Bouncy Castle Provider 1.77 · org.bouncycastle.pqc.legacy.math.linearalgebra.GF2Polynomial

Modifier and Type	Field and Description
private static final int[]	bitMask
private int	blocks
private int	len
private static final boolean[]	parity
private static Random	rand
private static final int[]	reverseRightMask
private static final short[]	squaringTable
private int[]	value

Access	Constructor and Description
public	GF2Polynomial(int the desired number of bits to store length) Creates a new GF2Polynomial of the given length and value zero.
public	GF2Polynomial(int the desired number of bits to store length, Random SecureRandom to use for randomization rand) Creates a new GF2Polynomial of the given length and random value.
public	GF2Polynomial(int the desired number of bits to store length, String the value described by a String value) Creates a new GF2Polynomial of the given length and value selected by value: ZERO ONE RANDOM X ALL
public	GF2Polynomial(int the desired number of bits to store length, int[] contains the desired value, LSB in bs[0] bs) Creates a new GF2Polynomial of the given length using the given int[].
public	GF2Polynomial(int the intended length of this polynomial length, byte[] the octet string to assign to this polynomial os) Creates a new GF2Polynomial by converting the given byte[] os according to 1363 and using the given length.
public	GF2Polynomial(int the intended length of this polynomial length, BigInteger the FlexiBigInt to assign to this polynomial bi) Creates a new GF2Polynomial by converting the given FlexiBigInt bi according to 1363 and using the given length.
public	GF2Polynomial(GF2Polynomial the GF2Polynomial to clone b) Creates a new GF2Polynomial by cloneing the given GF2Polynomial b.

