Struct MatNTTPolynomialRingZq 

pub struct MatNTTPolynomialRingZq {
    pub matrix: Vec<Z>,
    pub nr_rows: usize,
    pub nr_columns: usize,
    pub modulus: ModulusPolynomialRingZq,
}

MatNTTPolynomialRingZq contains the NTT representation of a matrix over polynomials with respect to a NTTBasisPolynomialRingZq that itself isn’t aware of.

Any polynomial in NTT representation in row i and column j can be accessed via matrix[j * nr_columns + i].

Attributes

• matrix: holds the matrix entries with its coefficients
• nr_rows: the number of rows of the matrix
• nr_columns: the number of columns of the matrix
• 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, MatPolynomialRingZq, MatNTTPolynomialRingZq, ModulusPolynomialRingZq};
use std::str::FromStr;

// setup modulus with ability to transform to NTT
let mut modulus = ModulusPolynomialRingZq::from_str("5  1 0 0 0 1 mod 257").unwrap();
modulus.set_ntt_unchecked(64);

// sample random matrix
let mat_rnd = MatNTTPolynomialRingZq::sample_uniform(2, 2, &modulus);
// or instantiate matrix from MatPolynomialRingZq
let mat_poly_ring = MatPolynomialRingZq::identity(2, 2, &modulus);
let mat_ntt_poly_ring = MatNTTPolynomialRingZq::from(&mat_poly_ring);

// multiply, add and subtract objects
let mut tmp_mat_ntt = mat_ntt_poly_ring * &mat_rnd;
tmp_mat_ntt += &mat_rnd;
tmp_mat_ntt -= &mat_rnd;

// Return to MatPolynomialRingZq
let res = tmp_mat_ntt.inv_ntt();

Fields

matrix: Vec<Z>

nr_rows: usize

nr_columns: usize

modulus: ModulusPolynomialRingZq

Implementations

impl MatNTTPolynomialRingZq

pub fn inv_ntt(self) -> MatPolynomialRingZq

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

Returns a new MatPolynomialRingZq with the entries from self.

Examples

use qfall_math::integer_mod_q::{MatPolynomialRingZq, MatNTTPolynomialRingZq, 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 ntt_mat = MatNTTPolynomialRingZq::sample_uniform(1, 1, &modulus);

let poly_ring_mat = ntt_mat.inv_ntt();

Panics …

• if the NTTBasisPolynomialRingZq in modulus is not set.

impl MatNTTPolynomialRingZq

pub fn get_mod(&self) -> ModulusPolynomialRingZq

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

Examples

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

let modulus = ModulusPolynomialRingZq::from_str("5  1 0 0 0 1 mod 17").unwrap();
let matrix = MatNTTPolynomialRingZq::sample_uniform(2, 2, &modulus);

let modulus = matrix.get_mod();

pub fn get_entry(&self, row: usize, column: usize) -> &[Z]

Returns the slice of matrix corresponding to the entry in row row and column column.

Parameters:

• row: defines the row where the entry to fetch is located
• column: defines the column where the entry to fetch is located

Returns a slice &[Z] containing the requested entry.

Examples

use qfall_math::integer_mod_q::{MatNTTPolynomialRingZq, 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 matrix = MatNTTPolynomialRingZq::sample_uniform(2, 2, &modulus);
let entry = matrix.get_entry(0, 0);

assert_eq!(4, entry.len());

Panics …

• if row >= self.get_num_rows() or column >= self.get_num_columns().

impl MatNTTPolynomialRingZq

pub fn sample_uniform( nr_rows: usize, nr_columns: usize, modulus: &ModulusPolynomialRingZq, ) -> Self

Generates a MatNTTPolynomialRingZq instance with maximum degree modulus_degree 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:

• num_rows: defines the number of rows of the matrix
• num_columns: defines the number of columns of the matrix
• 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 MatNTTPolynomialRingZq instance of length modulus_degree with entries chosen uniform at random in [0, modulus).

