Struct BFieldElement 

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

Base field element ∈ ℤ_{2^64 - 2^32 + 1}.

In Montgomery representation. This implementation follows https://eprint.iacr.org/2022/274.pdf and https://github.com/novifinancial/winterfell/pull/101/files.

Implementations

impl BFieldElement

pub const BYTES: usize = 8

pub const P: u64 = 0xffff_ffff_0000_0001

The base field’s prime, i.e., 2^64 - 2^32 + 1.

pub const MAX: u64

pub const MINUS_TWO_INVERSE: Self

-2^-1

pub const fn new(value: u64) -> Self

pub const fn value(&self) -> u64

pub fn inverse(&self) -> Self

pub const fn power_accumulator<const N: usize, const M: usize>( base: [Self; N], tail: [Self; N], ) -> [Self; N]

Square the base M times and multiply the result by the tail value

pub const fn generator() -> Self

A generator for the entire base field.

pub const fn lift(&self) -> XFieldElement

Turn this base field element into the corresponding extension field element.

pub fn increment(&mut self)

Add BFieldElement::ONE to self.

pub fn decrement(&mut self)

Subtract BFieldElement::ONE from self.

pub const fn mod_pow(&self, exp: u64) -> Self

pub const fn montyred(x: u128) -> u64

Montgomery reduction

pub const fn raw_bytes(&self) -> [u8; 8]

Return the raw bytes or 8-bit chunks of the Montgomery representation, in little-endian byte order

pub const fn from_raw_bytes(bytes: &[u8; 8]) -> Self

Take a slice of 8 bytes and interpret it as an integer in little-endian byte order, and cast it to a BFieldElement in Montgomery representation

pub const fn raw_u16s(&self) -> [u16; 4]

Return the raw 16-bit chunks of the Montgomery representation, in little-endian chunk order

pub const fn from_raw_u16s(chunks: &[u16; 4]) -> Self

Take a slice of 4 16-bit chunks and interpret it as an integer in little-endian chunk order, and cast it to a BFieldElement in Montgomery representation

pub fn raw_u128(&self) -> u128

pub const fn from_raw_u64(e: u64) -> BFieldElement

pub const fn raw_u64(&self) -> u64

pub const fn is_canonical(x: u64) -> bool

Trait Implementations

impl Add for BFieldElement

type Output = BFieldElement

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<BFieldElement> for XFieldElement

type Output = XFieldElement

The resulting type after applying the + operator.

fn add(self, other: BFieldElement) -> Self

Performs the + operation.

impl Add<XFieldElement> for BFieldElement

The bfe + xfe -> xfe instance belongs to BFieldElement.

type Output = XFieldElement

The resulting type after applying the + operator.

fn add(self, other: XFieldElement) -> XFieldElement

Performs the + operation.

impl AddAssign for BFieldElement

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl AddAssign<BFieldElement> for XFieldElement

fn add_assign(&mut self, rhs: BFieldElement)

Performs the += operation.

impl<'a> Arbitrary<'a> for BFieldElement

fn arbitrary(u: &mut Unstructured<'a>) -> Result<Self>

Generate an arbitrary value of Self from the given unstructured data.

fn size_hint(depth: usize) -> (usize, Option<usize>)

Get a size hint for how many bytes out of an Unstructured this type needs to construct itself.

fn arbitrary_take_rest(u: Unstructured<'a>) -> Result<Self, Error>

Generate an arbitrary value of Self from the entirety of the given unstructured data.

fn try_size_hint( depth: usize, ) -> Result<(usize, Option<usize>), MaxRecursionReached>

Get a size hint for how many bytes out of an Unstructured this type needs to construct itself.

impl BFieldCodec for BFieldElement

type Error = BFieldCodecError

fn decode(sequence: &[BFieldElement]) -> Result<Box<Self>, Self::Error>

fn encode(&self) -> Vec<BFieldElement>

fn static_length() -> Option<usize>

Returns the length in number of BFieldElements if it is known at compile-time. Otherwise, None.

