Struct SepticExtension 

#[repr(C)]
pub struct SepticExtension<F>(pub [F; 7]);

A septic extension with an irreducible polynomial z^7 - 3z - 5.

The field can be constructed as F_{p^7} = F_p[z]/(z^7 - 3z - 5).

Tuple Fields

0: [F; 7]

Implementations

impl<F: Field> SepticExtension<F>

pub fn sqrt(&self) -> Option<Self>

Computes the square root of the septic field extension element. Returns None if the element is not a square, and Some(result) if it is a square.

impl<F: PrimeField32> SepticExtension<F>

pub fn is_receive(&self) -> bool

Returns whether the extension field element viewed as an y-coordinate of a digest represents a receive interaction.

pub fn is_send(&self) -> bool

Returns whether the extension field element viewed as an y-coordinate of a digest represents a send interaction.

pub fn is_exception(&self) -> bool

Returns whether the extension field element viewed as an y-coordinate of a digest cannot represent anything.

Trait Implementations

impl<F: AbstractField> AbstractExtensionField<F> for SepticExtension<F>

const D: usize = 7

fn from_base(b: F) -> Self

fn from_base_slice(bs: &[F]) -> Self

Suppose this field extension is represented by the quotient ring B[X]/(f(X)) where B is Base and f is an irreducible polynomial of degree D. This function takes a slice bs of length at most D, and constructs the field element \sum_i bs[i] * X^i.

fn from_base_fn<G: FnMut(usize) -> F>(f: G) -> Self

Similar to core:array::from_fn, with the same caveats as from_base_slice.

fn as_base_slice(&self) -> &[F]

Suppose this field extension is represented by the quotient ring B[X]/(f(X)) where B is Base and f is an irreducible polynomial of degree D. This function takes a field element \sum_i bs[i] * X^i and returns the coefficients as a slice bs of length at most D containing, from lowest degree to highest.

fn monomial(exponent: usize) -> Self

Suppose this field extension is represented by the quotient ring B[X]/(f(X)) where B is Base and f is an irreducible polynomial of degree D. This function returns the field element X^exponent if exponent < D and panics otherwise. (The fact that f is not known at the point that this function is defined prevents implementing exponentiation of higher powers since the reduction cannot be performed.)

impl<F: AbstractField> AbstractField for SepticExtension<F>

type F = SepticExtension<<F as AbstractField>::F>

fn zero() -> Self

fn one() -> Self

fn two() -> Self

fn neg_one() -> Self

fn from_f(f: Self::F) -> Self

fn from_bool(b: bool) -> Self

fn from_canonical_u8(n: u8) -> Self

fn from_canonical_u16(n: u16) -> Self

fn from_canonical_u32(n: u32) -> Self

fn from_canonical_u64(n: u64) -> Self

fn from_canonical_usize(n: usize) -> Self

fn from_wrapped_u32(n: u32) -> Self

fn from_wrapped_u64(n: u64) -> Self

fn generator() -> Self

A generator of this field’s entire multiplicative group.

fn double(&self) -> Self

fn square(&self) -> Self

fn cube(&self) -> Self

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

Exponentiation by a u64 power.

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

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

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

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

fn powers_packed<P>(&self) -> PackedPowers<Self, P>

where P: PackedField<Scalar = Self>,

fn shifted_powers_packed<P>(&self, start: Self) -> PackedPowers<Self, P>

where P: PackedField<Scalar = Self>,

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

fn try_div<Rhs>(self, rhs: Rhs) -> Option<Self::Output>

where Rhs: Field, Self: Mul<Rhs>,

impl<F: AbstractField> Add<F> for SepticExtension<F>

type Output = SepticExtension<F>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<F: AbstractField> Add for SepticExtension<F>

type Output = SepticExtension<F>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<F: AbstractField> AddAssign<F> for SepticExtension<F>

fn add_assign(&mut self, rhs: F)

Performs the += operation.

impl<F: AbstractField> AddAssign for SepticExtension<F>

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl<F: Clone> Clone for SepticExtension<F>

fn clone(&self) -> SepticExtension<F>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F: Debug> Debug for SepticExtension<F>

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

Formats the value using the given formatter.

impl<F: DeepSizeOf> DeepSizeOf for SepticExtension<F>

fn deep_size_of_children(&self, context: &mut Context) -> usize

Returns an estimation of the heap-managed storage of this object. This does not include the size of the object itself.

fn deep_size_of(&self) -> usize

Returns an estimation of a total size of memory owned by the object, including heap-managed storage.

impl<F: Default> Default for SepticExtension<F>

fn default() -> SepticExtension<F>

Returns the “default value” for a type.

impl<'de, F> Deserialize<'de> for SepticExtension<F>

where F: Deserialize<'de>,

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<F: AbstractField> Display for SepticExtension<F>

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

Formats the value using the given formatter.

impl<F: Field> Div for SepticExtension<F>

type Output = SepticExtension<F>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<F: Field> ExtensionField<F> for SepticExtension<F>

type ExtensionPacking = SepticExtension<<F as Field>::Packing>

fn is_in_basefield(&self) -> bool

fn as_base(&self) -> Option<Base>

impl<F: Field> Field for SepticExtension<F>

type Packing = SepticExtension<F>

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

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

fn order() -> BigUint

fn is_zero(&self) -> bool

fn is_one(&self) -> bool

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

self * 2^exp

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

self / 2^exp

fn exp_u64_generic<AF>(val: AF, power: u64) -> AF

where AF: AbstractField<F = Self>,

Exponentiation by a u64 power. This is similar to exp_u64, but more general in that it can be used with AbstractFields, not just this concrete field.

fn inverse(&self) -> Self

fn halve(&self) -> Self

Computes input/2. Should be overwritten by most field implementations to use bitshifts. Will error if the field characteristic is 2.

fn bits() -> usize

impl<F: AbstractField> From<F> for SepticExtension<F>

fn from(f: F) -> Self

Converts to this type from the input type.

impl<F: Hash> Hash for SepticExtension<F>

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<F: AbstractField> Mul<F> for SepticExtension<F>

type Output = SepticExtension<F>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<F: AbstractField> Mul for SepticExtension<F>

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

The multiplication rule for F_{p^7} = F_p[z]/(z^7 - 3z - 5).

type Output = SepticExtension<F>

The resulting type after applying the * operator.

impl<F: AbstractField> MulAssign<F> for SepticExtension<F>

fn mul_assign(&mut self, rhs: F)

Performs the *= operation.

impl<F: AbstractField> MulAssign for SepticExtension<F>

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl<F: AbstractField> Neg for SepticExtension<F>

type Output = SepticExtension<F>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<F: PartialEq> PartialEq for SepticExtension<F>

fn eq(&self, other: &SepticExtension<F>) -> 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<F: AbstractField> Product for SepticExtension<F>

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

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

impl<F> Serialize for SepticExtension<F>

where F: Serialize,

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

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<F: AbstractField> Sub<F> for SepticExtension<F>

type Output = SepticExtension<F>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<F: AbstractField> Sub for SepticExtension<F>

type Output = SepticExtension<F>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<F: AbstractField> SubAssign<F> for SepticExtension<F>

fn sub_assign(&mut self, rhs: F)

Performs the -= operation.

impl<F: AbstractField> SubAssign for SepticExtension<F>

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<F: AbstractField> Sum for SepticExtension<F>

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

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

impl<F: Copy> Copy for SepticExtension<F>

impl<F: Eq> Eq for SepticExtension<F>

impl<F: Field> Packable for SepticExtension<F>

impl<F> StructuralPartialEq for SepticExtension<F>