Package org.bouncycastle.pqc.legacy.math.linearalgebra

Class GF2Polynomial

java.lang.Object
org.bouncycastle.pqc.legacy.math.linearalgebra.GF2Polynomial
public class GF2Polynomial extends Object
This class stores very long strings of bits and does some basic arithmetics. It is used by GF2nField, GF2nPolynomialField and GFnPolynomialElement.
See Also:

  • Constructor Summary

    Constructors
    Constructor
    Description
    GF2Polynomial(int length)
    Creates a new GF2Polynomial of the given length and value zero.
    GF2Polynomial(int length, byte[] os)
    Creates a new GF2Polynomial by converting the given byte[] os according to 1363 and using the given length.
    GF2Polynomial(int length, int[] bs)
    Creates a new GF2Polynomial of the given length using the given int[].
    GF2Polynomial(int length, String value)
    Creates a new GF2Polynomial of the given length and value selected by value: ZERO ONE RANDOM X ALL
    GF2Polynomial(int length, BigInteger bi)
    Creates a new GF2Polynomial by converting the given FlexiBigInt bi according to 1363 and using the given length.
    GF2Polynomial(int length, Random rand)
    Creates a new GF2Polynomial of the given length and random value.
    GF2Polynomial(GF2Polynomial b)
    Creates a new GF2Polynomial by cloneing the given GF2Polynomial b.

  • Method Summary

    Modifier and Type
    Method
    Description
    GF2Polynomial
    add(GF2Polynomial b)
    Adds two GF2Polynomials, this and b, and returns the result.
    void
    addToThis(GF2Polynomial b)
    Adds b to this GF2Polynomial and assigns the result to this GF2Polynomial.
    void
    assignAll()
    Sets all Bits to 1.
    void
    assignOne()
    Sets the LSB to 1 and all other to 0, assigning 'one' to this GF2Polynomial.
    void
    assignX()
    Sets Bit 1 to 1 and all other to 0, assigning 'x' to this GF2Polynomial.
    void
    assignZero()
    Resets all bits to zero.
    Object
    clone()
     
    GF2Polynomial[]
    divide(GF2Polynomial g)
    Divides this by g and returns the quotient and remainder in a new GF2Polynomial[2], quotient in [0], remainder in [1].
    boolean
    equals(Object other)
    Returns true if two GF2Polynomials have the same size and value and thus are equal.
    void
    expandN(int i)
    Expands len and int[] value to i.
    GF2Polynomial
    gcd(GF2Polynomial g)
    Returns the greatest common divisor of this and g in a new GF2Polynomial.
    int
    getBit(int i)
    Returns the bit at position i.
    int
    getLength()
    Returns the length of this GF2Polynomial.
    int
    hashCode()
     
    GF2Polynomial
    increase()
    Toggles the LSB of this GF2Polynomial, increasing the value by 'one' and returns the result in a new GF2Polynomial.
    void
    increaseThis()
    Toggles the LSB of this GF2Polynomial, increasing its value by 'one'.
    boolean
    isIrreducible()
    Checks if this is irreducible, according to IEEE P1363, A.5.5, p103.
    Note: The algorithm from IEEE P1363, A5.5 can be used to check a polynomial with coefficients in GF(2^r) for irreducibility.
    boolean
    isOne()
    Tests if all bits are reset to 0 and LSB is set to 1.
    boolean
    isZero()
    Tests if all bits equal zero.
    GF2Polynomial
    multiply(GF2Polynomial b)
    Multiplies this GF2Polynomial with b and returns the result in a new GF2Polynomial.
    GF2Polynomial
    multiplyClassic(GF2Polynomial b)
    Multiplies this GF2Polynomial with b and returns the result in a new GF2Polynomial.
    GF2Polynomial
    quotient(GF2Polynomial g)
    Returns the absolute quotient of this divided by g in a new GF2Polynomial.
    void
    randomize()
    Fills all len bits of this GF2Polynomial with random values.
    void
    randomize(Random rand)
    Fills all len bits of this GF2Polynomial with random values using the specified source of randomness.
    void
    reduceN()
    Reduces len by finding the most significant bit set to one and reducing len and blocks.
    GF2Polynomial
    remainder(GF2Polynomial g)
    Returns the remainder of this divided by g in a new GF2Polynomial.
    void
    resetBit(int i)
    Resets the bit at position i.
    void
    setBit(int i)
    Sets the bit at position i.
    GF2Polynomial
    shiftLeft()
    Returns this GF2Polynomial shift-left by 1 in a new GF2Polynomial.
    GF2Polynomial
    shiftLeft(int k)
    Returns this GF2Polynomial shift-left by k in a new GF2Polynomial.
    void
    shiftLeftAddThis(GF2Polynomial b, int k)
    Shifts left b and adds the result to Its a fast version of this = add(b.shl(k));
    void
    shiftLeftThis()
    Shifts-left this by one and enlarges the size of value if necesary.
    GF2Polynomial
    shiftRight()
    Returns this GF2Polynomial shift-right by 1 in a new GF2Polynomial.
    void
    shiftRightThis()
    Shifts-right this GF2Polynomial by 1.
    void
    squareThisBitwise()
    Squares this GF2Polynomial and expands it accordingly.
    void
    squareThisPreCalc()
    Squares this GF2Polynomial by using precomputed values of squaringTable.
    GF2Polynomial
    subtract(GF2Polynomial b)
    Subtracts two GF2Polynomials, this and b, and returns the result in a new GF2Polynomial.
    void
    subtractFromThis(GF2Polynomial b)
    Subtracts b from this GF2Polynomial and assigns the result to this GF2Polynomial.
    boolean
    testBit(int i)
    Tests the bit at position i.
    byte[]
    toByteArray()
    Converts this polynomial to a byte[] (octet string) according to 1363.
    BigInteger
    toFlexiBigInt()
    Converts this polynomial to an integer according to 1363.
    int[]
    toIntegerArray()
    Returns the value of this GF2Polynomial in an int[].
    String
    toString(int radix)
    Returns a string representing this GF2Polynomials value using hexadecimal or binary radix in MSB-first order.
    boolean
    vectorMult(GF2Polynomial b)
    Does a vector-multiplication modulo 2 and returns the result as boolean.
    GF2Polynomial
    xor(GF2Polynomial b)
    Returns the bitwise exclusive-or of this and b in a new GF2Polynomial.
    void
    xorBit(int i)
    Xors the bit at position i.
    void
    xorThisBy(GF2Polynomial b)
    Computes the bitwise exclusive-or of this GF2Polynomial and b and stores the result in this GF2Polynomial.

