Bouncy Castle Cryptography Library 1.80 · org.bouncycastle.pqc.legacy.math.ntru.polynomial.IntegerPolynomial

Modifier and Type	Class and Description
private static class	IntegerPolynomial.CombineTask Calls {@link ModularResultant#combineRho(ModularResultant, ModularResultant)
private class	IntegerPolynomial.ModResultantTask Calls {@link IntegerPolynomial#resultant(int)
private static class	IntegerPolynomial.PrimeGenerator

Modifier and Type	Field and Description
private static final List<E>	BIGINT_PRIMES
public int[]	coeffs
private static final int	NUM_EQUAL_RESULTANTS
private static final int[]	PRIMES Prime numbers > 4500 for resultant computation.

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

Method Summary

Modifier and Type	Method and Description
public void	add(IntegerPolynomial another polynomial b, int modulus) Adds another polynomial which can have a different number of coefficients, and takes the coefficient values mod `modulus`.
public void	add(IntegerPolynomial another polynomial b) Adds another polynomial which can have a different number of coefficients.
public void	center0(int a modulus q) Shifts the values of all coefficients to the interval `[-q/2, q/2]`.
public long	Returns: the centered norm centeredNormSq(int a modulus q) Computes the centered euclidean norm of the polynomial.
public void	clear()
public Object	clone() Overrides java.lang.Object.clone. Creates and returns a copy of this object.
public int	Returns: the number of coefficients equal to `value` count(int an integer value) Counts the number of coefficients equal to an integer
pack-priv int	Returns: the degree degree() Returns the degree of the polynomial
public void	div(int the divisor k) Divides each coefficient by `k` and rounds to the nearest integer.
public void	ensurePositive(int a modulus modulus) Adds `modulus` until all coefficients are above 0.
public boolean	equals(Object the reference object with which to compare. obj) Overrides java.lang.Object.equals. Indicates whether some other object is "equal to" this one.
private boolean	Returns: true iff all coefficients are equal to zero, except for the lowest coefficient which must equal 1 or -1 equalsAbsOne() Tests if `\|p(x)\| = 1`.
public boolean	Returns: true iff all coefficients are equal to zero, except for the lowest coefficient which must equal 1 equalsOne() Tests if `p(x) = 1`.
private boolean	Returns: true iff all coefficients are zeros equalsZero() Tests if `p(x) = 0`.
public static IntegerPolynomial	Returns: the decoded polynomial fromBinary(byte[] an encoded ternary polynomial data, int number of coefficients N, int q) Returns a polynomial with N coefficients between `0` and `q-1`.
public static IntegerPolynomial	Returns: the decoded polynomial fromBinary(InputStream an encoded ternary polynomial is, int number of coefficients N, int q) Returns a polynomial with N coefficients between `0` and `q-1`.
public static IntegerPolynomial	Returns: the decoded polynomial fromBinary3Sves(byte[] an encoded ternary polynomial data, int number of coefficients N) Decodes a byte array to a polynomial with `N` ternary coefficients Ignores any excess bytes.
public static IntegerPolynomial	Returns: the decoded polynomial fromBinary3Tight(byte[] a byte array b, int number of coefficients N) Converts a byte array produced by `toBinary3Tight()` to a polynomial.
public static IntegerPolynomial	Returns: the decoded polynomial fromBinary3Tight(InputStream an input stream is, int number of coefficients N) Reads data produced by `toBinary3Tight()` from an input stream and converts it to a polynomial.
public IntegerPolynomial	Returns: a new polynomial invertF3() Computes the inverse mod 3.
public IntegerPolynomial	Returns: a new polynomial invertFq(int the modulus q) Computes the inverse mod `q; q` must be a power of 2.
public void	mod(int modulus) Takes each coefficient modulo `modulus`.
private IntegerPolynomial	Returns: The inverse of this polynomial mod q mod2ToModq(IntegerPolynomial Fq, int q) Computes the inverse mod q from the inverse mod 2
public void	mod3() Takes each coefficient modulo 3 such that all coefficients are ternary.
pack-priv void	modCenter(int modulus) Reduces all coefficients to the interval [-modulus/2, modulus/2)
public void	modPositive(int a modulus modulus) Ensures all coefficients are between 0 and `modulus-1`
public IntegerPolynomial	mult(IntegerPolynomial a polynomial poly2, int a modulus to apply modulus) Implements org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult. Multiplies the polynomial with another, taking the values mod modulus and the indices mod N
public IntegerPolynomial	mult(IntegerPolynomial a polynomial poly2) Implements org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult. Multiplies the polynomial with another, taking the indices mod N
public BigIntPolynomial	mult(BigIntPolynomial the polynomial to multiply by poly2) Implements org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult. Multiplies the polynomial by a `BigIntPolynomial`, taking the indices mod N.
public void	mult(int factor) Multiplies each coefficient by a `int`.
private void	mult2(int a modulus modulus) Multiplies each coefficient by a 2 and applies a modulus.
public void	mult3(int a modulus modulus) Multiplies each coefficient by a 2 and applies a modulus.
private IntegerPolynomial	multRecursive(IntegerPolynomial poly2) Karazuba multiplication
private void	multShiftSub(IntegerPolynomial b, int c, int k, int p) Computes `this-bc(x^k) mod p` and stores the result in this polynomial.
public Resultant	Returns: `(rho, res)` satisfying `res = rhothis + t(x^n-1)` for some integer `t`. resultant() Resultant of this polynomial with `x^n-1` using a probabilistic algorithm.
public ModularResultant	Returns: `(rho, res)` satisfying `res = rhothis + t(x^n-1) mod p` for some integer `t`. resultant(int p) Resultant of this polynomial with `x^n-1 mod p`.
public Resultant	Returns: `(rho, res)` satisfying `res = rhothis + t(x^n-1)` for some integer `t`. resultantMultiThread() Multithreaded version of `resultant()`.
public void	rotate1() Multiplication by `X` in `Z[X]/Z[X^n-1]`.
pack-priv void	shiftGap(int a modulus q) Shifts all coefficients so the largest gap is centered around `-q/2`.
private void	sort(int[] ints)
private BigInteger	Returns: the sum of squares squareSum() Adds the squares of all coefficients.
public void	sub(IntegerPolynomial another polynomial b, int modulus) Subtracts another polynomial which can have a different number of coefficients, and takes the coefficient values mod `modulus`.
public void	sub(IntegerPolynomial another polynomial b) Subtracts another polynomial which can have a different number of coefficients.
pack-priv void	sub(int b) Subtracts a `int` from each coefficient.
public int	Returns: the sum of all coefficients sumCoeffs() Returns the sum of all coefficients, i.e. evaluates the polynomial at 0.
public byte[]	Returns: the encoded polynomial toBinary(int q) Encodes a polynomial whose coefficients are between 0 and q, to binary.
public byte[]	Returns: the encoded polynomial toBinary3Sves() Encodes a polynomial with ternary coefficients to binary.
public byte[]	Returns: the encoded polynomial toBinary3Tight() Converts a polynomial with ternary coefficients to binary.
public IntegerPolynomial	toIntegerPolynomial() Implements org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.toIntegerPolynomial. Returns a polynomial that is equal to this polynomial (in the sense that `mult(IntegerPolynomial, int)` returns equal `IntegerPolynomial`s).

