Struct Rq

pub struct Rq<const D: usize> { /* private fields */ }

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

Implementations

impl<const D: usize> Rq<D>

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

Constructor for the polynomial ring

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

Get the coefficients as a vector

pub fn iter_mut(&mut self) -> IterMut<'_, Zq>

pub fn inner_product(&self, other: &Self) -> Zq

Dot product between coefficients

pub fn scalar_mul(&self, s: Zq) -> Self

Scalar multiplication

pub fn eval(&self, x: Zq) -> Zq

Evaluate the polynomial at a specific point

pub fn is_zero(&self) -> bool

Check if Polynomial == 0

pub fn is_equal(&self, other: &Self) -> bool

Check if two polynomials are equal

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

Generate random polynomial with a provided cryptographically secure RNG

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

Generate random small polynomial with secure RNG implementation

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

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 encode_message(message: &[bool]) -> Option<Self>

Encode message into polynomial with small coefficients.

Arguments

• message - A slice of booleans representing a binary message

Returns

• Some(Rq) - A polynomial where each coefficient is 0 or 1 based on the message bits
• None - If the message length exceeds the polynomial degree D

Format

• Each boolean is encoded as a coefficient: false -> 0, true -> 1
• Message bits are mapped to coefficients in order (index 0 -> constant term)
• Remaining coefficients (if message is shorter than D) are set to 0

pub fn iter(&self) -> Iter<'_, Zq>

Iterator over coefficients

pub fn check_bounds(&self, bound: Zq) -> bool

Check if polynomial coefficients are within bounds

pub const fn zero() -> Self

Trait Implementations

impl<const D: usize> Add for Rq<D>

type Output = Rq<D>

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl<const D: usize> AddAssign for Rq<D>

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl<const D: usize> Clone for Rq<D>

fn clone(&self) -> Rq<D>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<const D: usize> Debug for Rq<D>

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

Formats the value using the given formatter.

impl<const D: usize> From<PolyRing> for Rq<D>

fn from(zqs: PolyRing) -> Self

Converts to this type from the input type.

impl<const D: usize> From<Vec<Zq>> for Rq<D>

fn from(vec: Vec<Zq>) -> Self

Converts to this type from the input type.

impl<const D: usize> From<ZqVector> for Rq<D>

fn from(zqs: ZqVector) -> Self

Converts to this type from the input type.

impl<const D: usize> Mul for Rq<D>

type Output = Rq<D>

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self::Output

Performs the * operation.

impl<const D: usize> MulAssign for Rq<D>

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl<const D: usize> Neg for Rq<D>

fn neg(self) -> Self

Polynomial negation

type Output = Rq<D>

The resulting type after applying the - operator.

impl<const D: usize> PartialEq for Rq<D>

fn eq(&self, other: &Rq<D>) -> 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<const D: usize> Sub for Rq<D>

type Output = Rq<D>

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl<const D: usize> SubAssign for Rq<D>

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<const D: usize> Eq for Rq<D>

impl<const D: usize> StructuralPartialEq for Rq<D>