Method Summary

Modifier and Type	Method and Description
public GF2Polynomial	Returns: a new GF2Polynomial (this + b) add(GF2Polynomial a GF2Polynomial b) Adds two GF2Polynomials, this and b, and returns the result.
public void	addToThis(GF2Polynomial GF2Polynomial to add to this GF2Polynomial b) Adds b to this GF2Polynomial and assigns the result to this GF2Polynomial.
public void	assignAll() Sets all Bits to 1.
public void	assignOne() Sets the LSB to 1 and all other to 0, assigning 'one' to this GF2Polynomial.
public void	assignX() Sets Bit 1 to 1 and all other to 0, assigning 'x' to this GF2Polynomial.
public void	assignZero() Resets all bits to zero.
public Object	Returns: a copy of this GF2Polynomial clone() Overrides java.lang.Object.clone. Creates and returns a copy of this object.
public GF2Polynomial[]	Returns: a new GF2Polynomial[2] containing quotient and remainder divide(GF2Polynomial GF2Polynomial != 0 g) Divides this by g and returns the quotient and remainder in a new GF2Polynomial[2], quotient in [0], remainder in [1].
private void	doShiftBlocksLeft(int shift amount (in blocks) b) Shifts left this GF2Polynomial's value blockwise b blocks resulting in a shift-left by b*32.
public boolean	Returns: true if this GF2Polynomial equals b (this == b) equals(Object the other GF2Polynomial other) Overrides java.lang.Object.equals. Returns true if two GF2Polynomials have the same size and value and thus are equal.
public void	expandN(int the intended length i) Expands len and int[] value to i.
public GF2Polynomial	Returns: a new GF2Polynomial gcd(this,g) gcd(GF2Polynomial GF2Polynomial != 0 g) Returns the greatest common divisor of this and g in a new GF2Polynomial.
public int	Returns: the bit at position i if i is a valid position, 0 otherwise. getBit(int int i) Returns the bit at position i.
public int	Returns: the length of this GF2Polynomial getLength() Returns the length of this GF2Polynomial.
public int	Returns: the hash code of this polynomial hashCode() Overrides java.lang.Object.hashCode. Returns a hash code value for the object.
public GF2Polynomial	Returns: `this + 1` increase() Toggles the LSB of this GF2Polynomial, increasing the value by 'one' and returns the result in a new GF2Polynomial.
public void	increaseThis() Toggles the LSB of this GF2Polynomial, increasing its value by 'one'.
public boolean	Returns: true if this is irreducible isIrreducible() Checks if this is irreducible, according to IEEE P1363, A.5.5, p103.
public boolean	Returns: true if this GF2Polynomial equals 'one' (this == 1) isOne() Tests if all bits are reset to 0 and LSB is set to 1.
public boolean	Returns: true if this GF2Polynomial equals 'zero' (this == 0) isZero() Tests if all bits equal zero.
private GF2Polynomial	karaMult(GF2Polynomial b) Does the recursion for Karatzuba multiplication.
private GF2Polynomial	Returns: a new GF2Polynomial containing the lower k bytes of this GF2Polynomial lower(int k) Returns a new GF2Polynomial containing the lower k bytes of this GF2Polynomial.
private static int[]	mult128(int[] a, int[] b) 4-Integer Version of Karatzuba multiplication.
private static int[]	mult256(int[] a, int[] b) 8-Integer Version of Karatzuba multiplication.
private static int[]	mult32(int a, int b) 4-Byte Version of Karatzuba multiplication.
private static int[]	mult512(int[] a, int[] b) 16-Integer Version of Karatzuba multiplication.
private static int[]	mult64(int[] a, int[] b) 2-Integer Version of Karatzuba multiplication.
public GF2Polynomial	Returns: a new GF2Polynomial (this * b) multiply(GF2Polynomial a GF2Polynomial b) Multiplies this GF2Polynomial with b and returns the result in a new GF2Polynomial.
public GF2Polynomial	Returns: a new GF2Polynomial (this * b) multiplyClassic(GF2Polynomial a GF2Polynomial b) Multiplies this GF2Polynomial with b and returns the result in a new GF2Polynomial.
public GF2Polynomial	Returns: a new GF2Polynomial \|_ this / g _\| quotient(GF2Polynomial GF2Polynomial != 0 g) Returns the absolute quotient of this divided by g in a new GF2Polynomial.
public void	randomize() Fills all len bits of this GF2Polynomial with random values.
public void	randomize(Random the source of randomness rand) Fills all len bits of this GF2Polynomial with random values using the specified source of randomness.
public void	reduceN() Reduces len by finding the most significant bit set to one and reducing len and blocks.
pack-priv void	reducePentanomial(int the degree of the used field m, int[] degrees of the middle x's in the pentanomial pc) Reduces this GF2Polynomial using the pentanomial x^m + x^pc[2] + x^pc[1] + x^pc[0] + 1.
pack-priv void	reduceTrinomial(int the degree of the used field m, int degree of the middle x in the trinomial tc) Reduces this GF2Polynomial using the trinomial x^m + x^tc + 1.
public GF2Polynomial	Returns: a new GF2Polynomial (this % g) remainder(GF2Polynomial GF2Polynomial != 0 g) Returns the remainder of this divided by g in a new GF2Polynomial.
public void	resetBit(int int i) Resets the bit at position i.
public void	setBit(int int i) Sets the bit at position i.
pack-priv void	shiftBlocksLeft() Shifts-left this GF2Polynomial's value blockwise 1 block resulting in a shift-left by 32.
public GF2Polynomial	Returns: a new GF2Polynomial (this << 1) shiftLeft() Returns this GF2Polynomial shift-left by 1 in a new GF2Polynomial.
public GF2Polynomial	Returns: a new GF2Polynomial (this << k) shiftLeft(int int k) Returns this GF2Polynomial shift-left by k in a new GF2Polynomial.
public void	shiftLeftAddThis(GF2Polynomial GF2Polynomial to shift and add to this b, int the amount to shift k) Shifts left b and adds the result to Its a fast version of `this = add(b.shl(k));`
public void	shiftLeftThis() Shifts-left this by one and enlarges the size of value if necesary.
public GF2Polynomial	Returns: a new GF2Polynomial (this << 1) shiftRight() Returns this GF2Polynomial shift-right by 1 in a new GF2Polynomial.
public void	shiftRightThis() Shifts-right this GF2Polynomial by 1.
public void	squareThisBitwise() Squares this GF2Polynomial and expands it accordingly.
public void	squareThisPreCalc() Squares this GF2Polynomial by using precomputed values of squaringTable.
public GF2Polynomial	Returns: a new GF2Polynomial (this - b) subtract(GF2Polynomial a GF2Polynomial b) Subtracts two GF2Polynomials, this and b, and returns the result in a new GF2Polynomial.
public void	subtractFromThis(GF2Polynomial a GF2Polynomial b) Subtracts b from this GF2Polynomial and assigns the result to this GF2Polynomial.
public boolean	Returns: true if the bit at position i is set (a(i) == 1). False if (i < 0) \|\| (i > (len - 1)) testBit(int the position of the bit to be tested i) Tests the bit at position i.
public byte[]	Returns: a byte[] representing the value of this polynomial toByteArray() Converts this polynomial to a byte[] (octet string) according to 1363.
public BigInteger	Returns: a FlexiBigInt representing the value of this polynomial toFlexiBigInt() Converts this polynomial to an integer according to 1363.
public int[]	Returns: the value of this GF2Polynomial in a new int[], LSB in int[0] toIntegerArray() Returns the value of this GF2Polynomial in an int[].
public String	Returns: a String representing this GF2Polynomials value. toString(int the radix to use (2 or 16, otherwise 2 is used) radix) Returns a string representing this GF2Polynomials value using hexadecimal or binary radix in MSB-first order.
private GF2Polynomial	Returns: a new GF2Polynomial containing the upper k bytes of this GF2Polynomial upper(int k) Returns a new GF2Polynomial containing the upper k bytes of this GF2Polynomial.
public boolean	Returns: this x b as boolean (1->true, 0->false) vectorMult(GF2Polynomial GF2Polynomial b) Does a vector-multiplication modulo 2 and returns the result as boolean.
public GF2Polynomial	Returns: a new GF2Polynomial (this ^ b) xor(GF2Polynomial GF2Polynomial b) Returns the bitwise exclusive-or of this and b in a new GF2Polynomial.
public void	xorBit(int int i) Xors the bit at position i.
public void	xorThisBy(GF2Polynomial GF2Polynomial b) Computes the bitwise exclusive-or of this GF2Polynomial and b and stores the result in this GF2Polynomial.
private void	zeroUnusedBits() If `len` is not a multiple of the block size (32), some extra bits of the last block might have been modified during a blockwise operation.

