Struct Rq

pub struct Rq { /* private fields */ }

This module provides implementations for various operations in the polynomial ring R = Z_q[X] / (X^d + 1).

Implementations

impl Rq

pub const DEGREE: usize = 64usize

pub const fn new(coeffs: [Zq; 64]) -> Self

Constructor for the polynomial ring

pub const fn zero() -> Self

Generate zero polynomial

pub fn into_coeffs(self) -> [Zq; 64]

pub fn get_coefficients(&self) -> &[Zq; 64]

Get the coefficients as a vector

pub fn random<R: Rng + CryptoRng>(rng: &mut R) -> Self

Generate random polynomial with a provided cryptographically secure RNG

pub fn random_with_bound<R: Rng + CryptoRng>(rng: &mut R, bound: u32) -> Self

Generate random polynomial with a provided cryptographically secure RNG and given bound

pub fn l2_norm_squared(&self) -> Zq

pub fn decompose(&self, base: Zq, num_parts: usize) -> Vec<Rq>

Decomposes a polynomial into base-B representation: p = p⁽⁰⁾ + p⁽¹⁾·B + p⁽²⁾·B² + … + p⁽ᵗ⁻¹⁾·B^(t-1) Where each p⁽ⁱ⁾ has small coefficients, using centered representatives

pub fn conjugate_automorphism(&self) -> Self

Compute the conjugate automorphism \sigma_{-1} of vector based on B) Constraints…, Page 21.

pub fn operator_norm(&self) -> f64

Compute the operator norm of a polynomial given its coefficients. The operator norm is defined as the maximum magnitude of the DFT (eigenvalues) of the coefficient vector.

Note that: The operator norm only affects the coefficients of the random PolyRings generated from the challenge space. Prover and Verifier will not do the operator norm check, because random PolyRings are determined after generation. Both party will have access to the same PolyRings through transcript,

Trait Implementations

impl Add<&Rq> for &Rq

fn add(self, other: &Rq) -> Rq

Add two polynomials

type Output = Rq

The resulting type after applying the + operator.

impl Clone for Rq

fn clone(&self) -> Rq

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Rq

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

Formats the value using the given formatter.

impl FromIterator<Rq> for RqVector

fn from_iter<T: IntoIterator<Item = Rq>>(iter: T) -> Self

Creates a value from an iterator.

impl Mul<&Rq> for &Rq

fn mul(self, other: &Rq) -> Rq

Polynomial multiplication modulo x^D + 1

type Output = Rq

The resulting type after applying the * operator.

impl Mul<&Rq> for &RqVector

type Output = RqVector

The resulting type after applying the * operator.

fn mul(self, other: &Rq) -> RqVector

Performs the * operation.

impl Mul<&Zq> for &Rq

fn mul(self, other: &Zq) -> Rq

Scalar multiplication of a polynomial

type Output = Rq

The resulting type after applying the * operator.

impl PartialEq for Rq

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

Tests for self and other values to be equal, and is used by ==.

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

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

impl Sub<&Rq> for &Rq

fn sub(self, other: &Rq) -> Rq

Add two polynomials

type Output = Rq

The resulting type after applying the - operator.

impl Eq for Rq

impl StructuralPartialEq for Rq