Inherited from java.lang.Object:: finalize getClass hashCode notify notifyAll toString wait wait wait

BIGINT_PRIMES	back to summary
private static final List<E> BIGINT_PRIMES

coeffs	back to summary
public int[] coeffs

NUM_EQUAL_RESULTANTS	back to summary
private static final int NUM_EQUAL_RESULTANTS

PRIMES	back to summary
private static final int[] PRIMES Prime numbers > 4500 for resultant computation. Starting them below ~4400 causes incorrect results occasionally. Fortunately, 4500 is about the optimum number for performance. This array contains enough prime numbers so primes never have to be computed on-line for any standard `org.bouncycastle.pqc.legacy.crypto.ntru.NTRUSigningParameters`.

IntegerPolynomial	back to summary
public IntegerPolynomial(int N) Constructs a new polynomial with `N` coefficients initialized to 0. Parameters N:int the number of coefficients

IntegerPolynomial	back to summary
public IntegerPolynomial(int[] coeffs) Constructs a new polynomial with a given set of coefficients. Parameters coeffs:int[] the coefficients

IntegerPolynomial	back to summary
public IntegerPolynomial(BigIntPolynomial p) Constructs a `IntegerPolynomial` from a `BigIntPolynomial`. The two polynomials are independent of each other. Parameters p:BigIntPolynomial the original polynomial

Method Detail

add back to summary

add	back to summary
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:IntegerPolynomial another polynomial

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:IntegerPolynomial: another polynomial

add	back to summary
public void add(IntegerPolynomial b) Adds another polynomial which can have a different number of coefficients. Parameters b:IntegerPolynomial another polynomial

add

back to summary

public void add(IntegerPolynomial b)

Adds another polynomial which can have a different number of coefficients.

