self; D]

Subtraction of elements in the algebra extension ring A<X> / (X^D - W).

fn binomial_base_mul(lhs: [Self; D], rhs: Self) -> [Self; D]

impl BinomiallyExtendableAlgebra<Goldilocks, 5> for Goldilocks

fn binomial_mul(a: &[Self; D], b: &[Self; D], res: &mut [Self; D], w: F)

Multiplication in the algebra extension ring A<X> / (X^D - W).

fn binomial_add(a: &[Self; D], b: &[Self; D]) -> [Self; D]

Addition of elements in the algebra extension ring A<X> / (X^D - W).

fn binomial_sub(a: &[Self; D], b: &[Self; D]) -> [Self; D]

Subtraction of elements in the algebra extension ring A<X> / (X^D - W).

fn binomial_base_mul(lhs: [Self; D], rhs: Self) -> [Self; D]

impl Clone for Goldilocks

fn clone(&self) -> Goldilocks

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Convolve<Goldilocks, i128, i64, i128> for SmallConvolveGoldilocks

fn read(input: Goldilocks) -> i128

Return the lift of a Goldilocks element, 0 <= input.value <= P < 2^64. We widen immediately, since some valid Goldilocks elements don’t fit in an i64, and since in any case overflow can occur for even the smallest convolutions.

fn parity_dot<const N: usize>(u: [i128; N], v: [i64; N]) -> i128

For a convolution of size N, |x| < N * 2^64 and (as per the assumption above), |y| < 2^51. So the product is at most N * 2^115 which will not overflow for N <= 16. We widen y at this point to perform the multiplication.

fn reduce(z: i128) -> Goldilocks

The assumptions above mean z < N^2 * 2^115, which is at most 2^123 when N <= 16.

NB: Even though intermediate values could be negative, the output must be non-negative since the inputs were non-negative.

fn apply<const N: usize, C>(lhs: [F; N], rhs: [U; N], conv: C) -> [F; N]

where C: Fn([T; N], [U; N], &mut [V]),

Convolve lhs and rhs.

fn conv3(lhs: [T; 3], rhs: [U; 3], output: &mut [V])

fn negacyclic_conv3(lhs: [T; 3], rhs: [U; 3], output: &mut [V])

fn conv4(lhs: [T; 4], rhs: [U; 4], output: &mut [V])

fn negacyclic_conv4(lhs: [T; 4], rhs: [U; 4], output: &mut [V])

fn conv6(lhs: [T; 6], rhs: [U; 6], output: &mut [V])

fn negacyclic_conv6(lhs: [T; 6], rhs: [U; 6], output: &mut [V])

fn conv8(lhs: [T; 8], rhs: [U; 8], output: &mut [V])

fn negacyclic_conv8(lhs: [T; 8], rhs: [U; 8], output: &mut [V])

fn conv12(lhs: [T; 12], rhs: [U; 12], output: &mut [V])

fn negacyclic_conv12(lhs: [T; 12], rhs: [U; 12], output: &mut [V])

fn conv16(lhs: [T; 16], rhs: [U; 16], output: &mut [V])

fn negacyclic_conv16(lhs: [T; 16], rhs: [U; 16], output: &mut [V])

fn conv24(lhs: [T; 24], rhs: [U; 24], output: &mut [V])

fn conv32(lhs: [T; 32], rhs: [U; 32], output: &mut [V])

fn negacyclic_conv32(lhs: [T; 32], rhs: [U; 32], output: &mut [V])

fn conv64(lhs: [T; 64], rhs: [U; 64], output: &mut [V])

impl Debug for Goldilocks

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

Formats the value using the given formatter.

impl Default for Goldilocks

fn default() -> Goldilocks

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Goldilocks

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for Goldilocks

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

Formats the value using the given formatter.

impl Distribution<Goldilocks> for StandardUniform

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

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 Goldilocks

type Output = Goldilocks

The resulting type after applying the / operator.

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

Performs the / operation.

impl DivAssign for Goldilocks

fn div_assign(&mut self, rhs: Goldilocks)

Performs the /= operation.

impl<const WIDTH: usize> ExternalLayerConstructor<Goldilocks, WIDTH> for Poseidon2ExternalLayerGoldilocks<WIDTH>

fn new_from_constants( external_constants: ExternalLayerConstants<Goldilocks, WIDTH>, ) -> Self

A constructor which internally will convert the supplied constants into the appropriate form for the implementation.

impl<const WIDTH: usize> ExternalLayerConstructor<Goldilocks, WIDTH> for Poseidon2ExternalLayerGoldilocksHL<WIDTH>

fn new_from_constants( external_constants: ExternalLayerConstants<Goldilocks, WIDTH>, ) -> Self

A constructor which internally will convert the supplied constants into the appropriate form for the implementation.

impl Field for Goldilocks

const GENERATOR: Self

A generator of this field’s multiplicative group.

type Packing = Goldilocks

fn is_zero(&self) -> bool

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

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

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

fn order() -> BigUint

The number of elements in the field.