    Methods inherited from class java.lang.Object

    finalize, getClass, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • GF2Polynomial

      public GF2Polynomial(int length)
      Creates a new GF2Polynomial of the given length and value zero.
      Parameters:
      length - the desired number of bits to store

    • GF2Polynomial

      public GF2Polynomial(int length, Random rand)
      Creates a new GF2Polynomial of the given length and random value.
      Parameters:
      length - the desired number of bits to store
      rand - SecureRandom to use for randomization

    • GF2Polynomial

      public GF2Polynomial(int length, String value)
      Creates a new GF2Polynomial of the given length and value selected by value:
      • ZERO
      • ONE
      • RANDOM
      • X
      • ALL
      Parameters:
      length - the desired number of bits to store
      value - the value described by a String

    • GF2Polynomial

      public GF2Polynomial(int length, int[] bs)
      Creates a new GF2Polynomial of the given length using the given int[]. LSB is contained in bs[0].
      Parameters:
      length - the desired number of bits to store
      bs - contains the desired value, LSB in bs[0]

    • GF2Polynomial

      public GF2Polynomial(int length, byte[] os)
      Creates a new GF2Polynomial by converting the given byte[] os according to 1363 and using the given length.
      Parameters:
      length - the intended length of this polynomial
      os - the octet string to assign to this polynomial
      See Also:
      • "P1363 5.5.2 p22f, OS2BSP"

    • GF2Polynomial

      public GF2Polynomial(int length, BigInteger bi)
      Creates a new GF2Polynomial by converting the given FlexiBigInt bi according to 1363 and using the given length.
      Parameters:
      length - the intended length of this polynomial
      bi - the FlexiBigInt to assign to this polynomial
      See Also:
      • "P1363 5.5.1 p22, I2BSP"

    • GF2Polynomial

      public GF2Polynomial(GF2Polynomial b)
      Creates a new GF2Polynomial by cloneing the given GF2Polynomial b.
      Parameters:
      b - the GF2Polynomial to clone

  • Method Details

    • clone

      public Object clone()
      Overrides:
      clone in class Object
      Returns:
      a copy of this GF2Polynomial

    • getLength

      public int getLength()
      Returns the length of this GF2Polynomial. The length can be greater than the degree. To get the degree call reduceN() before calling getLength().
      Returns:
      the length of this GF2Polynomial

    • toIntegerArray

      public int[] toIntegerArray()
      Returns the value of this GF2Polynomial in an int[].
      Returns:
      the value of this GF2Polynomial in a new int[], LSB in int[0]

    • toString

      public String toString(int radix)
      Returns a string representing this GF2Polynomials value using hexadecimal or binary radix in MSB-first order.
      Parameters:
      radix - the radix to use (2 or 16, otherwise 2 is used)
      Returns:
      a String representing this GF2Polynomials value.

