A C D E F G H I L M N P R S T U V W X

A

A - Variable in class HFE.Matrix2

Array for internal storage of elements.

add(AffinePolyVec) - Method in class HFE.AffinePolyVec

calculate this += whom as polynomial addition

add(AffinePolyVec) - Method in class HFE.SquarePolyVec

calculate this += whom as polynomial addition

add(AffinePolyVec, AffinePolyVec) - Method in class HFE.AffinePolyVec

calculates this = a + b as polynomial addition

add(Field2_n) - Method in class HFE.Field2_n

this += ter Adds two numbers using the xor function for intergers.

add(Field2_n, Field2_n) - Method in class HFE.Field2_n

this = ter1 + ter2 Adds two numbers using the xor function for intergers.

add(int, int) - Static method in class HFE.Field2

Adds two numbers using the xor function for intergers.

add(int, int) - Method in class HFE.Poly2MultiSquare

calculate this[i] += whom in terms of coefficient addition

add(Matrix2) - Method in class HFE.Matrix2

C = A + B

add(Poly2_nMax) - Method in class HFE.Poly2_nMax

calculate this += whom as polynomial addition

add(Poly2_nMax, Poly2_nMax) - Method in class HFE.Poly2_nMax

calculates this = wen1 + wen2 as polynomial addition

add(Poly2Max) - Method in class HFE.Poly2Max

calculate this += whom as polynomial addition

add(Poly2Max, Poly2Max) - Method in class HFE.Poly2Max

calculates this = wen1 + wen2 as polynomial addition

add(Poly2MultiLinear) - Method in class HFE.Poly2MultiLinear

calculate this += whom as polynomial addition

add(Poly2MultiLinear) - Method in class HFE.Poly2MultiSquare

calculate this += whom as polynomial addition

add(Poly2MultiLinear, Poly2MultiLinear) - Method in class HFE.Poly2MultiLinear

calculates this = a + b as polynomial addition

add(Poly2MultiSquare) - Method in class HFE.Poly2MultiSquare

calculate this += whom as polynomial addition

add(Poly2MultiSquare, Poly2MultiSquare) - Method in class HFE.Poly2MultiSquare

calculates this = a + b as polynomial addition

add(SquarePolyVec) - Method in class HFE.SquarePolyVec

calculate this += whom as polynomial addition

add(SquarePolyVec, SquarePolyVec) - Method in class HFE.SquarePolyVec

calculates this = a + b as polynomial addition

addEquals(Matrix2) - Method in class HFE.Matrix2

A += B

addMod(Poly2Max) - Method in class HFE.Poly2Max

Computes this = (this+b)%modul.

addMod(Poly2Max, Poly2Max) - Method in class HFE.Poly2Max

Computes this = (a+b)%modul.

addModul() - Method in class HFE.Field2_n

this += generating polynomial Adds the modul to this.

addOne() - Method in class HFE.Field2_n

this += 1 - adds one to this

addOne() - Method in class HFE.Poly2_nMax

calculate this += 1 as polynomial addition

addRowsEquals(int, int) - Method in class HFE.Matrix2

A[i] += A[j].

addRowsEquals(int, int, int) - Method in class HFE.Matrix2

A[i] += f*A[j].

AffinePolyVec - class HFE.AffinePolyVec.

This class provides a vector of polynomials of degree one in n independent variables.

AffinePolyVec() - Constructor for class HFE.AffinePolyVec

Initializes all coefficients to zero.

AffinePolyVec(AffinePolyVec) - Constructor for class HFE.AffinePolyVec

Creates a copy from the given polynomial.

