Struct NTTPolynomialRingZq 

pub struct NTTPolynomialRingZq {
    pub poly: Vec<Z>,
    pub modulus: ModulusPolynomialRingZq,
}

NTTPolynomialRingZq contains the NTT representation of some polynomial with respect to a NTTBasisPolynomialRingZq that itself isn’t aware of.

Attributes

• poly: holds the coefficients
• modulus: the ModulusPolynomialRingZq defining the modulus q, the ring Z_q[X]/f(X), and the NTT transform NTTBasisPolynomialRingZq

Examples

use qfall_math::integer_mod_q::{Modulus, PolynomialRingZq, NTTPolynomialRingZq, ModulusPolynomialRingZq};
use std::str::FromStr;
// Setup modulus with capability to perform NTT transform
let mut modulus = ModulusPolynomialRingZq::from_str("5  1 0 0 0 1 mod 257").unwrap();
modulus.set_ntt_unchecked(64);

// sample random polynomial
let rnd = NTTPolynomialRingZq::sample_uniform(&modulus);
// or instantiate polynomial from PolynomialRingZq (or PolyOverZq)

let poly_ring = PolynomialRingZq::sample_uniform(&modulus);
let ntt_poly_ring = NTTPolynomialRingZq::from(&poly_ring);

// multiply, add and subtract objects
let mod_q = Modulus::from(modulus.get_q());
let mut tmp_ntt = ntt_poly_ring * &rnd;
tmp_ntt += &rnd;
tmp_ntt -= &rnd;

// Return to PolynomialRingZq
let res = tmp_ntt.inv_ntt();

Fields

poly: Vec<Z>

modulus: ModulusPolynomialRingZq

Implementations

impl NTTPolynomialRingZq

pub fn inv_ntt(self) -> PolynomialRingZq

Computes the inverse NTT of self with respect to the given modulus.

Returns a new PolynomialRingZq with the specified ModulusPolynomialRingZq and values as defined in self.

Examples

use qfall_math::integer_mod_q::{PolynomialRingZq, PolyOverZq, ModulusPolynomialRingZq, NTTPolynomialRingZq};
use qfall_math::traits::SetCoefficient;

let n = 4;
let modulus = 7681;

let mut mod_poly = PolyOverZq::from(modulus);
mod_poly.set_coeff(0, 1).unwrap();
mod_poly.set_coeff(n, 1).unwrap();

let mut polynomial_modulus = ModulusPolynomialRingZq::from(&mod_poly);
polynomial_modulus.set_ntt_unchecked(1925);

let ntt = NTTPolynomialRingZq::sample_uniform(&polynomial_modulus);

let res = ntt.inv_ntt();

Panics …

• if the NTTBasisPolynomialRingZq in modulus is not set.

impl NTTPolynomialRingZq

pub fn get_mod(&self) -> ModulusPolynomialRingZq

Returns the modulus of the polynomial in NTT representation as a ModulusPolynomialRingZq.

Examples

use qfall_math::integer_mod_q::{NTTPolynomialRingZq, ModulusPolynomialRingZq};
use std::str::FromStr;

let modulus = ModulusPolynomialRingZq::from_str("5  1 0 0 0 1 mod 17").unwrap();
let matrix = NTTPolynomialRingZq::sample_uniform(&modulus);

let modulus = matrix.get_mod();

impl NTTPolynomialRingZq

pub fn sample_uniform(modulus: &ModulusPolynomialRingZq) -> Self

Generates a NTTPolynomialRingZq instance with degree modulus_degree - 1 and entries chosen uniform at random in [0, modulus).

The internally used uniform at random chosen bytes are generated by ThreadRng, which uses ChaCha12 and is considered cryptographically secure.

Parameters:

• modulus_degree: specifies the degree of the modulus polynomial, i.e. the maximum number of sampled coefficients is modulus_degree - 1
• modulus: specifies the modulus of the values and thus, the interval size over which is sampled

Returns a fresh NTTPolynomialRingZq instance of length modulus_degree with entries chosen uniform at random in [0, modulus).

Examples

use qfall_math::integer_mod_q::{NTTPolynomialRingZq, ModulusPolynomialRingZq};
use std::str::FromStr;
let mut modulus = ModulusPolynomialRingZq::from_str("5  1 0 0 0 1 mod 257").unwrap();
modulus.set_ntt_unchecked(64);

let sample = NTTPolynomialRingZq::sample_uniform(&modulus);

Trait Implementations

impl Add for &NTTPolynomialRingZq

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

Adds self with other.

Paramters:

• other: specifies the NTT-representation of the polynomial to add to self

Returns the NTT-representation of the sum of self and other.

