IntegerPolynomial (Bouncy Castle Library 1.57 API Specification)

java.lang.Object
- org.bouncycastle.pqc.math.ntru.polynomial.IntegerPolynomial

All Implemented Interfaces:

Polynomial

Direct Known Subclasses:

DenseTernaryPolynomial
```
public class IntegerPolynomial
extends java.lang.Object
implements Polynomial
```
A polynomial with int coefficients.
Some methods (like add) change the polynomial, others (like mult) do not but return the result as a new polynomial.

Field Summary

Fields
Modifier and Type Field and Description

int[] coeffs

Fields
Modifier and Type	Field and Description
`int[]`	`coeffs`

Constructor Summary

Constructors
Constructor and Description
`IntegerPolynomial(BigIntPolynomial p)` Constructs a `IntegerPolynomial` from a `BigIntPolynomial`.
`IntegerPolynomial(int N)` Constructs a new polynomial with `N` coefficients initialized to 0.
`IntegerPolynomial(int[] coeffs)` Constructs a new polynomial with a given set of coefficients.

Method Summary

Methods
Modifier and Type	Method and Description
`void`	`add(IntegerPolynomial b)` Adds another polynomial which can have a different number of coefficients.
`void`	`add(IntegerPolynomial b, int modulus)` Adds another polynomial which can have a different number of coefficients, and takes the coefficient values mod `modulus`.
`void`	`center0(int q)` Shifts the values of all coefficients to the interval `[-q/2, q/2]`.
`long`	`centeredNormSq(int q)` Computes the centered euclidean norm of the polynomial.
`void`	`clear()`
`java.lang.Object`	`clone()`
`int`	`count(int value)` Counts the number of coefficients equal to an integer
`void`	`div(int k)` Divides each coefficient by `k` and rounds to the nearest integer.
`void`	`ensurePositive(int modulus)` Adds `modulus` until all coefficients are above 0.
`boolean`	`equals(java.lang.Object obj)`
`boolean`	`equalsOne()` Tests if `p(x) = 1`.
`static IntegerPolynomial`	`fromBinary(byte[] data, int N, int q)` Returns a polynomial with N coefficients between `0` and `q-1`.
`static IntegerPolynomial`	`fromBinary(java.io.InputStream is, int N, int q)` Returns a polynomial with N coefficients between `0` and `q-1`.
`static IntegerPolynomial`	`fromBinary3Sves(byte[] data, int N)` Decodes a byte array to a polynomial with `N` ternary coefficients Ignores any excess bytes.
`static IntegerPolynomial`	`fromBinary3Tight(byte[] b, int N)` Converts a byte array produced by `toBinary3Tight()` to a polynomial.
`static IntegerPolynomial`	`fromBinary3Tight(java.io.InputStream is, int N)` Reads data produced by `toBinary3Tight()` from an input stream and converts it to a polynomial.
`IntegerPolynomial`	`invertF3()` Computes the inverse mod 3.
`IntegerPolynomial`	`invertFq(int q)` Computes the inverse mod `q; q` must be a power of 2.
`void`	`mod(int modulus)` Takes each coefficient modulo `modulus`.
`void`	`mod3()` Takes each coefficient modulo 3 such that all coefficients are ternary.
`void`	`modPositive(int modulus)` Ensures all coefficients are between 0 and `modulus-1`
`BigIntPolynomial`	`mult(BigIntPolynomial poly2)` Multiplies the polynomial by a `BigIntPolynomial`, taking the indices mod N.
`void`	`mult(int factor)` Multiplies each coefficient by a `int`.
`IntegerPolynomial`	`mult(IntegerPolynomial poly2)` Multiplies the polynomial with another, taking the indices mod N
`IntegerPolynomial`	`mult(IntegerPolynomial poly2, int modulus)` Multiplies the polynomial with another, taking the values mod modulus and the indices mod N
`void`	`mult3(int modulus)` Multiplies each coefficient by a 2 and applies a modulus.
`Resultant`	`resultant()` Resultant of this polynomial with `x^n-1` using a probabilistic algorithm.
`ModularResultant`	`resultant(int p)` Resultant of this polynomial with `x^n-1 mod p`.
`Resultant`	`resultantMultiThread()` Multithreaded version of `resultant()`.
`void`	`rotate1()` Multiplication by `X` in `Z[X]/Z[X^n-1]`.
`void`	`sub(IntegerPolynomial b)` Subtracts another polynomial which can have a different number of coefficients.
`void`	`sub(IntegerPolynomial b, int modulus)` Subtracts another polynomial which can have a different number of coefficients, and takes the coefficient values mod `modulus`.
`int`	`sumCoeffs()` Returns the sum of all coefficients, i.e. evaluates the polynomial at 0.
`byte[]`	`toBinary(int q)` Encodes a polynomial whose coefficients are between 0 and q, to binary. q must be a power of 2.
`byte[]`	`toBinary3Sves()` Encodes a polynomial with ternary coefficients to binary.
`byte[]`	`toBinary3Tight()` Converts a polynomial with ternary coefficients to binary.
`IntegerPolynomial`	`toIntegerPolynomial()` Returns a polynomial that is equal to this polynomial (in the sense that `Polynomial.mult(IntegerPolynomial, int)` returns equal `IntegerPolynomial`s).