impl Clone for BFieldElement

fn clone(&self) -> BFieldElement

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ConstOne for BFieldElement

const ONE: Self

The multiplicative identity element of Self, 1.

impl ConstZero for BFieldElement

const ZERO: Self

The additive identity element of Self, 0.

impl Copy for BFieldElement

impl CyclicGroupGenerator for BFieldElement

fn get_cyclic_group_elements(&self, max: Option<usize>) -> Vec<Self>

impl Debug for BFieldElement

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

Formats the value using the given formatter.

impl Default for BFieldElement

fn default() -> BFieldElement

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for BFieldElement

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for BFieldElement

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

Formats the value using the given formatter.

impl Distribution<BFieldElement> for StandardUniform

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

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 BFieldElement

type Output = BFieldElement

The resulting type after applying the / operator.

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

Performs the / operation.

impl Eq for BFieldElement

impl FiniteField for BFieldElement

fn batch_inversion(input: Vec<Self>) -> Vec<Self>

Montgomery Batch Inversion

fn square(self) -> Self

impl From<&BFieldElement> for u64

fn from(elem: &BFieldElement) -> Self

Converts to this type from the input type.

impl From<&BFieldElement> for u128

fn from(elem: &BFieldElement) -> Self

Converts to this type from the input type.

impl From<&BFieldElement> for i128

fn from(elem: &BFieldElement) -> Self

Converts to this type from the input type.

impl From<&BFieldElement> for i64

fn from(elem: &BFieldElement) -> Self

Converts to this type from the input type.

impl From<BFieldElement> for u64

fn from(elem: BFieldElement) -> Self

Converts to this type from the input type.

impl From<BFieldElement> for u128

fn from(elem: BFieldElement) -> Self

Converts to this type from the input type.

impl From<BFieldElement> for i128

fn from(elem: BFieldElement) -> Self

Converts to this type from the input type.

impl From<BFieldElement> for i64

fn from(elem: BFieldElement) -> Self

Converts to this type from the input type.

impl From<BFieldElement> for [u8; 8]

Convert a B-field element to a byte array. The client uses this for its database.

fn from(bfe: BFieldElement) -> Self

Converts to this type from the input type.

impl From<i8> for BFieldElement

fn from(value: i8) -> Self

Converts to this type from the input type.

impl From<i16> for BFieldElement

fn from(value: i16) -> Self

Converts to this type from the input type.

impl From<i32> for BFieldElement

fn from(value: i32) -> Self

Converts to this type from the input type.

impl From<i64> for BFieldElement

fn from(value: i64) -> Self

Converts to this type from the input type.

impl From<isize> for BFieldElement

fn from(value: isize) -> Self

Converts to this type from the input type.

impl From<u8> for BFieldElement

fn from(value: u8) -> Self

Converts to this type from the input type.

impl From<u16> for BFieldElement

fn from(value: u16) -> Self

Converts to this type from the input type.

impl From<u32> for BFieldElement

fn from(value: u32) -> Self

Converts to this type from the input type.

impl From<u64> for BFieldElement

fn from(value: u64) -> Self

Converts to this type from the input type.

impl From<u128> for BFieldElement

fn from(value: u128) -> Self

Converts to this type from the input type.

impl From<usize> for BFieldElement

fn from(value: usize) -> Self

Converts to this type from the input type.

impl FromStr for BFieldElement

type Err = ParseBFieldElementError

The associated error which can be returned from parsing.

fn from_str(s: &str) -> Result<Self, Self::Err>

Parses a string s to return a value of this type.

impl GetSize for BFieldElement

fn get_heap_size(&self) -> usize

Determines how many bytes this object occupies inside the heap.

fn get_heap_size_with_tracker<TRACKER: GetSizeTracker>( &self, tracker: TRACKER, ) -> (usize, TRACKER)

Determines how many bytes this object occupies inside the heap while using a tracker.

fn get_stack_size() -> usize

Determines how may bytes this object occupies inside the stack.

fn get_size(&self) -> usize

Determines the total size of the object.

