Trait PolynomialRingElement

pub trait PolynomialRingElement:
    FieldElement
    + Add<Output = Self>
    + AddAssign
    + Div<Output = Self>
    + Mul<Output = Self>
    + MulAssign
    + Neg<Output = Self>
    + Sub<Output = Self>
    + SubAssign
    + FromStr
    + PartialEq
    + Clone
    + Hash
    + Debug
    + From<u64>
    + From<Polynomial<Self::F>>
    + Display {
    type F: FieldElement;

    // Required methods
    fn modulus() -> Polynomial<Self::F>;
    fn polynomial(&self) -> &Polynomial<Self::F>;

    // Provided methods
    fn to_scalar(&self) -> Result<Self::F> { ... }
    fn norm_l1(&self) -> u64 { ... }
    fn norm_l2(&self) -> u64 { ... }
    fn norm_max(&self) -> u64 { ... }
    fn coef(&self) -> Vector<Self::F> { ... }
    fn rot(&self) -> Matrix2D<Self::F> { ... }
}

A trait representing a polynomial ring defined as T[X]/<Self::modulus()> where T is a FieldElement trait and modulus is a function implemented by the struct implementing PolynomialRingElement

Required Associated Types

type F: FieldElement

Required Methods

fn modulus() -> Polynomial<Self::F>

Modulus used in remainder division to form the polynomial ring.

Operations are done modulo this polynomial, in a way similar to scalar fields.

See the division implementation for more info.

fn polynomial(&self) -> &Polynomial<Self::F>

Return the Polynomial representation of the current value Used to automatically implement norms and other functions.

Provided Methods

fn to_scalar(&self) -> Result<Self::F>

Attempt to get a scalar representation of the polynomial. If the polynomial degree is > 0 this method will error.

fn norm_l1(&self) -> u64

Calculate the l1 norm for this polynomial. That is the summation of all coefficients

fn norm_l2(&self) -> u64

Calculate the l2 norm for this polynomial. That is the square root of the summation of each coefficient squared

Specifically, we’re calculating the square root in the integer field, not the prime field

fn norm_max(&self) -> u64

Calculate the l-infinity norm for this polynomial. That is the largest coefficient

fn coef(&self) -> Vector<Self::F>

Returns a coefficient vector of length equal to the ring modulus degree.

fn rot(&self) -> Matrix2D<Self::F>

Create a rotated matrix of polynomial coefficients

from LatticeFold page 9 https://eprint.iacr.org/2024/257.pdf

Object Safety

This trait is not object safe.

Implementors