Methods inherited from class java.lang.Object
finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - coeffs
```
public int[] coeffs
```
- Constructor Detail
  - IntegerPolynomial
```
public IntegerPolynomial(int N)
```
    Constructs a new polynomial with N coefficients initialized to 0.
    
    Parameters:
    N - the number of coefficients
  - IntegerPolynomial
```
public IntegerPolynomial(int[] coeffs)
```
    Constructs a new polynomial with a given set of coefficients.
    
    Parameters:
    coeffs - the coefficients
  - IntegerPolynomial
```
public IntegerPolynomial(BigIntPolynomial p)
```
    Constructs a IntegerPolynomial from a BigIntPolynomial. The two polynomials are independent of each other.
    
    Parameters:
    p - the original polynomial
- Method Detail
  - fromBinary3Sves
```
public static IntegerPolynomial fromBinary3Sves(byte[] data,
                                int N)
```
    Decodes a byte array to a polynomial with N ternary coefficients
    Ignores any excess bytes.
    
    Parameters:
    data - an encoded ternary polynomial
    N - number of coefficients
    
    Returns:
    the decoded polynomial
  - fromBinary3Tight
```
public static IntegerPolynomial fromBinary3Tight(byte[] b,
                                 int N)
```
    Converts a byte array produced by toBinary3Tight() to a polynomial.
    
    Parameters:
    b - a byte array
    N - number of coefficients
    
    Returns:
    the decoded polynomial
  - fromBinary3Tight
```
public static IntegerPolynomial fromBinary3Tight(java.io.InputStream is,
                                 int N)
                                          throws java.io.IOException
```
    Reads data produced by toBinary3Tight() from an input stream and converts it to a polynomial.
    
    Parameters:
    is - an input stream
    N - number of coefficients
    
    Returns:
    the decoded polynomial
    
    Throws:
    
    java.io.IOException
  - fromBinary
```
public static IntegerPolynomial fromBinary(byte[] data,
                           int N,
                           int q)
```
    Returns a polynomial with N coefficients between 0 and q-1.
    q must be a power of 2.
    Ignores any excess bytes.
    
    Parameters:
    data - an encoded ternary polynomial
    N - number of coefficients
    q -
    
    Returns:
    the decoded polynomial
  - fromBinary
```
public static IntegerPolynomial fromBinary(java.io.InputStream is,
                           int N,
                           int q)
                                    throws java.io.IOException
```
    Returns a polynomial with N coefficients between 0 and q-1.
    q must be a power of 2.
    Ignores any excess bytes.
    