    • toByteArray

      public byte[] toByteArray()
      Converts this polynomial to a byte[] (octet string) according to 1363.
      Returns:
      a byte[] representing the value of this polynomial
      See Also:
      • "P1363 5.5.2 p22f, BS2OSP"

    • toFlexiBigInt

      public BigInteger toFlexiBigInt()
      Converts this polynomial to an integer according to 1363.
      Returns:
      a FlexiBigInt representing the value of this polynomial
      See Also:
      • "P1363 5.5.1 p22, BS2IP"

    • assignOne

      public void assignOne()
      Sets the LSB to 1 and all other to 0, assigning 'one' to this GF2Polynomial.

    • assignX

      public void assignX()
      Sets Bit 1 to 1 and all other to 0, assigning 'x' to this GF2Polynomial.

    • assignAll

      public void assignAll()
      Sets all Bits to 1.

    • assignZero

      public void assignZero()
      Resets all bits to zero.

    • randomize

      public void randomize()
      Fills all len bits of this GF2Polynomial with random values.

    • randomize

      public void randomize(Random rand)
      Fills all len bits of this GF2Polynomial with random values using the specified source of randomness.
      Parameters:
      rand - the source of randomness

    • equals

      public boolean equals(Object other)
      Returns true if two GF2Polynomials have the same size and value and thus are equal.
      Overrides:
      equals in class Object
      Parameters:
      other - the other GF2Polynomial
      Returns:
      true if this GF2Polynomial equals b (this == b)

    • hashCode

      public int hashCode()
      Overrides:
      hashCode in class Object
      Returns:
      the hash code of this polynomial

    • isZero

      public boolean isZero()
      Tests if all bits equal zero.
      Returns:
      true if this GF2Polynomial equals 'zero' (this == 0)

    • isOne

      public boolean isOne()
      Tests if all bits are reset to 0 and LSB is set to 1.
      Returns:
      true if this GF2Polynomial equals 'one' (this == 1)

    • addToThis

      public void addToThis(GF2Polynomial b)
      Adds b to this GF2Polynomial and assigns the result to this GF2Polynomial. b can be of different size.
      Parameters:
      b - GF2Polynomial to add to this GF2Polynomial

    • add

      public GF2Polynomial add(GF2Polynomial b)
      Adds two GF2Polynomials, this and b, and returns the result. this and b can be of different size.
      Parameters:
      b - a GF2Polynomial
      Returns:
      a new GF2Polynomial (this + b)

    • subtractFromThis

      public void subtractFromThis(GF2Polynomial b)
      Subtracts b from this GF2Polynomial and assigns the result to this GF2Polynomial. b can be of different size.
      Parameters:
      b - a GF2Polynomial

    • subtract

      public GF2Polynomial subtract(GF2Polynomial b)
      Subtracts two GF2Polynomials, this and b, and returns the result in a new GF2Polynomial. this and b can be of different size.
      Parameters:
      b - a GF2Polynomial
      Returns:
      a new GF2Polynomial (this - b)

    • increaseThis

      public void increaseThis()
      Toggles the LSB of this GF2Polynomial, increasing its value by 'one'.

    • increase

      public GF2Polynomial increase()
      Toggles the LSB of this GF2Polynomial, increasing the value by 'one' and returns the result in a new GF2Polynomial.
      Returns:
      this + 1

    • multiplyClassic

      public GF2Polynomial multiplyClassic(GF2Polynomial b)
      Multiplies this GF2Polynomial with b and returns the result in a new GF2Polynomial. This method does not reduce the result in GF(2^N). This method uses classic multiplication (schoolbook).
      Parameters:
      b - a GF2Polynomial
      Returns:
      a new GF2Polynomial (this * b)

    • multiply

      public GF2Polynomial multiply(GF2Polynomial b)
      Multiplies this GF2Polynomial with b and returns the result in a new GF2Polynomial. This method does not reduce the result in GF(2^N). This method uses Karatzuba multiplication.
      Parameters:
      b - a GF2Polynomial
      Returns:
      a new GF2Polynomial (this * b)

    • remainder

      public GF2Polynomial remainder(GF2Polynomial g) throws RuntimeException
      Returns the remainder of this divided by g in a new GF2Polynomial.
      Parameters:
      g - GF2Polynomial != 0
      Returns:
      a new GF2Polynomial (this % g)
      Throws:
      RuntimeException

    • quotient

      public GF2Polynomial quotient(GF2Polynomial g) throws RuntimeException
      Returns the absolute quotient of this divided by g in a new GF2Polynomial.
      Parameters:
      g - GF2Polynomial != 0
      Returns:
      a new GF2Polynomial |_ this / g _|
      Throws:
      RuntimeException

    • divide

      public GF2Polynomial[] divide(GF2Polynomial g) throws RuntimeException
      Divides this by g and returns the quotient and remainder in a new GF2Polynomial[2], quotient in [0], remainder in [1].
      Parameters:
      g - GF2Polynomial != 0
      Returns:
      a new GF2Polynomial[2] containing quotient and remainder
      Throws:
      RuntimeException