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

bitMask	back to summary
private static final int[] bitMask

blocks	back to summary
private int blocks

len	back to summary
private int len

parity	back to summary
private static final boolean[] parity

rand	back to summary
private static Random rand

reverseRightMask	back to summary
private static final int[] reverseRightMask

squaringTable	back to summary
private static final short[] squaringTable

value	back to summary
private int[] value

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

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

GF2Polynomial	back to summary
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:int the desired number of bits to store value:String the value described by a String

GF2Polynomial	back to summary
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:int the desired number of bits to store bs:int[] contains the desired value, LSB in bs[0]

GF2Polynomial	back to summary
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:int the intended length of this polynomial os:byte[] the octet string to assign to this polynomial See Also P1363 5.5.2 p22f, OS2BSP

GF2Polynomial	back to summary
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:int the intended length of this polynomial bi:BigInteger the FlexiBigInt to assign to this polynomial See Also P1363 5.5.1 p22, I2BSP

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

Method Detail

add	back to summary
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:GF2Polynomial a GF2Polynomial Returns:GF2Polynomial a new GF2Polynomial (this + b)

add

back to summary

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:GF2Polynomial: a GF2Polynomial

Returns:GF2Polynomial

a new GF2Polynomial (this + b)

addToThis	back to summary
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 GF2Polynomial to add to this GF2Polynomial

addToThis

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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: GF2Polynomial to add to this GF2Polynomial

assignAll	back to summary
public void assignAll() Sets all Bits to 1.