AffinePolyVec(Transform2) - Constructor for class HFE.AffinePolyVec

AffinePolyVec.transform2poly(HFE.Transform2)

allocMem() - Method in class HFE.Poly2_nMax

Allocates new memory.

apply(Field2_n, Field2_n) - Method in class HFE.AffinePolyVec

Evaluate the polynomial using the given value vector

apply(Field2_n, Field2_n) - Method in class HFE.SquarePolyVec

Evaluate the polynomial using the given value vector The entry value[0] is _not_ uses, value[1] is the first valid entry.

apply(Field2_n, int[]) - Method in class HFE.AffinePolyVec

Evaluate the polynomial using the given value vector The entry value[0] is _not_ uses, value[1] is the first valid entry.

apply(Field2_n, int[]) - Method in class HFE.SquarePolyVec

Evaluate the polynomial using the given value vector The entry value[0] is _not_ uses, value[1] is the first valid entry.

apply(int[]) - Method in class HFE.Poly2MultiLinear

Evaluate the polynomial using the given value vector The entry value[0] is _not_ uses, value[1] is the first valid entry.

apply(int[]) - Method in class HFE.Poly2MultiSquare

Evaluate the polynomial using the given value vector.

apply(int[], int[]) - Static method in class HFE.Poly2MultiLinear

Evaluate the polynomial using the given value vector and the given coefficient vector.

apply(int[], int[]) - Static method in class HFE.Poly2MultiSquare

Evaluate the polynomial using the given value vector and the given coefficient vector.

applyLinear(Field2_n, Field2_n) - Method in class HFE.AffinePolyVec

Evaluate the polynomial using the given value vector.

applyPoly(Field2_n) - Method in class HFE.Poly2_nMax

Uses the given polynomial as a function.

applyQL(Field2_n, Field2_n) - Method in class HFE.Poly2_nMax

res = P(num) Assumes that the polynomial has a special form, namely no constant term, and all other terms have a power of Hamming weight 2 at most.

aqlTmp - Static variable in class HFE.Poly2_nMax

register for the use in applyQL.

aqlTmp2 - Static variable in class HFE.Poly2_nMax

register for the use in applyQL.

aqlVec - Static variable in class HFE.Poly2_nMax

registers for the use in applyQL.

array2poly(int[]) - Method in class HFE.Poly2Max

Sets the coefficients using the given power array.

array2poly(int[]) - Method in class HFE.Poly2MultiLinear

Sets the coefficients using the given coefficient.

array2poly(int[]) - Method in class HFE.Poly2MultiSquare

Sets the coefficients using the given coefficient.

assert(boolean) - Static method in class HFE.Check

Throws an Illegal Argument Exception if (statement == false).

assert(boolean, String) - Static method in class HFE.Check

Throws an Illegal Argument Exception if (statement == false).

C

Check - class HFE.Check.

Provides a assertion checker for HFE which is quite similar to the assertion facility of Java 1.4.

Check() - Constructor for class HFE.Check

checkBit(int) - Method in class HFE.Field2_n

Checks if the bit at position where is set.

checkMatrixDimensions(Matrix2) - Method in class HFE.Matrix2

Check if size(A) == size(B)

CheckRoot - interface HFE.CheckRoot.

Interface for RootFinding.

checkRoot(CheckRoot) - Method in class HFE.RootFinding

checks if S obtains a new root for f[0..regNum-1]

checkRoot(Field2_n) - Method in interface HFE.CheckRoot

Checks if the root is the one which is wanted by HFE.

checkRoot(Field2_n) - Method in class HFE.HFE2_n

Collects the roots.

checkRoot(Field2_n) - Method in class HFE.RootFinding

for debugging purposes only: returns if the root which was found is correct!

clearBit(int) - Method in class HFE.Field2_n

Clears bit at position where.

clone() - Method in class HFE.Matrix2

Clone the Matrix object.

cntDegree() - Method in class HFE.Field2_n

find the degree of this - i.e.

codeVec - Static variable in class HFE.HFE2_n

Cipher as a vector.

coeff - Variable in class HFE.AffinePolyVec

Coefficients for the variables.

coeff - Variable in class HFE.Poly2MultiLinear

Coefficients for the variables.

coeff - Variable in class HFE.Poly2MultiSquare

Coefficients for the variables.

coeff - Variable in class HFE.SquarePolyVec

Coefficients for the variables.

coeff(int) - Method in class HFE.AffinePolyVec

Returns the coefficients for a given variable.