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 bits() -> usize

The number of bits required to define an element of this field.

impl HasTwoAdicBinomialExtension<2> for Goldilocks

const EXT_TWO_ADICITY: usize = 33usize

Two-adicity of the multiplicative group of the extension field.

fn ext_two_adic_generator(bits: usize) -> [Self; 2]

Returns a two-adic generator for the extension field.

impl HasTwoAdicBinomialExtension<5> for Goldilocks

const EXT_TWO_ADICITY: usize = 32usize

Two-adicity of the multiplicative group of the extension field.

fn ext_two_adic_generator(bits: usize) -> [Self; 5]

Returns a two-adic generator for the extension field.

impl Hash for Goldilocks

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 InjectiveMonomial<7> for Goldilocks

Degree of the smallest permutation polynomial for Goldilocks.

As p - 1 = 2^32 * 3 * 5 * 17 * … the smallest choice for a degree D satisfying gcd(p - 1, D) = 1 is 7.

fn injective_exp_n(&self) -> Self

Compute x -> x^n for a given n > 1 such that this map is injective.

impl InternalLayerConstructor<Goldilocks> for Poseidon2InternalLayerGoldilocks

fn new_from_constants(internal_constants: Vec<Goldilocks>) -> Self

A constructor which internally will convert the supplied constants into the appropriate form for the implementation.

impl Mul for Goldilocks

type Output = Goldilocks

The resulting type after applying the * operator.

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

Performs the * operation.

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

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl Neg for Goldilocks

type Output = Goldilocks

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Ord for Goldilocks

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.

impl PartialEq for Goldilocks

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

Tests for self and other values to be equal, and is used by ==.

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

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

impl PartialOrd for Goldilocks

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 PermutationMonomial<7> for Goldilocks

fn injective_exp_root_n(&self) -> Self

In the field Goldilocks, a^{1/7} is equal to a^{10540996611094048183}.

This follows from the calculation 7*10540996611094048183 = 4*(2^64 - 2**32) + 1 = 1 mod (p - 1).

impl PrimeCharacteristicRing for Goldilocks

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 = Goldilocks

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 halve(&self) -> Self

The elementary function halve(a) = a/2.

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

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

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

Divide by a given power of two. div_2exp_u64(a, exp) = a/2^exp

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 dot_product<const N: usize>(lhs: &[Self; N], rhs: &[Self; N]) -> Self

Compute the dot product of two vectors.

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.

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 double(&self) -> Self

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

fn square(&self) -> Self

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

fn cube(&self) -> Self

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

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

Computes the arithmetic generalization of boolean xor.

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

The elementary function exp_power_of_2(a, power_log) = a^{2^power_log}.

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, ....

impl PrimeField for Goldilocks

fn as_canonical_biguint(&self) -> BigUint

Return the representative of value in canonical form which lies in the range 0 <= x < self.order().

impl PrimeField64 for Goldilocks

const ORDER_U64: u64 = 18_446_744_069_414_584_321u64

fn as_canonical_u64(&self) -> u64

Return the representative of value in canonical form which lies in the range 0 <= x < ORDER_U64.

fn to_unique_u64(&self) -> u64

Convert a field element to a u64 such that any two field elements are converted to the same u64 if and only if they represent the same value.

impl Product for Goldilocks

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

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

impl QuotientMap<i128> for Goldilocks

fn from_int(int: i128) -> Goldilocks

Convert a given i128 integer into an element of the Goldilocks field.

This checks the sign and then makes use of the equivalent method for unsigned integers. This should be avoided in performance critical locations.

fn from_canonical_checked(int: i128) -> Option<Goldilocks>

Convert a given u128 integer into an element of the Goldilocks field.

Returns None if the input does not lie in the range:[-(2^63 - 2^31), 2^63 - 2^31].

unsafe fn from_canonical_unchecked(int: i128) -> Goldilocks

Convert a given u128 integer into an element of the Goldilocks field.

Safety

The input must lie in the range:[1 + 2^32 - 2^64, 2^64 - 1].

impl QuotientMap<i16> for Goldilocks

fn from_int(int: i16) -> Self

Convert a given i16 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

fn from_canonical_checked(int: i16) -> Option<Self>

Convert a given i16 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: i16) -> Self

Convert a given i16 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

impl QuotientMap<i32> for Goldilocks

fn from_int(int: i32) -> Self

Convert a given i32 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

fn from_canonical_checked(int: i32) -> Option<Self>

Convert a given i32 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: i32) -> Self

Convert a given i32 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

impl QuotientMap<i64> for Goldilocks

fn from_int(int: i64) -> Self

Convert a given i64 integer into an element of the Goldilocks field.

