Struct winter_math::fields::f62::BaseElement

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

Represents base field element in the field.

Internal values are stored in Montgomery representation and can be in the range [0; 2M). The backing type is u64.

Implementations

impl BaseElement

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

Creates a new field element from the provided value; the value is converted into Montgomery representation.

Trait Implementations

impl Add for BaseElement

type Output = BaseElement

The resulting type after applying the + operator.

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

Performs the + operation.

impl AddAssign for BaseElement

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl AsBytes for BaseElement

fn as_bytes(&self) -> &[u8]

Returns a byte representation of self.

impl Clone for BaseElement

fn clone(&self) -> BaseElement

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for BaseElement

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

Formats the value using the given formatter.

impl Default for BaseElement

fn default() -> BaseElement

Returns the “default value” for a type.

impl Deserializable for BaseElement

fn read_from<R: ByteReader>( source: &mut R ) -> Result<Self, DeserializationError>

Reads a sequence of bytes from the provided source, attempts to deserialize these bytes into Self, and returns the result.

fn read_from_bytes(bytes: &[u8]) -> Result<Self, DeserializationError>

Attempts to deserialize the provided bytes into Self and returns the result.

impl Display for BaseElement

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

Formats the value using the given formatter.

impl Div for BaseElement

type Output = BaseElement

The resulting type after applying the / operator.

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

Performs the / operation.

impl DivAssign for BaseElement

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl ExtensibleField<2> for BaseElement

Defines a quadratic extension of the base field over an irreducible polynomial x² - x - 1. Thus, an extension element is defined as α + β * φ, where φ is a root of this polynomial, and α and β are base field elements.

fn mul(a: [Self; 2], b: [Self; 2]) -> [Self; 2]

Returns a product of a and b in the field defined by this extension.

fn mul_base(a: [Self; 2], b: Self) -> [Self; 2]

Returns a product of a and b in the field defined by this extension. b represents an element in the base field.

fn frobenius(x: [Self; 2]) -> [Self; 2]

Returns Frobenius automorphisms for x in the field defined by this extension.

fn square(a: [Self; N]) -> [Self; N]

Returns the square of a in the field defined by this extension.

fn is_supported() -> bool

Returns true if this extension is supported for the underlying base field.

impl ExtensibleField<3> for BaseElement

Defines a cubic extension of the base field over an irreducible polynomial x³ + 2x + 2. Thus, an extension element is defined as α + β * φ + γ * φ^2, where φ is a root of this polynomial, and α, β and γ are base field elements.

fn mul(a: [Self; 3], b: [Self; 3]) -> [Self; 3]

Returns a product of a and b in the field defined by this extension.

fn mul_base(a: [Self; 3], b: Self) -> [Self; 3]

Returns a product of a and b in the field defined by this extension. b represents an element in the base field.

fn frobenius(x: [Self; 3]) -> [Self; 3]

Returns Frobenius automorphisms for x in the field defined by this extension.

fn square(a: [Self; N]) -> [Self; N]

Returns the square of a in the field defined by this extension.

fn is_supported() -> bool

Returns true if this extension is supported for the underlying base field.

impl FieldElement for BaseElement

type PositiveInteger = u64

A type defining positive integers big enough to describe a field modulus for Self::BaseField with no loss of precision.

type BaseField = BaseElement

Base field type for this finite field. For prime fields, BaseField should be set to Self.

const EXTENSION_DEGREE: usize = 1usize

Extension degree of this field with respect to Self::BaseField. For prime fields, extension degree should be set to 1.

const ZERO: Self = _

The additive identity.

const ONE: Self = _

The multiplicative identity.

const ELEMENT_BYTES: usize = 8usize

Number of bytes needed to encode an element

const IS_CANONICAL: bool = false

True if internal representation of the element is the same as its canonical representation.

fn double(self) -> Self

Returns this field element added to itself.

fn exp(self, power: Self::PositiveInteger) -> Self

Exponentiates this field element by power parameter.

fn inv(self) -> Self

Returns a multiplicative inverse of this field element. If this element is ZERO, ZERO is returned.

fn conjugate(&self) -> Self

Returns a conjugate of this field element.

fn base_element(&self, i: usize) -> Self::BaseField

Return base filed element component of this field element at the specified index i.

fn slice_as_base_elements(elements: &[Self]) -> &[Self::BaseField]

Converts a slice of field elements into a slice of elements in the underlying base field.