    • gcd

      public GF2Polynomial gcd(GF2Polynomial g) throws RuntimeException
      Returns the greatest common divisor of this and g in a new GF2Polynomial.
      Parameters:
      g - GF2Polynomial != 0
      Returns:
      a new GF2Polynomial gcd(this,g)
      Throws:
      ArithmeticException - if this and g both are equal to zero
      RuntimeException

    • isIrreducible

      public boolean isIrreducible()
      Checks if this is irreducible, according to IEEE P1363, A.5.5, p103.
      Note: The algorithm from IEEE P1363, A5.5 can be used to check a polynomial with coefficients in GF(2^r) for irreducibility. As this class only represents polynomials with coefficients in GF(2), the algorithm is adapted to the case r=1.
      Returns:
      true if this is irreducible
      See Also:
      • "P1363, A.5.5, p103"

    • reduceN

      public void reduceN()
      Reduces len by finding the most significant bit set to one and reducing len and blocks.

    • expandN

      public void expandN(int i)
      Expands len and int[] value to i. This is useful before adding two GF2Polynomials of different size.
      Parameters:
      i - the intended length

    • squareThisBitwise

      public void squareThisBitwise()
      Squares this GF2Polynomial and expands it accordingly. This method does not reduce the result in GF(2^N). There exists a faster method for squaring in GF(2^N).
      See Also:

    • squareThisPreCalc

      public void squareThisPreCalc()
      Squares this GF2Polynomial by using precomputed values of squaringTable. This method does not reduce the result in GF(2^N).

    • vectorMult

      public boolean vectorMult(GF2Polynomial b) throws RuntimeException
      Does a vector-multiplication modulo 2 and returns the result as boolean.
      Parameters:
      b - GF2Polynomial
      Returns:
      this x b as boolean (1->true, 0->false)
      Throws:
      RuntimeException

    • xor

      public GF2Polynomial xor(GF2Polynomial b)
      Returns the bitwise exclusive-or of this and b in a new GF2Polynomial. this and b can be of different size.
      Parameters:
      b - GF2Polynomial
      Returns:
      a new GF2Polynomial (this ^ b)

    • xorThisBy

      public void xorThisBy(GF2Polynomial b)
      Computes the bitwise exclusive-or of this GF2Polynomial and b and stores the result in this GF2Polynomial. b can be of different size.
      Parameters:
      b - GF2Polynomial

    • setBit

      public void setBit(int i) throws RuntimeException
      Sets the bit at position i.
      Parameters:
      i - int
      Throws:
      RuntimeException - if (i < 0) || (i > (len - 1))

    • getBit

      public int getBit(int i)
      Returns the bit at position i.
      Parameters:
      i - int
      Returns:
      the bit at position i if i is a valid position, 0 otherwise.

    • resetBit

      public void resetBit(int i) throws RuntimeException
      Resets the bit at position i.
      Parameters:
      i - int
      Throws:
      RuntimeException - if (i < 0) || (i > (len - 1))

    • xorBit

      public void xorBit(int i) throws RuntimeException
      Xors the bit at position i.
      Parameters:
      i - int
      Throws:
      RuntimeException - if (i < 0) || (i > (len - 1))

    • testBit

      public boolean testBit(int i)
      Tests the bit at position i.
      Parameters:
      i - the position of the bit to be tested
      Returns:
      true if the bit at position i is set (a(i) == 1). False if (i < 0) || (i > (len - 1))

    • shiftLeft

      public GF2Polynomial shiftLeft()
      Returns this GF2Polynomial shift-left by 1 in a new GF2Polynomial.
      Returns:
      a new GF2Polynomial (this << 1)

    • shiftLeftThis

      public void shiftLeftThis()
      Shifts-left this by one and enlarges the size of value if necesary.

    • shiftLeft

      public GF2Polynomial shiftLeft(int k)
      Returns this GF2Polynomial shift-left by k in a new GF2Polynomial.
      Parameters:
      k - int
      Returns:
      a new GF2Polynomial (this << k)

    • shiftLeftAddThis

      public void shiftLeftAddThis(GF2Polynomial b, int k)
      Shifts left b and adds the result to Its a fast version of this = add(b.shl(k));
      Parameters:
      b - GF2Polynomial to shift and add to this
      k - the amount to shift
      See Also:

    • shiftRight

      public GF2Polynomial shiftRight()
      Returns this GF2Polynomial shift-right by 1 in a new GF2Polynomial.
      Returns:
      a new GF2Polynomial (this << 1)

    • shiftRightThis

      public void shiftRightThis()
      Shifts-right this GF2Polynomial by 1.