Example

use qfall_math::integer_mod_q::{NTTPolynomialRingZq, ModulusPolynomialRingZq};
use std::str::FromStr;
let mut modulus = ModulusPolynomialRingZq::from_str("5  1 0 0 0 1 mod 257").unwrap();
modulus.set_ntt_unchecked(64);

let a = NTTPolynomialRingZq::sample_uniform(&modulus);
let b = NTTPolynomialRingZq::sample_uniform(&modulus);

let c = a + b;

Panics …

• if the moduli are not equal.

type Output = NTTPolynomialRingZq

The resulting type after applying the + operator.

impl AddAssign<&NTTPolynomialRingZq> for NTTPolynomialRingZq

fn add_assign(&mut self, other: &Self)

Adds self with other reusing the memory of self.

Paramters:

• other: specifies the NTT-representation of the polynomial to add to self

Computes the NTT-representation of the sum of self and other.

Example

use qfall_math::integer_mod_q::{NTTPolynomialRingZq, ModulusPolynomialRingZq};
use std::str::FromStr;
let mut modulus = ModulusPolynomialRingZq::from_str("5  1 0 0 0 1 mod 257").unwrap();
modulus.set_ntt_unchecked(64);

let mut a = NTTPolynomialRingZq::sample_uniform(&modulus);
let b = NTTPolynomialRingZq::sample_uniform(&modulus);

a += b;

Panics …

• if the moduli are not equal.

impl AddAssign for NTTPolynomialRingZq

fn add_assign(&mut self, other: NTTPolynomialRingZq)

Documentation at NTTPolynomialRingZq::add_assign.

impl Clone for NTTPolynomialRingZq

fn clone(&self) -> NTTPolynomialRingZq

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl CompareBase<&NTTPolynomialRingZq> for NTTPolynomialRingZq

fn compare_base(&self, other: &&NTTPolynomialRingZq) -> bool

Compares the moduli of the two elements.

Parameters:

• other: The other object whose base is compared to self

Returns true if the moduli match and false otherwise.

fn call_compare_base_error( &self, other: &&NTTPolynomialRingZq, ) -> Option<MathError>

Returns an error that gives a small explanation of how the moduli are incomparable.

Parameters:

• other: The other object whose base is compared to self

Returns a MathError of type MismatchingModulus.

impl CompareBase<&PolyOverZ> for NTTPolynomialRingZq

fn compare_base(&self, other: &T) -> bool

Compares the base elements of the objects and returns true if they match and an operation between the two provided types is possible.

fn call_compare_base_error(&self, other: &T) -> Option<MathError>

Calls an error that gives small explanation how the base elements differ. This function only calls the error and does not check if the two actually differ.

impl CompareBase<&PolyOverZq> for NTTPolynomialRingZq

fn compare_base(&self, other: &&PolyOverZq) -> bool

Compares the moduli of the two elements.

Parameters:

• other: The other object whose base is compared to self

Returns true if the moduli match and false otherwise.

fn call_compare_base_error(&self, other: &&PolyOverZq) -> Option<MathError>

Returns an error that gives a small explanation of how the moduli are incomparable.

Parameters:

• other: The other object whose base is compared to self

Returns a MathError of type MismatchingModulus.

impl CompareBase<&PolynomialRingZq> for NTTPolynomialRingZq

fn compare_base(&self, other: &&PolynomialRingZq) -> bool

Compares the moduli of the two elements.

Parameters:

• other: The other object whose base is compared to self

Returns true if the moduli match and false otherwise.

fn call_compare_base_error( &self, other: &&PolynomialRingZq, ) -> Option<MathError>

Returns an error that gives a small explanation of how the moduli are incomparable.

Parameters:

• other: The other object whose base is compared to self

Returns a MathError of type MismatchingModulus.

impl CompareBase<&Zq> for NTTPolynomialRingZq

fn compare_base(&self, other: &&Zq) -> bool

Compares the moduli of the two elements.

Parameters:

• other: The other object whose base is compared to self

Returns true if the moduli match and false otherwise.

fn call_compare_base_error(&self, other: &&Zq) -> Option<MathError>

Returns an error that gives a small explanation of how the moduli are incomparable.