coeff(int) - Method in class HFE.Poly2Max

Returns te coefficient for a given degree which (i.e.

coeff(int) - Method in class HFE.Poly2MultiLinear

Returns the coefficient for a given variable.

coeff(int) - Method in class HFE.SquarePolyVec

Returns the coefficients for a given variable.

coeffNum - Static variable in class HFE.SquarePolyVec

The number of coefficients in this polynomial

coeffs() - Method in class HFE.AffinePolyVec

returns the coefficient array without copying it.

coeffs() - Method in class HFE.Poly2MultiLinear

returns the coefficient array without copying it.

coeffs() - Method in class HFE.Poly2MultiSquare

returns the coefficient array without copying it.

coeffs() - Method in class HFE.SquarePolyVec

returns the coefficient array without copying it.

compDeg(int) - Method in class HFE.RootFinding

Method for register handling.

copy() - Method in class HFE.Matrix2

Make a deep copy of a matrix Allocates new memory

copy(Field2_n) - Method in class HFE.Field2_n

this = ter - copies father integerwise into this

copy(Poly2_nMax) - Method in class HFE.Poly2_nMax

Takes one polynomial and copies it.

copy(SquarePolyVec) - Method in class HFE.SquarePolyVec

Copies the coefficients from another polynomial vector

copyShift(Poly2_nMax, int) - Method in class HFE.Poly2_nMax

Takes one polynomial and shifts it by the given shift.

D

degF - Variable in class HFE.RootFinding

registers for root finding algorithm.

degree - Static variable in class HFE.Field2_n

Degree of the underlying irreducible polynomial.

degree() - Method in class HFE.Poly2Max

Returns the degree of the object.

degree() - Method in class HFE.Poly2_nMax

Returns the degree of the object.

det() - Method in class HFE.LUDecomposition2

Determinant

div_A - Static variable in class HFE.Field2_n

static registers for division

div_B - Static variable in class HFE.Field2_n

static registers for division

div_tmp - Static variable in class HFE.Field2_n

static register for division

div_tmp - Static variable in class HFE.Poly2_nMax

static variable for method div

div_V - Static variable in class HFE.Field2_n

static registers for division

div(Field2_n) - Method in class HFE.Field2_n

this /= fac - divides this by fac usind finite field arithmetic in GF(2^n) and stores the result in this.

div(Field2_n, Field2_n) - Method in class HFE.Field2_n

this = whom / by in GF(2^n) - divides two numbers using finite field arithmetic in GF(2^n).

div(int, int) - Static method in class HFE.Field2

Divides two numbers using finite field arithmetic in F_2.

div(Poly2_nMax, Poly2_nMax) - Method in class HFE.Poly2_nMax

Calculates this = a / b and assumes that there is _no_ remainder, i.e.

divS(Poly2_nMax, Poly2_nMax) - Method in class HFE.Poly2_nMax

Calculates this = a / b and assumes that there is _no_ remainder! Slow implementation, use Poly2_nMax.div(HFE.Poly2_nMax, HFE.Poly2_nMax) instead!

dummy - Static variable in class HFE.Field2_n

dummy value, which is initialized only once.

E

elements - Static variable in class HFE.Field2

number of elements in this field

elemNum - Static variable in class HFE.AffinePolyVec

The number of rows in this vector.

elemNum - Static variable in class HFE.SquarePolyVec

The number of rows in this vector.

encryptPrivate(Field2_n, Field2_n) - Method in class HFE.HFE2_n

Encryptes a given, n bit plain text.

even() - Method in class HFE.Field2_n

Checks if bit[0] is _not_ set, i.e.

extensionDegree - Static variable in class HFE.HFE2_n

Holds the degree of the irreducible polynomial and thereby also the degree of the extension field

F

f - Variable in class HFE.RootFinding

registers for root finding algorithm.

Field2 - class HFE.Field2.

This class encapsulates the operations for a finite field with 2 elements.

Field2_n - class HFE.Field2_n.

This class encapsulates the operations for a finite field with 2^n elements.