We simply need to deal with the sign.

fn from_canonical_checked(int: i64) -> Option<Self>

Convert a given i64 integer into an element of the Goldilocks field.

Returns none if the input does not lie in the range (-(2^63 - 2^31), 2^63 - 2^31).

unsafe fn from_canonical_unchecked(int: i64) -> Self

Convert a given i64 integer into an element of the Goldilocks field.

Safety

In this case this function is actually always safe as the internal value is allowed to be any u64.

impl QuotientMap<i8> for Goldilocks

fn from_int(int: i8) -> Self

Convert a given i8 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

fn from_canonical_checked(int: i8) -> Option<Self>

Convert a given i8 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: i8) -> Self

Convert a given i8 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

impl QuotientMap<u128> for Goldilocks

fn from_int(int: u128) -> Goldilocks

Convert a given u128 integer into an element of the Goldilocks field.

Uses a modular reduction to reduce to canonical form. This should be avoided in performance critical locations.

fn from_canonical_checked(int: u128) -> Option<Goldilocks>

Convert a given u128 integer into an element of the Goldilocks field.

Returns None if the input does not lie in the range:[0, 2^64 - 2^32].

unsafe fn from_canonical_unchecked(int: u128) -> Goldilocks

Convert a given u128 integer into an element of the Goldilocks field.

Safety

The input must lie in the range:[0, 2^64 - 1].

impl QuotientMap<u16> for Goldilocks

fn from_int(int: u16) -> Self

Convert a given u16 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

fn from_canonical_checked(int: u16) -> Option<Self>

Convert a given u16 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: u16) -> Self

Convert a given u16 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

impl QuotientMap<u32> for Goldilocks

fn from_int(int: u32) -> Self

Convert a given u32 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

fn from_canonical_checked(int: u32) -> Option<Self>

Convert a given u32 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: u32) -> Self

Convert a given u32 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

impl QuotientMap<u64> for Goldilocks

fn from_int(int: u64) -> Self

Convert a given u64 integer into an element of the Goldilocks field.

No reduction is needed as the internal value is allowed to be any u64.

fn from_canonical_checked(int: u64) -> Option<Self>

Convert a given u64 integer into an element of the Goldilocks field.

Return None if the given integer is greater than p = 2^64 - 2^32 + 1.

unsafe fn from_canonical_unchecked(int: u64) -> Self

Convert a given u64 integer into an element of the Goldilocks field.

Safety

In this case this function is actually always safe as the internal value is allowed to be any u64.

impl QuotientMap<u8> for Goldilocks

fn from_int(int: u8) -> Self

Convert a given u8 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

fn from_canonical_checked(int: u8) -> Option<Self>

Convert a given u8 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

unsafe fn from_canonical_unchecked(int: u8) -> Self

Convert a given u8 integer into an element of the Goldilocks field.

Due to the integer type, the input value is always canonical.

impl RawDataSerializable for Goldilocks

const NUM_BYTES: usize = 8usize

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) -> [u8; 8]

Convert a field element into a collection 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.

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

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

impl Serialize for Goldilocks

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

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl Sub for Goldilocks

type Output = Goldilocks

The resulting type after applying the - operator.

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

Performs the - operation.

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

fn sub_assign(&mut self, rhs: T)

Performs the -= operation.

impl Sum for Goldilocks

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

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

impl TwoAdicField for Goldilocks

const TWO_ADICITY: usize = 32usize

The number of factors of two in this field’s multiplicative group.

fn two_adic_generator(bits: usize) -> Self

Returns a generator of the multiplicative group of order 2^bits. Assumes bits <= TWO_ADICITY, otherwise the result is undefined.

impl UniformSamplingField for Goldilocks

const MAX_SINGLE_SAMPLE_BITS: usize = 24usize

Maximum number of bits we can sample at negligible (~1/field prime) probability of triggering an error / requiring a resample.

const SAMPLING_BITS_M: [u64; 64]

An array storing the largest value m_k for each k in [0, 31], such that m_k is a multiple of 2^k and less than P. m_k is defined as:

impl Copy for Goldilocks

impl Eq for Goldilocks

impl MdsPermutation<Goldilocks, 12> for MdsMatrixGoldilocks

impl MdsPermutation<Goldilocks, 16> for MdsMatrixGoldilocks

impl MdsPermutation<Goldilocks, 24> for MdsMatrixGoldilocks

impl MdsPermutation<Goldilocks, 32> for MdsMatrixGoldilocks

impl MdsPermutation<Goldilocks, 64> for MdsMatrixGoldilocks

impl MdsPermutation<Goldilocks, 68> for MdsMatrixGoldilocks

impl MdsPermutation<Goldilocks, 8> for MdsMatrixGoldilocks

impl Packable for Goldilocks