Parameters:

• other: The other object whose base is compared to self

Returns a MathError of type MismatchingModulus.

impl<Integer: Into<Z>> CompareBase<Integer> for NTTPolynomialRingZq

fn compare_base(&self, other: &T) -> bool

Compares the base elements of the objects and returns true if they match and an operation between the two provided types is possible.

fn call_compare_base_error(&self, other: &T) -> Option<MathError>

Calls an error that gives small explanation how the base elements differ. This function only calls the error and does not check if the two actually differ.

impl CompareBase<PolyOverZ> for NTTPolynomialRingZq

fn compare_base(&self, other: &T) -> bool

Compares the base elements of the objects and returns true if they match and an operation between the two provided types is possible.

fn call_compare_base_error(&self, other: &T) -> Option<MathError>

Calls an error that gives small explanation how the base elements differ. This function only calls the error and does not check if the two actually differ.

impl CompareBase<PolyOverZq> for NTTPolynomialRingZq

fn compare_base(&self, other: &PolyOverZq) -> bool

Compares the moduli of the two elements.

Parameters:

• other: The other object whose base is compared to self

Returns true if the moduli match and false otherwise.

fn call_compare_base_error(&self, other: &PolyOverZq) -> Option<MathError>

Returns an error that gives a small explanation of how the moduli are incomparable.

Parameters:

• other: The other object whose base is compared to self

Returns a MathError of type MismatchingModulus.

impl CompareBase<PolynomialRingZq> for NTTPolynomialRingZq

fn compare_base(&self, other: &PolynomialRingZq) -> bool

Compares the moduli of the two elements.

Parameters:

• other: The other object whose base is compared to self

Returns true if the moduli match and false otherwise.

fn call_compare_base_error(&self, other: &PolynomialRingZq) -> Option<MathError>

Returns an error that gives a small explanation of how the moduli are incomparable.

Parameters:

• other: The other object whose base is compared to self

Returns a MathError of type MismatchingModulus.

impl CompareBase<Zq> for NTTPolynomialRingZq

fn compare_base(&self, other: &Zq) -> bool

Compares the moduli of the two elements.

Parameters:

• other: The other object whose base is compared to self

Returns true if the moduli match and false otherwise.

fn call_compare_base_error(&self, other: &Zq) -> Option<MathError>

Returns an error that gives a small explanation of how the moduli are incomparable.

Parameters:

• other: The other object whose base is compared to self

Returns a MathError of type MismatchingModulus.

impl CompareBase for NTTPolynomialRingZq

fn compare_base(&self, other: &NTTPolynomialRingZq) -> bool

Compares the moduli of the two elements.

Parameters:

• other: The other object whose base is compared to self

Returns true if the moduli match and false otherwise.

fn call_compare_base_error( &self, other: &NTTPolynomialRingZq, ) -> Option<MathError>

Returns an error that gives a small explanation of how the moduli are incomparable.

Parameters:

• other: The other object whose base is compared to self

Returns a MathError of type MismatchingModulus.

impl Debug for NTTPolynomialRingZq

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for NTTPolynomialRingZq

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for NTTPolynomialRingZq

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

Formats the value using the given formatter.

impl From<&PolynomialRingZq> for NTTPolynomialRingZq

fn from(poly: &PolynomialRingZq) -> Self

Computes the NTT representation of poly.

Parameters:

• poly: the polynomial that’s going to be represented in NTT form.

Returns the NTT representation as a NTTPolynomialRingZq of poly.

Examples

use qfall_math::integer_mod_q::{NTTPolynomialRingZq, PolynomialRingZq, ModulusPolynomialRingZq, PolyOverZq};
use crate::qfall_math::traits::SetCoefficient;
use std::str::FromStr;

let n = 4;
let modulus = 7681;

let mut mod_poly = PolyOverZq::from(modulus);
mod_poly.set_coeff(0, 1).unwrap();
mod_poly.set_coeff(n, 1).unwrap();

let mut polynomial_modulus = ModulusPolynomialRingZq::from(&mod_poly);
polynomial_modulus.set_ntt_unchecked(1925);

let poly_ring = PolynomialRingZq::sample_uniform(&polynomial_modulus);

let ntt_poly_ring = NTTPolynomialRingZq::from(&poly_ring);

Panics …

• if the NTTBasisPolynomialRingZq, which is part of the ModulusPolynomialRingZq in poly is not set.

impl From<NTTPolynomialRingZq> for PolynomialRingZq

fn from(ntt: NTTPolynomialRingZq) -> Self

Creates a polynomial from NTTPolynomialRingZq generated with respect to the NTTBasisPolynomialRingZq as part of ModulusPolynomialRingZq.

Parameters:

• ntt: the NTT representation of the polynomial.
• modulus: the modulus that is applied to the polynomial ring element.

Returns a new PolynomialRingZq with the specified ModulusPolynomialRingZq and values as defined in ntt.