Field2_n() - Constructor for class HFE.Field2_n

Standart Constructor to obtain an element with all bits = 0

Field2_n(Field2_n) - Constructor for class HFE.Field2_n

Constructor to produce a copy of another Field2_n element

Field2_n(int) - Constructor for class HFE.Field2_n

Constructor to obtain an element with least significant integer set and the rest being 0

Field2_n(Random) - Constructor for class HFE.Field2_n

Constructor to obtain a random element

Field2() - Constructor for class HFE.Field2

findRoots(Poly2_nMax, CheckRoot) - Method in class HFE.RootFinding

finds all roots of given polynomial poly

foundRoot - Variable in class HFE.HFE2_n

signals if we found a root or not, i.e., if the root-field is valid or not.

G

gcd_tmp - Static variable in class HFE.Poly2_nMax

local variable for gcd algorithm.

gcd_tmpCoeff - Static variable in class HFE.Poly2_nMax

local variable for gcd algorithm.

gcd(Poly2_nMax, Poly2_nMax) - Method in class HFE.Poly2_nMax

Computes this = gcd(a,b) using an iterative gcd algorithm for polynomials.

generateKeys(byte[]) - Method in class HFE.HFE2_n

Generates the public and the private key from a given seed and stores them in the object's fields.

generateKeysInterpoly(byte[]) - Method in class HFE.HFE2_n

Generates the public and the private key from a given seed and stores them in the object's fields.

generateNonsingular(int, Random) - Static method in class HFE.LUDecomposition2

Generates a random nonsingular matrix of the given size.

generatingPolynomial - Static variable in class HFE.HFE2_n

Central switch to change generating polynomial.

generatingPolynomialAsMaxPoly - Static variable in class HFE.HFE2_n

Polynomial set in variable HFE2_n.generatingPolynomial but as a Poly2Max polynomial.

genPolyPrivate(SecureRandom) - Static method in class HFE.HFE2_n

Generates a private polynomial for HFE.

genPolyPublic() - Method in class HFE.HFE2_n

Generats the public polynomials from the private polynomial using base transformation.

genPolyPublicInterpoly(Poly2MultiSquare[]) - Method in class HFE.HFE2_n

Generats the public polynomials from the private polynomial using polynomial interpolation.

genPolyPublicSlow() - Method in class HFE.HFE2_n

Generats the public polynomials from the private polynomial using base transformation.

genSign(int[], int[]) - Method in class HFE.HFE2_n

Generates signature for given message using (S,P,T).

get(int, int) - Method in class HFE.Matrix2

Get a single element.

getArray() - Method in class HFE.Matrix2

Returns a pointer to the internal two-dimensional array.

getArrayCopy() - Method in class HFE.Matrix2

Copy the internal two-dimensional array.

getCoeff(Field2_n, int) - Method in class HFE.Poly2_nMax

get coefficient at position pos by copying it to res

getCoeff(int) - Method in class HFE.Poly2_nMax

get coefficient at position pos by constructing a new object from type Field2_n

getColumnDimension() - Method in class HFE.Matrix2

Get column dimension.

getColumnPackedCopy() - Method in class HFE.Matrix2

Make a one-dimensional column packed copy of the internal array.

getElement(int[]) - Method in class HFE.Field2_n

copies this to a bit vector

getMatrix(int[], int[]) - Method in class HFE.Matrix2

Get a submatrix.

getMatrix(int[], int, int) - Method in class HFE.Matrix2

Get a submatrix.

getMatrix(int, int, int[]) - Method in class HFE.Matrix2

Get a submatrix.

getMatrix(int, int, int, int) - Method in class HFE.Matrix2

Get a submatrix.

getRowDimension() - Method in class HFE.Matrix2

Get row dimension.

getRowPackedCopy() - Method in class HFE.Matrix2

Make a one-dimensional row packed copy of the internal array.

getTransform() - Method in class HFE.Transform2

returns the transformation in terms of polynomials

getValues(int[], int[]) - Static method in class HFE.Poly2MultiSquare

Calculates the square values using the linear values.

giveFree() - Method in class HFE.RootFinding

Method for register handling.

givePower(int) - Method in class HFE.Multi2Power

Returns the polynomial vector for a given power which.

giveVarNum() - Method in class HFE.Poly2MultiLinear

returns the number of variables for that object

H

HFE2_n - class HFE.HFE2_n.

