Trait winter_math::StarkField [−][src]
pub trait StarkField: FieldElement<BaseField = Self> {
type QuadExtension: FieldElement<BaseField = Self>;
const MODULUS: Self::PositiveInteger;
const MODULUS_BITS: u32;
const GENERATOR: Self;
const TWO_ADICITY: u32;
const TWO_ADIC_ROOT_OF_UNITY: Self;
fn get_modulus_le_bytes() -> Vec<u8>;
fn as_int(&self) -> Self::PositiveInteger;
fn get_root_of_unity(n: u32) -> Self { ... }
}Expand description
Defines an element in a STARK-friendly finite field.
A STARK-friendly field is defined as a prime field with high two-addicity. That is, the
the modulus of the field should be a prime number of the form k * 2^n + 1 (a Proth prime),
where n is relatively larger (e.g., greater than 32).
Associated Types
type QuadExtension: FieldElement<BaseField = Self>
type QuadExtension: FieldElement<BaseField = Self>
Type describing quadratic extension of this StarkField.
Associated Constants
const MODULUS: Self::PositiveInteger
const MODULUS: Self::PositiveInteger
Prime modulus of the field. Must be of the form k * 2^n + 1 (a Proth prime).
This ensures that the field has high 2-adicity.
const MODULUS_BITS: u32
const MODULUS_BITS: u32
The number of bits needed to represents Self::MODULUS.
const TWO_ADICITY: u32
const TWO_ADICITY: u32
Let Self::MODULUS = k * 2^n + 1; then, TWO_ADICITY is n.
const TWO_ADIC_ROOT_OF_UNITY: Self
const TWO_ADIC_ROOT_OF_UNITY: Self
Let Self::MODULUS = k * 2^n + 1; then, TWO_ADIC_ROOT_OF_UNITY is 2^n root of unity
computed as Self::GENERATOR^k.
Required methods
fn get_modulus_le_bytes() -> Vec<u8>
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
fn as_int(&self) -> Self::PositiveInteger
Returns a canonical integer representation of the field element.
Provided methods
fn get_root_of_unity(n: u32) -> Self
fn get_root_of_unity(n: u32) -> Self
Returns the root of unity of order 2^n.
Panics
Panics if the root of unity for the specified order does not exist in this field.