Examples

use qfall_math::integer_mod_q::{MatNTTPolynomialRingZq, 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 = MatNTTPolynomialRingZq::sample_uniform(3, 2, &modulus);

Panics …

• if nr_rows or nr_columns is 0.

Trait Implementations

impl Add for &MatNTTPolynomialRingZq

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::{MatNTTPolynomialRingZq, ModulusPolynomialRingZq};
use crate::qfall_math::traits::SetCoefficient;
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 = MatNTTPolynomialRingZq::sample_uniform(2, 3, &modulus);
let b = MatNTTPolynomialRingZq::sample_uniform(2, 3, &modulus);

let c = a + b;

Panics …

• if the number of rows of self and other or their number of columns is not equal.
• if their moduli do not match.

type Output = MatNTTPolynomialRingZq

The resulting type after applying the + operator.

impl AddAssign<&MatNTTPolynomialRingZq> for MatNTTPolynomialRingZq

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::{MatNTTPolynomialRingZq, ModulusPolynomialRingZq};
use crate::qfall_math::traits::SetCoefficient;
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 = MatNTTPolynomialRingZq::sample_uniform(2, 3, &modulus);
let b = MatNTTPolynomialRingZq::sample_uniform(2, 3, &modulus);

a += b;

Panics …

• if the number of rows of self and other or their number of columns is not equal.
• if their moduli do not match.

impl AddAssign for MatNTTPolynomialRingZq

fn add_assign(&mut self, other: MatNTTPolynomialRingZq)

Documentation at MatNTTPolynomialRingZq::add_assign.

impl Clone for MatNTTPolynomialRingZq

fn clone(&self) -> MatNTTPolynomialRingZq

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl CompareBase<&MatNTTPolynomialRingZq> for MatNTTPolynomialRingZq

fn compare_base(&self, other: &&MatNTTPolynomialRingZq) -> 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: &&MatNTTPolynomialRingZq, ) -> 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<&MatPolyOverZ> for MatNTTPolynomialRingZq

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<&MatPolynomialRingZq> for MatNTTPolynomialRingZq

fn compare_base(&self, other: &&MatPolynomialRingZq) -> 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: &&MatPolynomialRingZq, ) -> 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<&MatZ> for MatNTTPolynomialRingZq

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<&MatZq> for MatNTTPolynomialRingZq

fn compare_base(&self, other: &&MatZq) -> 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: &&MatZq) -> 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 MatNTTPolynomialRingZq

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 MatNTTPolynomialRingZq

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 MatNTTPolynomialRingZq

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 MatNTTPolynomialRingZq

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 MatNTTPolynomialRingZq

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<MatPolyOverZ> for MatNTTPolynomialRingZq

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<MatPolynomialRingZq> for MatNTTPolynomialRingZq

fn compare_base(&self, other: &MatPolynomialRingZq) -> 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: &MatPolynomialRingZq, ) -> 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<MatZ> for MatNTTPolynomialRingZq

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<MatZq> for MatNTTPolynomialRingZq

fn compare_base(&self, other: &MatZq) -> 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: &MatZq) -> 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 MatNTTPolynomialRingZq

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 MatNTTPolynomialRingZq

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 MatNTTPolynomialRingZq

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 MatNTTPolynomialRingZq

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 MatNTTPolynomialRingZq

fn compare_base(&self, other: &MatNTTPolynomialRingZq) -> 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: &MatNTTPolynomialRingZq, ) -> 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 MatNTTPolynomialRingZq

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for MatNTTPolynomialRingZq

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for MatNTTPolynomialRingZq

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

Formats the value using the given formatter.

impl From<&MatPolynomialRingZq> for MatNTTPolynomialRingZq

fn from(matrix: &MatPolynomialRingZq) -> Self

Computes the NTT representation of matrix.

Parameters:

• matrix: the matrix that’s going to be represented in NTT format.

Returns the NTT representation as a MatNTTPolynomialRingZq of matrix.