This class is the "central class" of QuartzLight and is used for speed measurement.

HFE2_n(byte[]) - Constructor for class HFE.HFE2_n

Initializes HFE2_n by generating the public and the private key from the given seed.

I

identity(int, int) - Static method in class HFE.Matrix2

Generate identity matrix

initAll() - Static method in class HFE.Field2_n

initializes the static variables.

initAll() - Static method in class HFE.Multi2Mul

Init method for this class

initAll() - Static method in class HFE.Poly2_nMax

Initializes the static variables

initMem() - Method in class HFE.AffinePolyVec

Allocates new memory for the coefficients.

initMem() - Method in class HFE.Poly2MultiLinear

Allocates new memory for the coefficients.

initMem() - Method in class HFE.Poly2MultiSquare

Allocates new memory for the coefficients.

initMem() - Method in class HFE.SquarePolyVec

Allocates new memory for the coefficients.

int2poly(int) - Method in class HFE.Poly2Max

Sets the coefficients according to intValue.

isElement() - Method in class HFE.Field2_n

Checks if the current element is from Field2_n

isElement(Field2_n) - Static method in class HFE.Field2_n

Checks if a given integer is within the range of a GF(2^n) element.

isElement(Field2_n[]) - Static method in class HFE.Field2_n

Checks if a given vector consists only of Field2_n elements.

isElement(Field2_n[][]) - Static method in class HFE.Field2_n

Checks if a given matrix consists only of Field2_n elements.

isElement(int) - Static method in class HFE.Field2

Checks if a given integer is within the range of a Field2 element.

isElement(int[]) - Static method in class HFE.Field2

Checks if a given vector consists only of Field2 elements.

isElement(int[][]) - Static method in class HFE.Field2

Checks if a given matrix consists only of Field2 elements.

isEqual(AffinePolyVec) - Method in class HFE.AffinePolyVec

Compares this and whom coefficientwise.

isEqual(Field2_n) - Method in class HFE.Field2_n

Checks if this and who are bitwise equal

isEqual(Matrix2) - Method in class HFE.Matrix2

Compares two matrices.

isEqual(Poly2_nMax) - Method in class HFE.Poly2_nMax

Compares the current polynomial with the given one.

isEqual(Poly2Max) - Method in class HFE.Poly2Max

Compares the current polynomial with the given one.

isEqual(Poly2MultiLinear) - Method in class HFE.Poly2MultiLinear

Compares this and whom coefficientwise.

isEqual(Poly2MultiSquare) - Method in class HFE.Poly2MultiSquare

Compares this and whom coefficientwise.

isEqual(SquarePolyVec) - Method in class HFE.SquarePolyVec

Compares this and whom coefficientwise.

isNonsingular() - Method in class HFE.LUDecomposition2

Is the matrix nonsingular?

isZero() - Method in class HFE.Field2_n

Checks if the element is the zero element

isZero() - Method in class HFE.Poly2Max

Checks if a polynomial is the zero polynomial.

isZero() - Method in class HFE.Poly2MultiLinear

Checks if the polynomial is the zero polynomial.

isZero() - Method in class HFE.Poly2MultiSquare

Checks if the polynomial is the zero polynomial.

isZero() - Method in class HFE.Poly2_nMax

Checks if a polynomial is the zero polynomial.

L

lu - Variable in class HFE.Transform2

holds the LU decomposition of matrix M for the reverse affine transformation.

LU - Variable in class HFE.LUDecomposition2

Array for internal storage of decomposition.

lu() - Method in class HFE.Matrix2

LU Decomposition

LUDecomposition2 - class HFE.LUDecomposition2.

This class encapsulates the operations for LUDecomposition for matrices over the finite field F_2).