    Parameters:
    is - an encoded ternary polynomial
    N - number of coefficients
    q -
    
    Returns:
    the decoded polynomial
    
    Throws:
    
    java.io.IOException
  - toBinary3Sves
```
public byte[] toBinary3Sves()
```
    Encodes a polynomial with ternary coefficients to binary. coeffs[2*i] and coeffs[2*i+1] must not both equal -1 for any integer i, so this method is only safe to use with polynomials produced by fromBinary3Sves().
    
    Returns:
    the encoded polynomial
  - toBinary3Tight
```
public byte[] toBinary3Tight()
```
    Converts a polynomial with ternary coefficients to binary.
    
    Returns:
    the encoded polynomial
  - toBinary
```
public byte[] toBinary(int q)
```
    Encodes a polynomial whose coefficients are between 0 and q, to binary. q must be a power of 2.
    
    Parameters:
    q -
    
    Returns:
    the encoded polynomial
  - mult
```
public IntegerPolynomial mult(IntegerPolynomial poly2,
                     int modulus)
```
    Multiplies the polynomial with another, taking the values mod modulus and the indices mod N
    
    Specified by:
    
    mult in interface Polynomial
    
    Parameters:
    poly2 - a polynomial
    modulus - a modulus to apply
    
    Returns:
    the product of the two polynomials
  - mult
```
public IntegerPolynomial mult(IntegerPolynomial poly2)
```
    Multiplies the polynomial with another, taking the indices mod N
    
    Specified by:
    
    mult in interface Polynomial
    
    Parameters:
    poly2 - a polynomial
    
    Returns:
    the product of the two polynomials
  - mult
```
public BigIntPolynomial mult(BigIntPolynomial poly2)
```
    Description copied from interface: Polynomial
    
    Multiplies the polynomial by a BigIntPolynomial, taking the indices mod N. Does not change this polynomial but returns the result as a new polynomial.
    Both polynomials must have the same number of coefficients.
    
    Specified by:
    
    mult in interface Polynomial
    
    Parameters:
    poly2 - the polynomial to multiply by
    
    Returns:
    a new polynomial
  - invertFq
```
public IntegerPolynomial invertFq(int q)
```
    Computes the inverse mod q; q must be a power of 2.
    Returns null if the polynomial is not invertible.
    
    Parameters:
    q - the modulus
    
    Returns:
    a new polynomial
  - invertF3
```
public IntegerPolynomial invertF3()
```
    Computes the inverse mod 3. Returns null if the polynomial is not invertible.
    
    Returns:
    a new polynomial
  - resultant
```
public Resultant resultant()
```
    Resultant of this polynomial with x^n-1 using a probabilistic algorithm.
    Unlike EESS, this implementation does not compute all resultants modulo primes such that their product exceeds the maximum possible resultant, but rather stops when NUM_EQUAL_RESULTANTS consecutive modular resultants are equal.
    This means the return value may be incorrect. Experiments show this happens in about 1 out of 100 cases when N=439 and NUM_EQUAL_RESULTANTS=2, so the likelyhood of leaving the loop too early is (1/100)^(NUM_EQUAL_RESULTANTS-1).
    Because of the above, callers must verify the output and try a different polynomial if necessary.
    
    Returns:
    (rho, res) satisfying res = rho*this + t*(x^n-1) for some integer t.
  - resultantMultiThread
```
public Resultant resultantMultiThread()
```
    Multithreaded version of resultant().
    
    Returns:
    (rho, res) satisfying res = rho*this + t*(x^n-1) for some integer t.
  - resultant
```
public ModularResultant resultant(int p)
```
    Resultant of this polynomial with x^n-1 mod p.
    
    Returns:
    (rho, res) satisfying res = rho*this + t*(x^n-1) mod p for some integer t.
  - add
```
public void add(IntegerPolynomial b,
       int modulus)
```
    Adds another polynomial which can have a different number of coefficients, and takes the coefficient values mod modulus.
    
    Parameters:
    b - another polynomial
  - add
```
public void add(IntegerPolynomial b)
```
    Adds another polynomial which can have a different number of coefficients.
    
