GF2Polynomial (Bouncy Castle Cryptography 1.58 API Specification)

java.lang.Object
- org.bouncycastle.pqc.math.linearalgebra.GF2Polynomial

```
public class GF2Polynomial
extends java.lang.Object
```
This class stores very long strings of bits and does some basic arithmetics. It is used by GF2nField, GF2nPolynomialField and GFnPolynomialElement.

See Also:

GF2nPolynomialElement, GF2nField

Constructor Summary

Constructors
Constructor and Description
`GF2Polynomial(GF2Polynomial b)` Creates a new GF2Polynomial by cloneing the given GF2Polynomial b.
`GF2Polynomial(int length)` Creates a new GF2Polynomial of the given length and value zero.
`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.
`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, java.util.Random rand)` Creates a new GF2Polynomial of the given length and random value.
`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

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and 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.
`java.lang.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(java.lang.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(java.util.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.
`java.math.BigInteger`	`toFlexiBigInt()` Converts this polynomial to an integer according to 1363.
`int[]`	`toIntegerArray()` Returns the value of this GF2Polynomial in an int[].
`java.lang.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 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.

Class GF2Polynomial

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

GF2Polynomial

GF2Polynomial

GF2Polynomial

GF2Polynomial

GF2Polynomial

GF2Polynomial

GF2Polynomial

Method Detail

clone

getLength

toIntegerArray

toString

toByteArray

toFlexiBigInt

assignOne

assignX

assignAll

assignZero

randomize

randomize

equals

hashCode

isZero

isOne

addToThis

add

subtractFromThis

subtract

increaseThis

increase

multiplyClassic

multiply

remainder

quotient

divide

gcd

isIrreducible

reduceN

expandN

squareThisBitwise

squareThisPreCalc

vectorMult

xor

xorThisBy

setBit

getBit

resetBit

xorBit

testBit

shiftLeft

shiftLeftThis

shiftLeft

shiftLeftAddThis

shiftRight

shiftRightThis