LUDecomposition2(Matrix2) - Constructor for class HFE.LUDecomposition2

LU Decomposition

M

m - Variable in class HFE.LUDecomposition2

Row and column dimensions, and pivot sign.

m - Variable in class HFE.Matrix2

Row (m) and column (n) dimensions.

m - Variable in class HFE.Transform2

holds the vector m for the affine transformation.

M - Variable in class HFE.Transform2

holds the bijective matrix M for the affine transformation.

main(String[]) - Static method in class HFE.AffinePolyVec

Mainly invoces the AffinePolyVec.testIt() method.

main(String[]) - Static method in class HFE.Check

main(String[]) - Static method in class HFE.Field2

Tests everything in this class

main(String[]) - Static method in class HFE.Field2_n

Tests everything in this class

main(String[]) - Static method in class HFE.HFE2_n

Tests everything in this class

main(String[]) - Static method in class HFE.LUDecomposition2

Tests everything in this class

main(String[]) - Static method in class HFE.Matrix2

Tests everything in this class

main(String[]) - Static method in class HFE.Multi2Mul

Calls the Multi2Mul.testIt() method

main(String[]) - Static method in class HFE.Multi2Power

Calls the Multi2Power.testIt() method

main(String[]) - Static method in class HFE.Poly2Max

Mainly invoces the Poly2Max.testIt() method.

main(String[]) - Static method in class HFE.Poly2MultiLinear

Mainly invoces the Poly2MultiLinear.testIt() method.

main(String[]) - Static method in class HFE.Poly2MultiSquare

Mainly invoces the Poly2MultiSquare.testIt() method.

main(String[]) - Static method in class HFE.Poly2_nMax

Mainly invoces the Poly2_nMax.testIt() method.

main(String[]) - Static method in class HFE.RootFinding

Tests everything in this class

main(String[]) - Static method in class HFE.SpeedTest

Has some speed measurements

main(String[]) - Static method in class HFE.SquarePolyVec

Mainly invoces the SquarePolyVec.testIt() method.

main(String[]) - Static method in class HFE.Transform2

Calls the Transform2.testIt() method

Matrix2 - class HFE.Matrix2.

The class Matrix2 provides matrix operations for matrices over the finite field F_2 which is specified in Field2.

Matrix2(int[][]) - Constructor for class HFE.Matrix2

Construct a matrix using the given array with checking.

Matrix2(int[][], int, int) - Constructor for class HFE.Matrix2

Construct a matrix using the given array without checking.

Matrix2(int, int) - Constructor for class HFE.Matrix2

Construct an m-by-n matrix of zeros.

Matrix2(int, int, Random) - Constructor for class HFE.Matrix2

Generats an m-by-n random matrix.

maxLen - Static variable in class HFE.Poly2Max

Maximal length of the polynomials

maxLen - Static variable in class HFE.Poly2_nMax

Maximal length of the polynomials

messageSigLength - Static variable in class HFE.HFE2_n

Holds the number of bits for a message in terms of a signature.

mod_divRes - Static variable in class HFE.Poly2_nMax

second static variable for our mod method

mod_tmp - Static variable in class HFE.Poly2_nMax

static variable for mod method

mod() - Method in class HFE.Poly2Max

Calculates this %= moduls.

mod() - Method in class HFE.Poly2_nMax

Calculates this %= moduls.

mod(Poly2_nMax) - Method in class HFE.Poly2_nMax

Calculates this %= b

mod(Poly2_nMax, Poly2_nMax) - Method in class HFE.Poly2_nMax

Calculates this = a % b

mod(Poly2Max) - Method in class HFE.Poly2Max

Calculates this %= b

mod(Poly2Max, Poly2Max) - Method in class HFE.Poly2Max

Calculates this = a % b

modS_additive - Static variable in class HFE.Poly2_nMax

static variable for our mod method

modS_tmp - Static variable in class HFE.Poly2_nMax

second static variable for our mod method

modS(Poly2_nMax) - Method in class HFE.Poly2_nMax

Calculates this %= b slow but working implementation of mod

modulus - Static variable in class HFE.Poly2Max

Modulus for the mod version of the operations

modulus - Static variable in class HFE.Poly2_nMax

Modulus for the mod version of the operations

mul_resL - Static variable in class HFE.Multi2Mul

Holds a static variable for the sake of speed which is used in mul.