Examples

use qfall_math::integer_mod_q::{MatNTTPolynomialRingZq, MatPolynomialRingZq, 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 mat_poly_ring = MatPolynomialRingZq::sample_uniform(2, 3, &modulus);

let mat_ntt_poly_ring = MatNTTPolynomialRingZq::from(&mat_poly_ring);

Panics …

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

impl From<MatNTTPolynomialRingZq> for MatPolynomialRingZq

fn from(matrix: MatNTTPolynomialRingZq) -> Self

Creates a polynomial ring matrix of type MatPolynomialRingZq from the corresponding MatNTTPolynomialRingZq.

Parameters:

• matrix: the polynomial matrix defining each entry.

Returns a new MatPolynomialRingZq with the entries from matrix.

Examples

use qfall_math::integer_mod_q::{MatPolynomialRingZq, MatNTTPolynomialRingZq, 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 ntt_mat = MatNTTPolynomialRingZq::sample_uniform(1, 1, &modulus);

let poly_ring_mat = MatPolynomialRingZq::from(ntt_mat);

Panics …

• if the NTTBasisPolynomialRingZq in modulus is not set.

impl MatrixDimensions for MatNTTPolynomialRingZq

fn get_num_rows(&self) -> i64

Returns the number of rows of the matrix as an i64.

Examples

use qfall_math::{integer_mod_q::{MatNTTPolynomialRingZq, ModulusPolynomialRingZq}, traits::MatrixDimensions};
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 matrix = MatNTTPolynomialRingZq::sample_uniform(3, 2, &modulus);
let nr_rows = matrix.get_num_rows();

fn get_num_columns(&self) -> i64

Returns the number of columns of the matrix as an i64.

Examples

use qfall_math::{integer_mod_q::{MatNTTPolynomialRingZq, ModulusPolynomialRingZq}, traits::MatrixDimensions};
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 matrix = MatNTTPolynomialRingZq::sample_uniform(3, 2, &modulus);
let nr_columns = matrix.get_num_columns();

impl Mul for &MatNTTPolynomialRingZq

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

Multiplies self with other.

Paramters:

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

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

Example

use qfall_math::integer_mod_q::{MatNTTPolynomialRingZq, ModulusPolynomialRingZq};
use crate::qfall_math::traits::SetCoefficient;
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 = MatNTTPolynomialRingZq::sample_uniform(2, 3, &modulus);
let b = MatNTTPolynomialRingZq::sample_uniform(3, 4, &modulus);

let c = a * b;

Panics …

• if the number of rows of self and the number of columns of other does not match up.
• if their moduli do not match.

type Output = MatNTTPolynomialRingZq

The resulting type after applying the * operator.

impl PartialEq for MatNTTPolynomialRingZq

fn eq(&self, other: &MatNTTPolynomialRingZq) -> 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 MatNTTPolynomialRingZq

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 &MatNTTPolynomialRingZq

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::{MatNTTPolynomialRingZq, 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 = MatNTTPolynomialRingZq::sample_uniform(2, 3, &modulus);
let b = MatNTTPolynomialRingZq::sample_uniform(2, 3, &modulus);

let c = a - b;

Panics …

• if the number of rows of self and other or their number of columns is not equal.
• if their moduli do not match.

type Output = MatNTTPolynomialRingZq

The resulting type after applying the - operator.

impl SubAssign<&MatNTTPolynomialRingZq> for MatNTTPolynomialRingZq

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::{MatNTTPolynomialRingZq, 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 = MatNTTPolynomialRingZq::sample_uniform(2, 3, &modulus);
let b = MatNTTPolynomialRingZq::sample_uniform(2, 3, &modulus);

a -= b;

Panics …

• if the number of rows of self and other or their number of columns is not equal.
• if their moduli do not match.

impl SubAssign for MatNTTPolynomialRingZq

fn sub_assign(&mut self, other: MatNTTPolynomialRingZq)

Documentation at MatNTTPolynomialRingZq::sub_assign.

impl Eq for MatNTTPolynomialRingZq

impl StructuralPartialEq for MatNTTPolynomialRingZq