    Parameters:
    b - another polynomial
  - sub
```
public void sub(IntegerPolynomial b,
       int modulus)
```
    Subtracts another polynomial which can have a different number of coefficients, and takes the coefficient values mod modulus.
    
    Parameters:
    b - another polynomial
  - sub
```
public void sub(IntegerPolynomial b)
```
    Subtracts another polynomial which can have a different number of coefficients.
    
    Parameters:
    b - another polynomial
  - mult
```
public void mult(int factor)
```
    Multiplies each coefficient by a int. Does not return a new polynomial but modifies this polynomial.
    
    Parameters:
    factor -
  - mult3
```
public void mult3(int modulus)
```
    Multiplies each coefficient by a 2 and applies a modulus. Does not return a new polynomial but modifies this polynomial.
    
    Parameters:
    modulus - a modulus
  - div
```
public void div(int k)
```
    Divides each coefficient by k and rounds to the nearest integer. Does not return a new polynomial but modifies this polynomial.
    
    Parameters:
    k - the divisor
  - mod3
```
public void mod3()
```
    Takes each coefficient modulo 3 such that all coefficients are ternary.
  - modPositive
```
public void modPositive(int modulus)
```
    Ensures all coefficients are between 0 and modulus-1
    
    Parameters:
    modulus - a modulus
  - mod
```
public void mod(int modulus)
```
    Takes each coefficient modulo modulus.
  - ensurePositive
```
public void ensurePositive(int modulus)
```
    Adds modulus until all coefficients are above 0.
    
    Parameters:
    modulus - a modulus
  - centeredNormSq
```
public long centeredNormSq(int q)
```
    Computes the centered euclidean norm of the polynomial.
    
    Parameters:
    q - a modulus
    
    Returns:
    the centered norm
  - center0
```
public void center0(int q)
```
    Shifts the values of all coefficients to the interval [-q/2, q/2].
    
    Parameters:
    q - a modulus
  - sumCoeffs
```
public int sumCoeffs()
```
    Returns the sum of all coefficients, i.e. evaluates the polynomial at 0.
    
    Returns:
    the sum of all coefficients
  - equalsOne
```
public boolean equalsOne()
```
    Tests if p(x) = 1.
    
    Returns:
    true iff all coefficients are equal to zero, except for the lowest coefficient which must equal 1
  - count
```
public int count(int value)
```
    Counts the number of coefficients equal to an integer
    
    Parameters:
    value - an integer
    
    Returns:
    the number of coefficients equal to value
  - rotate1
```
public void rotate1()
```
    Multiplication by X in Z[X]/Z[X^n-1].
  - clear
```
public void clear()
```
  - toIntegerPolynomial
```
public IntegerPolynomial toIntegerPolynomial()
```
    Description copied from interface: Polynomial
    
    Returns a polynomial that is equal to this polynomial (in the sense that Polynomial.mult(IntegerPolynomial, int) returns equal IntegerPolynomials). The new polynomial is guaranteed to be independent of the original.
    
    Specified by:
    
    toIntegerPolynomial in interface Polynomial
    
    Returns:
    a new IntegerPolynomial.
  - clone
```
public java.lang.Object clone()
```
    Overrides:
    
    clone in class java.lang.Object
  - equals
```
public boolean equals(java.lang.Object obj)
```
    Overrides:
    
    equals in class java.lang.Object

Class IntegerPolynomial

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

coeffs

Constructor Detail

IntegerPolynomial

IntegerPolynomial

IntegerPolynomial

Method Detail

fromBinary3Sves

fromBinary3Tight

fromBinary3Tight

fromBinary

fromBinary

toBinary3Sves

toBinary3Tight

toBinary

mult

mult

mult

invertFq

invertF3

resultant

resultantMultiThread

resultant

add

add

sub

sub

mult

mult3

div

mod3

modPositive

mod

ensurePositive

centeredNormSq

center0

sumCoeffs

equalsOne

count

rotate1

clear

toIntegerPolynomial

clone

equals