Parameters

b:IntegerPolynomial: another polynomial

center0 back to summary

center0	back to summary
public void center0(int q) Shifts the values of all coefficients to the interval `[-q/2, q/2]`. Parameters q:int a modulus

public void center0(int q)

Shifts the values of all coefficients to the interval [-q/2, q/2].

Parameters

q:int: a modulus

centeredNormSq	back to summary
public long centeredNormSq(int q) Computes the centered euclidean norm of the polynomial. Parameters q:int a modulus Returns:long the centered norm

centeredNormSq

back to summary

public long centeredNormSq(int q)

Computes the centered euclidean norm of the polynomial.

Parameters

q:int: a modulus

Returns:long

the centered norm

clear	back to summary
public void clear()

clone back to summary

clone	back to summary
public Object clone() Overrides java.lang.Object.clone. Doc from java.lang.Object.clone. Creates and returns a copy of this object. The precise meaning of "copy" may depend on the class of the object. The general intent is that, for any object `x`, the expression: x.clone() != x will be true, and that the expression: x.clone().getClass() == x.getClass() will be `true`, but these are not absolute requirements. While it is typically the case that: x.clone().equals(x) will be `true`, this is not an absolute requirement. By convention, the returned object should be obtained by calling `super.clone`. If a class and all of its superclasses (except `Object`) obey this convention, it will be the case that `x.clone().getClass() == x.getClass()`. By convention, the object returned by this method should be independent of this object (which is being cloned). To achieve this independence, it may be necessary to modify one or more fields of the object returned by `super.clone` before returning it. Typically, this means copying any mutable objects that comprise the internal "deep structure" of the object being cloned and replacing the references to these objects with references to the copies. If a class contains only primitive fields or references to immutable objects, then it is usually the case that no fields in the object returned by `super.clone` need to be modified. Returns:Object a clone of this instance.

public Object clone()

Overrides java.lang.Object.clone.

Doc from java.lang.Object.clone.

Creates and returns a copy of this object. The precise meaning of "copy" may depend on the class of the object. The general intent is that, for any object x, the expression:

x.clone() != x

will be true, and that the expression:

x.clone().getClass() == x.getClass()

will be true, but these are not absolute requirements. While it is typically the case that:

x.clone().equals(x)

will be true, this is not an absolute requirement.

By convention, the returned object should be obtained by calling super.clone. If a class and all of its superclasses (except Object) obey this convention, it will be the case that x.clone().getClass() == x.getClass().

By convention, the object returned by this method should be independent of this object (which is being cloned). To achieve this independence, it may be necessary to modify one or more fields of the object returned by super.clone before returning it. Typically, this means copying any mutable objects that comprise the internal "deep structure" of the object being cloned and replacing the references to these objects with references to the copies. If a class contains only primitive fields or references to immutable objects, then it is usually the case that no fields in the object returned by super.clone need to be modified.

Returns:Object: a clone of this instance.

count back to summary

count	back to summary
public int count(int value) Counts the number of coefficients equal to an integer Parameters value:int an integer Returns:int the number of coefficients equal to `value`

public int count(int value)

Counts the number of coefficients equal to an integer

Parameters

value:int: an integer

Returns:int

the number of coefficients equal to value

degree	back to summary
pack-priv int degree() Returns the degree of the polynomial Returns:int the degree

degree

back to summary

pack-priv int degree()

Returns the degree of the polynomial

Returns:int: the degree

div back to summary

div	back to summary
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:int the divisor

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:int: the divisor

ensurePositive back to summary

ensurePositive	back to summary
public void ensurePositive(int modulus) Adds `modulus` until all coefficients are above 0. Parameters modulus:int a modulus

public void ensurePositive(int modulus)

Adds modulus until all coefficients are above 0.

