Trait oberon::inner_types::PrimeField
pub trait PrimeField: Field + From<u64> {
type Repr: Copy + Default + Send + Sync + 'static + AsRef<[u8]> + AsMut<[u8]>;
const MODULUS: &'static str;
const NUM_BITS: u32;
const CAPACITY: u32;
const TWO_INV: Self;
const MULTIPLICATIVE_GENERATOR: Self;
const S: u32;
const ROOT_OF_UNITY: Self;
const ROOT_OF_UNITY_INV: Self;
const DELTA: Self;
// Required methods
fn from_repr(repr: Self::Repr) -> CtOption<Self>;
fn to_repr(&self) -> Self::Repr;
fn is_odd(&self) -> Choice;
// Provided methods
fn from_str_vartime(s: &str) -> Option<Self> { ... }
fn from_u128(v: u128) -> Self { ... }
fn from_repr_vartime(repr: Self::Repr) -> Option<Self> { ... }
fn is_even(&self) -> Choice { ... }
}Expand description
This represents an element of a non-binary prime field.
Required Associated Types§
Required Associated Constants§
const MODULUS: &'static str
const MODULUS: &'static str
Modulus of the field written as a string for debugging purposes.
The encoding of the modulus is implementation-specific. Generic users of the
PrimeField trait should treat this string as opaque.
const CAPACITY: u32
const CAPACITY: u32
How many bits of information can be reliably stored in the field element.
This is usually Self::NUM_BITS - 1.
const TWO_INV: Self
const TWO_INV: Self
Inverse of $2$ in the field.
const MULTIPLICATIVE_GENERATOR: Self
const MULTIPLICATIVE_GENERATOR: Self
A fixed multiplicative generator of modulus - 1 order. This element must also be
a quadratic nonresidue.
It can be calculated using SageMath as GF(modulus).primitive_element().
Implementations of this trait MUST ensure that this is the generator used to
derive Self::ROOT_OF_UNITY.
const S: u32
const S: u32
An integer s satisfying the equation 2^s * t = modulus - 1 with t odd.
This is the number of leading zero bits in the little-endian bit representation of
modulus - 1.
const ROOT_OF_UNITY: Self
const ROOT_OF_UNITY: Self
The 2^s root of unity.
It can be calculated by exponentiating Self::MULTIPLICATIVE_GENERATOR by t,
where t = (modulus - 1) >> Self::S.
const ROOT_OF_UNITY_INV: Self
const ROOT_OF_UNITY_INV: Self
Inverse of Self::ROOT_OF_UNITY.
const DELTA: Self
const DELTA: Self
Generator of the t-order multiplicative subgroup.
It can be calculated by exponentiating Self::MULTIPLICATIVE_GENERATOR by 2^s,
where s is Self::S.
Required Methods§
fn from_repr(repr: Self::Repr) -> CtOption<Self>
fn from_repr(repr: Self::Repr) -> CtOption<Self>
Attempts to convert a byte representation of a field element into an element of this prime field, failing if the input is not canonical (is not smaller than the field’s modulus).
The byte representation is interpreted with the same endianness as elements
returned by PrimeField::to_repr.
Provided Methods§
fn from_str_vartime(s: &str) -> Option<Self>
fn from_str_vartime(s: &str) -> Option<Self>
Interpret a string of numbers as a (congruent) prime field element. Does not accept unnecessary leading zeroes or a blank string.
Security
This method provides no constant-time guarantees.
fn from_u128(v: u128) -> Self
fn from_u128(v: u128) -> Self
Obtains a field element congruent to the integer v.
For fields where Self::CAPACITY >= 128, this is injective and will produce a
unique field element.
For fields where Self::CAPACITY < 128, this is surjective; some field elements
will be produced by multiple values of v.
If you want to deterministically sample a field element representing a value, use
FromUniformBytes instead.
fn from_repr_vartime(repr: Self::Repr) -> Option<Self>
fn from_repr_vartime(repr: Self::Repr) -> Option<Self>
Attempts to convert a byte representation of a field element into an element of this prime field, failing if the input is not canonical (is not smaller than the field’s modulus).
The byte representation is interpreted with the same endianness as elements
returned by PrimeField::to_repr.
Security
This method provides no constant-time guarantees. Implementors of the
PrimeField trait may optimise this method using non-constant-time logic.