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

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

assignZero	back to summary
public void assignZero() Resets all bits to zero.

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 copy of this GF2Polynomial

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 copy of this GF2Polynomial

divide	back to summary
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 GF2Polynomial != 0 Returns:GF2Polynomial[] a new GF2Polynomial[2] containing quotient and remainder

divide

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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: GF2Polynomial != 0

Returns:GF2Polynomial[]

a new GF2Polynomial[2] containing quotient and remainder

doShiftBlocksLeft back to summary

doShiftBlocksLeft	back to summary
private void doShiftBlocksLeft(int b) Shifts left this GF2Polynomial's value blockwise b blocks resulting in a shift-left by b*32. This method assumes that `len` and `blocks` have already been updated to reflect the final state. Parameters b:int shift amount (in blocks)

private void doShiftBlocksLeft(int b)

Shifts left this GF2Polynomial's value blockwise b blocks resulting in a shift-left by b*32. This method assumes that len and blocks have already been updated to reflect the final state.

Parameters

b:int: shift amount (in blocks)

equals	back to summary
public boolean equals(Object other) Overrides java.lang.Object.equals. Returns true if two GF2Polynomials have the same size and value and thus are equal. Parameters other:Object the other GF2Polynomial Returns:boolean true if this GF2Polynomial equals b (this == b)

equals

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public boolean equals(Object other)

Overrides java.lang.Object.equals.

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

Parameters

other:Object: the other GF2Polynomial

Returns:boolean

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

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

expandN

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public void expandN(int i)

Expands len and int[] value to i. This is useful before adding two GF2Polynomials of different size.

Parameters

i:int: the intended length

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

gcd

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public GF2Polynomial gcd(GF2Polynomial g) throws RuntimeException

Returns the greatest common divisor of this and g in a new GF2Polynomial.

Parameters

g:GF2Polynomial: GF2Polynomial != 0

Returns:GF2Polynomial

a new GF2Polynomial gcd(this,g)

Exceptions

ArithmeticException:: if this and g both are equal to zero

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

getBit

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public int getBit(int i)

Returns the bit at position i.

Parameters

i:int: int

Returns:int

the bit at position i if i is a valid position, 0 otherwise.

getLength	back to summary
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:int the length of this GF2Polynomial

getLength

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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:int: the length of this GF2Polynomial

hashCode back to summary

hashCode	back to summary
public int hashCode() Overrides java.lang.Object.hashCode. Doc from java.lang.Object.hashCode. Returns a hash code value for the object. This method is supported for the benefit of hash tables such as those provided by `java.util.HashMap`. The general contract of `hashCode` is: Whenever it is invoked on the same object more than once during an execution of a Java application, the `hashCode` method must consistently return the same integer, provided no information used in `equals` comparisons on the object is modified. This integer need not remain consistent from one execution of an application to another execution of the same application. If two objects are equal according to the `equals` method, then calling the `hashCode` method on each of the two objects must produce the same integer result. It is not required that if two objects are unequal according to the `equals` method, then calling the `hashCode` method on each of the two objects must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal objects may improve the performance of hash tables. Returns:int the hash code of this polynomial

public int hashCode()

Overrides java.lang.Object.hashCode.

Doc from java.lang.Object.hashCode.

Returns a hash code value for the object. This method is supported for the benefit of hash tables such as those provided by java.util.HashMap.

The general contract of hashCode is:

Whenever it is invoked on the same object more than once during an execution of a Java application, the hashCode method must consistently return the same integer, provided no information used in equals comparisons on the object is modified. This integer need not remain consistent from one execution of an application to another execution of the same application.
If two objects are equal according to the equals method, then calling the hashCode method on each of the two objects must produce the same integer result.
It is not required that if two objects are unequal according to the equals method, then calling the hashCode method on each of the two objects must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal objects may improve the performance of hash tables.

Returns:int: the hash code of this polynomial

increase back to summary

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

public GF2Polynomial increase()

Toggles the LSB of this GF2Polynomial, increasing the value by 'one' and returns the result in a new GF2Polynomial.