Parameters

modulus:int: a modulus

equals back to summary

equals	back to summary
public boolean equals(Object obj) Overrides java.lang.Object.equals. Doc from java.lang.Object.equals. Indicates whether some other object is "equal to" this one. The `equals` method implements an equivalence relation on non-null object references: It is reflexive: for any non-null reference value `x`, `x.equals(x)` should return `true`. It is symmetric: for any non-null reference values `x` and `y`, `x.equals(y)` should return `true` if and only if `y.equals(x)` returns `true`. It is transitive: for any non-null reference values `x`, `y`, and `z`, if `x.equals(y)` returns `true` and `y.equals(z)` returns `true`, then `x.equals(z)` should return `true`. It is consistent: for any non-null reference values `x` and `y`, multiple invocations of `x.equals(y)` consistently return `true` or consistently return `false`, provided no information used in `equals` comparisons on the objects is modified. For any non-null reference value `x`, `x.equals(null)` should return `false`. An equivalence relation partitions the elements it operates on into equivalence classes; all the members of an equivalence class are equal to each other. Members of an equivalence class are substitutable for each other, at least for some purposes. Parameters obj:Object the reference object with which to compare. Returns:boolean `true` if this object is the same as the obj argument; `false` otherwise.

public boolean equals(Object obj)

Overrides java.lang.Object.equals.

Doc from java.lang.Object.equals.

Indicates whether some other object is "equal to" this one.

The equals method implements an equivalence relation on non-null object references:

It is reflexive: for any non-null reference value x, x.equals(x) should return true.
It is symmetric: for any non-null reference values x and y, x.equals(y) should return true if and only if y.equals(x) returns true.
It is transitive: for any non-null reference values x, y, and z, if x.equals(y) returns true and y.equals(z) returns true, then x.equals(z) should return true.
It is consistent: for any non-null reference values x and y, multiple invocations of x.equals(y) consistently return true or consistently return false, provided no information used in equals comparisons on the objects is modified.
For any non-null reference value x, x.equals(null) should return false.

An equivalence relation partitions the elements it operates on into equivalence classes; all the members of an equivalence class are equal to each other. Members of an equivalence class are substitutable for each other, at least for some purposes.

Parameters

obj:Object: the reference object with which to compare.

Returns:boolean

true if this object is the same as the obj argument; false otherwise.

equalsAbsOne back to summary

equalsAbsOne	back to summary
private boolean equalsAbsOne() Tests if `\|p(x)\| = 1`. Returns:boolean true iff all coefficients are equal to zero, except for the lowest coefficient which must equal 1 or -1

private boolean equalsAbsOne()

Tests if |p(x)| = 1.

Returns:boolean: true iff all coefficients are equal to zero, except for the lowest coefficient which must equal 1 or -1

equalsOne back to summary

equalsOne	back to summary
public boolean equalsOne() Tests if `p(x) = 1`. Returns:boolean true iff all coefficients are equal to zero, except for the lowest coefficient which must equal 1

public boolean equalsOne()

Tests if p(x) = 1.

Returns:boolean: true iff all coefficients are equal to zero, except for the lowest coefficient which must equal 1

equalsZero back to summary

equalsZero	back to summary
private boolean equalsZero() Tests if `p(x) = 0`. Returns:boolean true iff all coefficients are zeros

private boolean equalsZero()

Tests if p(x) = 0.

Returns:boolean: true iff all coefficients are zeros

fromBinary back to summary

fromBinary	back to summary
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:byte[] an encoded ternary polynomial N:int number of coefficients Returns:IntegerPolynomial the decoded polynomial

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:byte[]: an encoded ternary polynomial
N:int: number of coefficients

Returns:IntegerPolynomial

the decoded polynomial

fromBinary back to summary

fromBinary	back to summary
public static IntegerPolynomial fromBinary(InputStream is, int N, int q) throws 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:InputStream an encoded ternary polynomial N:int number of coefficients Returns:IntegerPolynomial the decoded polynomial

public static IntegerPolynomial fromBinary(InputStream is, int N, int q) throws 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:InputStream: an encoded ternary polynomial
N:int: number of coefficients

Returns:IntegerPolynomial

the decoded polynomial

fromBinary3Sves back to summary

fromBinary3Sves	back to summary
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:byte[] an encoded ternary polynomial N:int number of coefficients Returns:IntegerPolynomial the decoded polynomial

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:byte[]: an encoded ternary polynomial
N:int: number of coefficients

Returns:IntegerPolynomial

the decoded polynomial

fromBinary3Tight back to summary

fromBinary3Tight	back to summary
public static IntegerPolynomial fromBinary3Tight(byte[] b, int N) Converts a byte array produced by `toBinary3Tight()` to a polynomial. Parameters b:byte[] a byte array N:int number of coefficients Returns:IntegerPolynomial the decoded polynomial

public static IntegerPolynomial fromBinary3Tight(byte[] b, int N)

Converts a byte array produced by toBinary3Tight() to a polynomial.

