Package org.bouncycastle.pqc.legacy.math.ntru.polynomial

Class IntegerPolynomial

java.lang.Object
org.bouncycastle.pqc.legacy.math.ntru.polynomial.IntegerPolynomial
All Implemented Interfaces:
Polynomial
Direct Known Subclasses:
DenseTernaryPolynomial
public class IntegerPolynomial extends 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 Details

    • coeffs

      public int[] coeffs

  • Constructor Details

    • 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 Details

    • 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(InputStream is, int N) throws 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:
      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(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 - an encoded ternary polynomial
      N - number of coefficients
      q -
      Returns:
      the decoded polynomial
      Throws:
      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 Object clone()
      Overrides:
      clone in class Object

    • equals

      public boolean equals(Object obj)
      Overrides:
      equals in class Object