Returns:GF2Polynomial: this + 1

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

isIrreducible	back to summary
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:boolean true if this is irreducible See Also P1363, A.5.5, p103

isIrreducible

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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:boolean: true if this is irreducible
See Also: P1363, A.5.5, p103

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

isOne

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public boolean isOne()

Tests if all bits are reset to 0 and LSB is set to 1.

Returns:boolean: true if this GF2Polynomial equals 'one' (this == 1)

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

isZero

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public boolean isZero()

Tests if all bits equal zero.

Returns:boolean: true if this GF2Polynomial equals 'zero' (this == 0)

karaMult	back to summary
private GF2Polynomial karaMult(GF2Polynomial b) Does the recursion for Karatzuba multiplication.

lower back to summary

lower	back to summary
private GF2Polynomial lower(int k) Returns a new GF2Polynomial containing the lower k bytes of this GF2Polynomial. Returns:GF2Polynomial a new GF2Polynomial containing the lower k bytes of this GF2Polynomial See Also `GF2Polynomial#karaMult`

private GF2Polynomial lower(int k)

Returns a new GF2Polynomial containing the lower k bytes of this GF2Polynomial.

Returns:GF2Polynomial: a new GF2Polynomial containing the lower k bytes of this GF2Polynomial
See Also: GF2Polynomial#karaMult

mult128	back to summary
private static int[] mult128(int[] a, int[] b) 4-Integer Version of Karatzuba multiplication.

mult256	back to summary
private static int[] mult256(int[] a, int[] b) 8-Integer Version of Karatzuba multiplication.

mult32	back to summary
private static int[] mult32(int a, int b) 4-Byte Version of Karatzuba multiplication. Here the actual work is done.

mult512	back to summary
private static int[] mult512(int[] a, int[] b) 16-Integer Version of Karatzuba multiplication.

mult64	back to summary
private static int[] mult64(int[] a, int[] b) 2-Integer Version of Karatzuba multiplication.

multiply	back to summary
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:GF2Polynomial a GF2Polynomial Returns:GF2Polynomial a new GF2Polynomial (this * b)

multiply

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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:GF2Polynomial: a GF2Polynomial

Returns:GF2Polynomial

a new GF2Polynomial (this * b)

multiplyClassic	back to summary
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:GF2Polynomial a GF2Polynomial Returns:GF2Polynomial a new GF2Polynomial (this * b)

multiplyClassic

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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:GF2Polynomial: a GF2Polynomial

Returns:GF2Polynomial

a new GF2Polynomial (this * b)

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

quotient

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public GF2Polynomial quotient(GF2Polynomial g) throws RuntimeException

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

Parameters

g:GF2Polynomial: GF2Polynomial != 0

Returns:GF2Polynomial

a new GF2Polynomial |_ this / g _|

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

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

randomize

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public void randomize(Random rand)

Fills all len bits of this GF2Polynomial with random values using the specified source of randomness.

Parameters

rand:Random: the source of randomness

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

reducePentanomial

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pack-priv void reducePentanomial(int m, int[] pc)

Reduces this GF2Polynomial using the pentanomial x^m + x^pc[2] + x^pc[1] + x^pc[0] + 1.

Parameters

m:int: the degree of the used field
pc:int[]: degrees of the middle x's in the pentanomial

reduceTrinomial

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pack-priv void reduceTrinomial(int m, int tc)

Reduces this GF2Polynomial using the trinomial x^m + x^tc + 1.

Parameters

m:int: the degree of the used field
tc:int: degree of the middle x in the trinomial

remainder

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public GF2Polynomial remainder(GF2Polynomial g) throws RuntimeException

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

Parameters

g:GF2Polynomial: GF2Polynomial != 0

Returns:GF2Polynomial

a new GF2Polynomial (this % g)

resetBit

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public void resetBit(int i) throws RuntimeException

Resets the bit at position i.