Parameters

b:byte[]: a byte array
N:int: number of coefficients

Returns:IntegerPolynomial

the decoded polynomial

fromBinary3Tight back to summary

fromBinary3Tight	back to summary
public static IntegerPolynomial fromBinary3Tight(InputStream is, int N) throws IOException Reads data produced by `toBinary3Tight()` from an input stream and converts it to a polynomial. Parameters is:InputStream an input stream N:int number of coefficients Returns:IntegerPolynomial the decoded polynomial

public static IntegerPolynomial fromBinary3Tight(InputStream is, int N) throws IOException

Reads data produced by toBinary3Tight() from an input stream and converts it to a polynomial.

Parameters

is:InputStream: an input stream
N:int: number of coefficients

Returns:IntegerPolynomial

the decoded polynomial

invertF3 back to summary

invertF3	back to summary
public IntegerPolynomial invertF3() Computes the inverse mod 3. Returns `null` if the polynomial is not invertible. Returns:IntegerPolynomial a new polynomial

public IntegerPolynomial invertF3()

Computes the inverse mod 3. Returns null if the polynomial is not invertible.

Returns:IntegerPolynomial: a new polynomial

invertFq back to summary

invertFq	back to summary
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:int the modulus Returns:IntegerPolynomial a new polynomial

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:int: the modulus

Returns:IntegerPolynomial

a new polynomial

mod	back to summary
public void mod(int modulus) Takes each coefficient modulo `modulus`.

mod2ToModq	back to summary
private IntegerPolynomial mod2ToModq(IntegerPolynomial Fq, int q) Computes the inverse mod q from the inverse mod 2 Returns:IntegerPolynomial The inverse of this polynomial mod q

mod2ToModq

back to summary

private IntegerPolynomial mod2ToModq(IntegerPolynomial Fq, int q)

Computes the inverse mod q from the inverse mod 2

Returns:IntegerPolynomial: The inverse of this polynomial mod q

mod3	back to summary
public void mod3() Takes each coefficient modulo 3 such that all coefficients are ternary.

modCenter	back to summary
pack-priv void modCenter(int modulus) Reduces all coefficients to the interval [-modulus/2, modulus/2)

modPositive back to summary

modPositive	back to summary
public void modPositive(int modulus) Ensures all coefficients are between 0 and `modulus-1` Parameters modulus:int a modulus

public void modPositive(int modulus)

Ensures all coefficients are between 0 and modulus-1

Parameters

modulus:int: a modulus

mult	back to summary
public IntegerPolynomial mult(IntegerPolynomial poly2, int modulus) Implements org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult. Multiplies the polynomial with another, taking the values mod modulus and the indices mod N Parameters poly2:IntegerPolynomial Doc from org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult. a polynomial modulus:int Doc from org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult. a modulus to apply Returns:IntegerPolynomial Doc from org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult. the product of the two polynomials

mult

back to summary

public IntegerPolynomial mult(IntegerPolynomial poly2, int modulus)

Implements org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult.

Multiplies the polynomial with another, taking the values mod modulus and the indices mod N

Parameters

poly2:IntegerPolynomial

Doc from org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult.

a polynomial

modulus:int

Doc from org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult.

a modulus to apply

Returns:IntegerPolynomial

Doc from org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult.

the product of the two polynomials

mult	back to summary
public IntegerPolynomial mult(IntegerPolynomial poly2) Implements org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult. Multiplies the polynomial with another, taking the indices mod N Parameters poly2:IntegerPolynomial Doc from org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult. a polynomial Returns:IntegerPolynomial Doc from org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult. the product of the two polynomials

mult

back to summary

public IntegerPolynomial mult(IntegerPolynomial poly2)

Implements org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult.

Multiplies the polynomial with another, taking the indices mod N

Parameters

poly2:IntegerPolynomial

Doc from org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult.

a polynomial

Returns:IntegerPolynomial

Doc from org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult.

the product of the two polynomials

mult back to summary

mult	back to summary
public BigIntPolynomial mult(BigIntPolynomial poly2) Implements org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult. Doc from org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult. 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. Parameters poly2:BigIntPolynomial the polynomial to multiply by Returns:BigIntPolynomial a new polynomial

public BigIntPolynomial mult(BigIntPolynomial poly2)

Implements org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult.

Doc from org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.mult.

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.