fn slice_from_base_elements(elements: &[Self::BaseField]) -> &[Self]

Convert a slice of base field elements into a slice of field elements.

fn elements_as_bytes(elements: &[Self]) -> &[u8]

Converts a list of elements into a list of bytes.

unsafe fn bytes_as_elements( bytes: &[u8] ) -> Result<&[Self], DeserializationError>

Converts a list of bytes into a list of field elements.

fn square(self) -> Self

Returns this field element raised to power 2.

fn cube(self) -> Self

Returns this field element raised to power 3.

fn exp_vartime(self, power: Self::PositiveInteger) -> Self

Exponentiates this field element by power parameter. This function is expressly variable time, to speed-up verifier computations.

impl From<BaseElement> for u128

fn from(value: BaseElement) -> Self

Converts to this type from the input type.

impl From<BaseElement> for u64

fn from(value: BaseElement) -> Self

Converts to this type from the input type.

impl From<u16> for BaseElement

fn from(value: u16) -> Self

Converts a 16-bit value into a field element.

impl From<u32> for BaseElement

fn from(value: u32) -> Self

Converts a 32-bit value into a field element.

impl From<u8> for BaseElement

fn from(value: u8) -> Self

Converts an 8-bit value into a field element.

impl Mul for BaseElement

type Output = BaseElement

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign for BaseElement

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl Neg for BaseElement

type Output = BaseElement

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl PartialEq for BaseElement

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

This method tests for self and other values to be equal, and is used by ==.

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

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

impl Randomizable for BaseElement

const VALUE_SIZE: usize = 8usize

Size of Self in bytes.

fn from_random_bytes(bytes: &[u8]) -> Option<Self>

Returns Self if the set of bytes forms a valid value, otherwise returns None.

impl Serializable for BaseElement

fn write_into<W: ByteWriter>(&self, target: &mut W)

Serializes self into bytes and writes these bytes into the target.

fn to_bytes(&self) -> Vec<u8>

Serializes self into a vector of bytes.

fn get_size_hint(&self) -> usize

Returns an estimate of how many bytes are needed to represent self.

impl StarkField for BaseElement

const MODULUS: Self::PositiveInteger = {transmute(0x3fffc88000000001): <field::f62::BaseElement as field::traits::FieldElement>::PositiveInteger}

sage: MODULUS = 2^62 - 111 * 2^39 + 1
sage: GF(MODULUS).is_prime_field()
True
sage: GF(MODULUS).order()
4611624995532046337

const GENERATOR: Self = _

sage: GF(MODULUS).primitive_element()
3

const TWO_ADICITY: u32 = 39u32

sage: is_odd((MODULUS - 1) / 2^39)
True

const TWO_ADIC_ROOT_OF_UNITY: Self = _

sage: k = (MODULUS - 1) / 2^39
sage: GF(MODULUS).primitive_element()^k
4421547261963328785

const MODULUS_BITS: u32 = 62u32

The number of bits needed to represents Self::MODULUS.

fn get_modulus_le_bytes() -> Vec<u8>

Returns byte representation of the field modulus in little-endian byte order.

fn as_int(&self) -> Self::PositiveInteger

Returns a canonical integer representation of this field element.

fn get_root_of_unity(n: u32) -> Self

Returns the root of unity of order 2^n.

fn from_bytes_with_padding(bytes: &[u8]) -> Self

Converts a slice of bytes into a field element. Pads the slice if it is smaller than the number of bytes needed to represent an element.

impl Sub for BaseElement

type Output = BaseElement

The resulting type after applying the - operator.

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

Performs the - operation.

impl SubAssign for BaseElement

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<'a> TryFrom<&'a [u8]> for BaseElement

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

Converts a slice of bytes into a field element; returns error if the value encoded in bytes is not a valid field element. The bytes are assumed to encode the element in the canonical representation in little-endian byte order.

type Error = DeserializationError

The type returned in the event of a conversion error.

impl TryFrom<[u8; 8]> for BaseElement

type Error = String

The type returned in the event of a conversion error.

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

Performs the conversion.

impl TryFrom<u128> for BaseElement

type Error = String

The type returned in the event of a conversion error.

fn try_from(value: u128) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<u64> for BaseElement

type Error = String

The type returned in the event of a conversion error.

fn try_from(value: u64) -> Result<Self, Self::Error>

Performs the conversion.

impl Copy for BaseElement

impl Eq for BaseElement