Parameters

i:int: int

Exceptions

RuntimeException:: if (i < 0) || (i > (len - 1))

setBit

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public void setBit(int i) throws RuntimeException

Sets the bit at position i.

Parameters

i:int: int

Exceptions

RuntimeException:: if (i < 0) || (i > (len - 1))

shiftBlocksLeft back to summary

pack-priv void shiftBlocksLeft()

Shifts-left this GF2Polynomial's value blockwise 1 block resulting in a shift-left by 32.

See Also: GF2Polynomial#multiply

shiftLeft

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public GF2Polynomial shiftLeft()

Returns this GF2Polynomial shift-left by 1 in a new GF2Polynomial.

Returns:GF2Polynomial: a new GF2Polynomial (this << 1)

shiftLeft

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public GF2Polynomial shiftLeft(int k)

Returns this GF2Polynomial shift-left by k in a new GF2Polynomial.

Parameters

k:int: int

Returns:GF2Polynomial

a new GF2Polynomial (this << k)

shiftLeftAddThis back to summary

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: GF2Polynomial to shift and add to this
k:int: the amount to shift

See Also

GF2nPolynomialElement#invertEEA

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

shiftRight

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public GF2Polynomial shiftRight()

Returns this GF2Polynomial shift-right by 1 in a new GF2Polynomial.

Returns:GF2Polynomial: a new GF2Polynomial (this << 1)

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

squareThisBitwise back to summary

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

subtract

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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:GF2Polynomial: a GF2Polynomial

Returns:GF2Polynomial

a new GF2Polynomial (this - b)

subtractFromThis

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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:GF2Polynomial: a GF2Polynomial

testBit

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public boolean testBit(int i)

Tests the bit at position i.

Parameters

i:int: the position of the bit to be tested

Returns:boolean

true if the bit at position i is set (a(i) == 1). False if (i < 0) || (i > (len - 1))

toByteArray

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public byte[] toByteArray()

Converts this polynomial to a byte[] (octet string) according to 1363.

Returns:byte[]: a byte[] representing the value of this polynomial
See Also: P1363 5.5.2 p22f, BS2OSP

toFlexiBigInt

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public BigInteger toFlexiBigInt()

Converts this polynomial to an integer according to 1363.

Returns:BigInteger: a FlexiBigInt representing the value of this polynomial
See Also: P1363 5.5.1 p22, BS2IP

toIntegerArray

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public int[] toIntegerArray()

Returns the value of this GF2Polynomial in an int[].

Returns:int[]: the value of this GF2Polynomial in a new int[], LSB in int[0]

toString

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public String toString(int radix)

Returns a string representing this GF2Polynomials value using hexadecimal or binary radix in MSB-first order.

Parameters

radix:int: the radix to use (2 or 16, otherwise 2 is used)

Returns:String

a String representing this GF2Polynomials value.

upper back to summary

private GF2Polynomial upper(int k)

Returns a new GF2Polynomial containing the upper k bytes of this GF2Polynomial.

Returns:GF2Polynomial: a new GF2Polynomial containing the upper k bytes of this GF2Polynomial
See Also: GF2Polynomial#karaMult

vectorMult

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public boolean vectorMult(GF2Polynomial b) throws RuntimeException

Does a vector-multiplication modulo 2 and returns the result as boolean.

Parameters

b:GF2Polynomial: GF2Polynomial

Returns:boolean

this x b as boolean (1->true, 0->false)

xor

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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: GF2Polynomial

Returns:GF2Polynomial

a new GF2Polynomial (this ^ b)

xorBit

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public void xorBit(int i) throws RuntimeException

Xors the bit at position i.

Parameters

i:int: int

Exceptions

RuntimeException:: if (i < 0) || (i > (len - 1))

xorThisBy

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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: GF2Polynomial

zeroUnusedBits	back to summary
private void zeroUnusedBits() If `len` is not a multiple of the block size (32), some extra bits of the last block might have been modified during a blockwise operation. This method compensates for that by restoring these "extra" bits to zero.

public Class GF2Polynomial

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Field Detail

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Method Detail