Constructor Detail

• 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,
                       java.util.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,
                       java.lang.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,
                       java.math.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 Detail

• clone

  public java.lang.Object clone()

  Overrides:

  clone in class java.lang.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 java.lang.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 java.math.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​(java.util.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​(java.lang.Object other)

  Returns true if two GF2Polynomials have the same size and value and thus are equal.

  Overrides:

  equals in class java.lang.Object

  Parameters:

  other - the other GF2Polynomial

  Returns:

  true if this GF2Polynomial equals b (this == b)

• hashCode

  public int hashCode()

  Overrides:

  hashCode in class java.lang.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 java.lang.RuntimeException

  Returns the remainder of this divided by g in a new GF2Polynomial.

  Parameters:

  g - GF2Polynomial != 0

  Returns:

  a new GF2Polynomial (this % g)

  Throws:

  java.lang.RuntimeException

• quotient

  public GF2Polynomial quotient​(GF2Polynomial g)
                         throws java.lang.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:

  java.lang.RuntimeException

• divide

  public GF2Polynomial[] divide​(GF2Polynomial g)
                         throws java.lang.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:

  java.lang.RuntimeException

• gcd

  public GF2Polynomial gcd​(GF2Polynomial g)
                    throws java.lang.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:

  java.lang.ArithmeticException - if this and g both are equal to zero

  java.lang.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:

  GF2nPolynomialElement.square()

• 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 java.lang.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:

  java.lang.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 java.lang.RuntimeException

  Sets the bit at position i.

  Parameters:

  i - int

  Throws:

  java.lang.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 java.lang.RuntimeException

  Resets the bit at position i.

  Parameters:

  i - int

  Throws:

  java.lang.RuntimeException - if (i < 0) || (i > (len - 1))

• xorBit

  public void xorBit​(int i)
              throws java.lang.RuntimeException

  Xors the bit at position i.

  Parameters:

  i - int

  Throws:

  java.lang.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:

  GF2nPolynomialElement.invertEEA()

• 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.