Parameters

poly2:BigIntPolynomial: the polynomial to multiply by

Returns:BigIntPolynomial

a new polynomial

mult	back to summary
public void mult(int factor) Multiplies each coefficient by a `int`. Does not return a new polynomial but modifies this polynomial.

mult2	back to summary
private void mult2(int modulus) Multiplies each coefficient by a 2 and applies a modulus. Does not return a new polynomial but modifies this polynomial. Parameters modulus:int a modulus

mult2

back to summary

private void mult2(int modulus)

Multiplies each coefficient by a 2 and applies a modulus. Does not return a new polynomial but modifies this polynomial.

Parameters

modulus:int: a modulus

mult3	back to summary
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:int a modulus

mult3

back to summary

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:int: a modulus

multRecursive	back to summary
private IntegerPolynomial multRecursive(IntegerPolynomial poly2) Karazuba multiplication

multShiftSub	back to summary
private void multShiftSub(IntegerPolynomial b, int c, int k, int p) Computes `this-bc(x^k) mod p` and stores the result in this polynomial. See steps 4a,4b in EESS algorithm 2.2.7.1.

resultant back to summary

resultant	back to summary
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:Resultant `(rho, res)` satisfying `res = rhothis + t(x^n-1)` for some integer `t`.

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:Resultant: (rho, res) satisfying res = rho*this + t*(x^n-1) for some integer t.

resultant back to summary

resultant	back to summary
public ModularResultant resultant(int p) Resultant of this polynomial with `x^n-1 mod p`. Returns:ModularResultant `(rho, res)` satisfying `res = rhothis + t(x^n-1) mod p` for some integer `t`.

public ModularResultant resultant(int p)

Resultant of this polynomial with x^n-1 mod p.

Returns:ModularResultant: (rho, res) satisfying res = rho*this + t*(x^n-1) mod p for some integer t.

resultantMultiThread back to summary

resultantMultiThread	back to summary
public Resultant resultantMultiThread() Multithreaded version of `resultant()`. Returns:Resultant `(rho, res)` satisfying `res = rhothis + t(x^n-1)` for some integer `t`.

public Resultant resultantMultiThread()

Multithreaded version of resultant().

Returns:Resultant: (rho, res) satisfying res = rho*this + t*(x^n-1) for some integer t.

rotate1	back to summary
public void rotate1() Multiplication by `X` in `Z[X]/Z[X^n-1]`.

shiftGap back to summary

shiftGap	back to summary
pack-priv void shiftGap(int q) Shifts all coefficients so the largest gap is centered around `-q/2`. Parameters q:int a modulus

pack-priv void shiftGap(int q)

Shifts all coefficients so the largest gap is centered around -q/2.

Parameters

q:int: a modulus

sort	back to summary
private void sort(int[] ints)

squareSum

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private BigInteger squareSum()

Adds the squares of all coefficients.

Returns:BigInteger: the sum of squares

sub back to summary

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:IntegerPolynomial: another polynomial

sub

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public void sub(IntegerPolynomial b)

Subtracts another polynomial which can have a different number of coefficients.

Parameters

b:IntegerPolynomial: another polynomial

sub	back to summary
pack-priv void sub(int b) Subtracts a `int` from each coefficient. Does not return a new polynomial but modifies this polynomial.

sumCoeffs

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public int sumCoeffs()

Returns the sum of all coefficients, i.e. evaluates the polynomial at 0.

Returns:int: the sum of all coefficients

toBinary

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public byte[] toBinary(int q)

Encodes a polynomial whose coefficients are between 0 and q, to binary. q must be a power of 2.

Returns:byte[]: the encoded polynomial

toBinary3Sves back to summary

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:byte[]: the encoded polynomial

toBinary3Tight

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public byte[] toBinary3Tight()

Converts a polynomial with ternary coefficients to binary.

Returns:byte[]: the encoded polynomial

toIntegerPolynomial back to summary

public IntegerPolynomial toIntegerPolynomial()

Implements org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.toIntegerPolynomial.

Doc from org.bouncycastle.pqc.legacy.math.ntru.polynomial.Polynomial.toIntegerPolynomial.

Returns a polynomial that is equal to this polynomial (in the sense that mult(IntegerPolynomial, int) returns equal IntegerPolynomials). The new polynomial is guaranteed to be independent of the original.

Returns:IntegerPolynomial: a new IntegerPolynomial.

Modifier and Type	Field and Description
private ModularResultant	modRes1
private ModularResultant	modRes2

public Class IntegerPolynomial

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private Class IntegerPolynomial.CombineTask

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private Class IntegerPolynomial.ModResultantTask

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private Class IntegerPolynomial.PrimeGenerator

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