Trait miden_processor::StarkField[−]

pub trait StarkField: FieldElement<BaseField = Self> {
    type QuadExtension: FieldElement;

    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, Global>;

    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 describing quadratic extension of this StarkField.

Associated Constants

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.

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

A multiplicative generator of the field.

Let Self::MODULUS = k * 2^n + 1; then, TWO_ADICITY is n.

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

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

Returns a canonical integer representation of the field element.

Provided methods

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.

Implementations on Foreign Types

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

sage: GF(MODULUS).primitive_element()
3

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

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

Implementors