fn get_size_with_tracker<T>(&self, tracker: T) -> (usize, T)

where T: GetSizeTracker,

Determines the total size of the object while using a tracker.

impl Hash for BFieldElement

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 Inverse for BFieldElement

fn inverse(&self) -> Self

The multiplicative inverse: a * a.inverse() == 1

fn inverse_or_zero(&self) -> Self

impl LowerHex for BFieldElement

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

Formats the value using the given formatter.

impl ModPowU32 for BFieldElement

fn mod_pow_u32(&self, exp: u32) -> Self

impl ModPowU64 for BFieldElement

fn mod_pow_u64(&self, pow: u64) -> Self

impl Mul for BFieldElement

type Output = BFieldElement

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<BFieldElement> for XFieldElement

XField * BField means scalar multiplication of the BFieldElement onto each coefficient of the XField.

type Output = XFieldElement

The resulting type after applying the * operator.

fn mul(self, other: BFieldElement) -> Self

Performs the * operation.

impl<FF, FF2> Mul<Polynomial<'_, FF>> for BFieldElement

where FF: FiniteField + Mul<BFieldElement, Output = FF2>, FF2: 'static + FiniteField,

type Output = Polynomial<'static, FF2>

The resulting type after applying the * operator.

fn mul(self, other: Polynomial<'_, FF>) -> Self::Output

Performs the * operation.

impl Mul<XFieldElement> for BFieldElement

type Output = XFieldElement

The resulting type after applying the * operator.

fn mul(self, other: XFieldElement) -> XFieldElement

Performs the * operation.

impl MulAssign for BFieldElement

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl MulAssign<BFieldElement> for XFieldElement

fn mul_assign(&mut self, rhs: BFieldElement)

Performs the *= operation.

impl Neg for BFieldElement

type Output = BFieldElement

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl One for BFieldElement

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

impl PartialEq for BFieldElement

fn eq(&self, other: &BFieldElement) -> 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 PrimitiveRootOfUnity for BFieldElement

fn primitive_root_of_unity(n: u64) -> Option<BFieldElement>

impl Serialize for BFieldElement

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 BFieldElement

impl Sub for BFieldElement

type Output = BFieldElement

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<BFieldElement> for XFieldElement

type Output = XFieldElement

The resulting type after applying the - operator.

fn sub(self, other: BFieldElement) -> Self

Performs the - operation.

impl Sub<XFieldElement> for BFieldElement

type Output = XFieldElement

The resulting type after applying the - operator.

fn sub(self, other: XFieldElement) -> XFieldElement

Performs the - operation.

impl SubAssign for BFieldElement

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl SubAssign<BFieldElement> for XFieldElement

fn sub_assign(&mut self, rhs: BFieldElement)

Performs the -= operation.

impl Sum for BFieldElement

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

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

impl TryFrom<&BFieldElement> for u8

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: &BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<&BFieldElement> for i8

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: &BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<&BFieldElement> for u16

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: &BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<&BFieldElement> for i16

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: &BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<&BFieldElement> for u32

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: &BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<&BFieldElement> for i32

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: &BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<&BFieldElement> for usize

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: &BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<&BFieldElement> for isize

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: &BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<&[u8]> for BFieldElement

type Error = ParseBFieldElementError

The type returned in the event of a conversion error.

fn try_from(bytes: &[u8]) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<BFieldElement> for u8

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<BFieldElement> for i8

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<BFieldElement> for u16

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<BFieldElement> for i16

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<BFieldElement> for u32

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<BFieldElement> for i32

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<BFieldElement> for usize

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<BFieldElement> for isize

type Error = TryFromIntError

The type returned in the event of a conversion error.

fn try_from(value: BFieldElement) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<[u8; 8]> for BFieldElement

type Error = ParseBFieldElementError

The type returned in the event of a conversion error.

fn try_from(array: [u8; 8]) -> Result<Self, Self::Error>

Performs the conversion.

impl UpperHex for BFieldElement

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

Formats the value using the given formatter.

impl Zero for BFieldElement

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.