Examples

use qfall_math::integer_mod_q::{PolynomialRingZq, PolyOverZq, ModulusPolynomialRingZq, NTTPolynomialRingZq};
use qfall_math::traits::SetCoefficient;

let n = 4;
let modulus = 7681;

let mut mod_poly = PolyOverZq::from(modulus);
mod_poly.set_coeff(0, 1).unwrap();
mod_poly.set_coeff(n, 1).unwrap();

let mut polynomial_modulus = ModulusPolynomialRingZq::from(&mod_poly);
polynomial_modulus.set_ntt_unchecked(1925);

let ntt = NTTPolynomialRingZq::sample_uniform(&polynomial_modulus);

let res = PolynomialRingZq::from(ntt);

Panics …

• if the NTTBasisPolynomialRingZq in modulus is not set.

impl Mul for &NTTPolynomialRingZq

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

Multiplies self with other.

Paramters:

• other: specifies the NTT-representation of the polynomial to multiply to self
• modulus: defines the modulus q

Returns the NTT-representation of the multiplication of self and other.

Example

use qfall_math::integer_mod_q::{NTTPolynomialRingZq, ModulusPolynomialRingZq};
use std::str::FromStr;
let mut modulus = ModulusPolynomialRingZq::from_str("5  1 0 0 0 1 mod 257").unwrap();
modulus.set_ntt_unchecked(64);

let a = NTTPolynomialRingZq::sample_uniform(&modulus);
let b = NTTPolynomialRingZq::sample_uniform(&modulus);

let c = a * b;

Panics …

• if the moduli are not equal.

type Output = NTTPolynomialRingZq

The resulting type after applying the * operator.

impl MulAssign<&NTTPolynomialRingZq> for NTTPolynomialRingZq

fn mul_assign(&mut self, other: &NTTPolynomialRingZq)

Multiplies self with other reusing the memory of self.

Paramters:

• other: specifies the NTT-representation of the polynomial to multiply with self

Computes the NTT-representation of the multiplication of self and other.

Example

use qfall_math::integer_mod_q::{NTTPolynomialRingZq, ModulusPolynomialRingZq};
use std::str::FromStr;
let mut modulus = ModulusPolynomialRingZq::from_str("5  1 0 0 0 1 mod 257").unwrap();
modulus.set_ntt_unchecked(64);

let mut a = NTTPolynomialRingZq::sample_uniform(&modulus);
let b = NTTPolynomialRingZq::sample_uniform(&modulus);

a *= b;

Panics …

• if the moduli are not equal.

impl MulAssign for NTTPolynomialRingZq

fn mul_assign(&mut self, other: NTTPolynomialRingZq)

Documentation at NTTPolynomialRingZq::mul_assign.

impl PartialEq for NTTPolynomialRingZq

fn eq(&self, other: &NTTPolynomialRingZq) -> 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 Serialize for NTTPolynomialRingZq

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl Sub for &NTTPolynomialRingZq

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

Subtracts other from self.

Paramters:

• other: specifies the NTT-representation of the polynomial to subtract from self

Returns the NTT-representation of the subtraction of other from self.

Example

use qfall_math::integer_mod_q::{NTTPolynomialRingZq, ModulusPolynomialRingZq};
use std::str::FromStr;
let mut modulus = ModulusPolynomialRingZq::from_str("5  1 0 0 0 1 mod 257").unwrap();
modulus.set_ntt_unchecked(64);

let a = NTTPolynomialRingZq::sample_uniform(&modulus);
let b = NTTPolynomialRingZq::sample_uniform(&modulus);

let c = a - b;

Panics …

• if the moduli are not equal.

type Output = NTTPolynomialRingZq

The resulting type after applying the - operator.

impl SubAssign<&NTTPolynomialRingZq> for NTTPolynomialRingZq

fn sub_assign(&mut self, other: &Self)

Subtracts other from self reusing the memory of self.

Paramters:

• other: specifies the NTT-representation of the polynomial to subtract from self

Computes the NTT-representation of the subtraction of other from self.

Example

use qfall_math::integer_mod_q::{NTTPolynomialRingZq, ModulusPolynomialRingZq};
use std::str::FromStr;
let mut modulus = ModulusPolynomialRingZq::from_str("5  1 0 0 0 1 mod 257").unwrap();
modulus.set_ntt_unchecked(64);

let mut a = NTTPolynomialRingZq::sample_uniform(&modulus);
let b = NTTPolynomialRingZq::sample_uniform(&modulus);

a -= b;

Panics …

• if the moduli are not equal.

impl SubAssign for NTTPolynomialRingZq

fn sub_assign(&mut self, other: NTTPolynomialRingZq)

Documentation at NTTPolynomialRingZq::sub_assign.

impl Eq for NTTPolynomialRingZq

impl StructuralPartialEq for NTTPolynomialRingZq