mul_tmp - Static variable in class HFE.Field2_n

static register for multiplication

mul_tmp - Static variable in class HFE.Poly2_nMax

Static register for multiplication

mul_tmpL - Static variable in class HFE.Multi2Mul

Holds a static variable for the sake of speed which is used in mul.

mul_tmpS - Static variable in class HFE.Multi2Mul

Holds a static variable for the sake of speed which is used in mul.

mul(AffinePolyVec, AffinePolyVec) - Method in class HFE.SquarePolyVec

res = fac1*fac2 in terms of affine polynomial vector multiplication

mul(AffinePolyVec, Field2_n) - Method in class HFE.AffinePolyVec

res = fac*this in terms of affine polynomial vector multiplication

mul(Field2_n) - Method in class HFE.Field2_n

this *= fac - multiplies two numbers using finite field arithmetic in GF(2^n) and stores the result in this.

mul(Field2_n) - Method in class HFE.SquarePolyVec

this *= fac in terms of quadratic polynomial vector multiplication

mul(Field2_n, Field2_n) - Method in class HFE.Field2_n

this = fac1 * fac2 - multiplies two numbers using finite field arithmetic in GF(2^n) and stores the result in this.

mul(int[], int[]) - Method in class HFE.Matrix2

Linear algebraic matrix/vector multiplication, res = A * b.

mul(int[], Poly2MultiLinear[]) - Method in class HFE.Multi2Mul

Computes res = con * poly in terms of vector multiplication of polynomials.

mul(int[], Poly2MultiLinear[], Poly2MultiLinear[]) - Method in class HFE.Multi2Mul

Computes res = con * a * b in terms of vector multiplication of polynomials.

mul(int, int) - Static method in class HFE.Field2

Multiplies two numbers using finite field arithmetic in F_4.

mul(Matrix2) - Method in class HFE.Matrix2

Linear algebraic matrix multiplication, A * B.

mul(Poly2_nMax, Poly2_nMax) - Method in class HFE.Poly2_nMax

calculates this = a * b as polynomial multiplication Assumes that a.degree + b.degree < maxLen

mul(Poly2Max, Poly2Max) - Method in class HFE.Poly2Max

calculates this = a * b as polynomial addition.

mul(Poly2MultiLinear[], int[], Poly2MultiLinear[]) - Method in class HFE.Multi2Mul

Computes res = con * poly in terms of vector multiplication of polynomials.

mul(Poly2MultiLinear[], Poly2MultiLinear[]) - Method in class HFE.Multi2Mul

Computes res = a * b in terms of vector multiplication of polynomials.

mul(Poly2MultiLinear, Poly2MultiLinear) - Method in class HFE.Poly2MultiSquare

Calculates this = a*b in terms of polynomial multiplication.

mul(Poly2MultiSquare[], int[], Poly2MultiLinear[], Poly2MultiLinear[]) - Method in class HFE.Multi2Mul

Computes res = con * a * b in terms of vector multiplication of polynomials.

mul2(int[], Poly2MultiLinear[], Poly2MultiLinear[]) - Method in class HFE.Multi2Mul

Computes res = con * a * b in terms of vector multiplication of polynomials.

mul2(Poly2MultiLinear[], Poly2MultiLinear[]) - Method in class HFE.Multi2Mul

Computes res = a * b in terms of vector multiplication of polynomials.

mulAdd_coeff - Variable in class HFE.Poly2_nMax

static variable for mulAdd

mulAdd(Field2_n, Poly2_nMax) - Method in class HFE.Poly2_nMax

compute this = coeff*poly where coeff is from GF(2^n) and poly is an object of type Poly2_nMax

mulAdd(int, Poly2MultiSquare) - Method in class HFE.Poly2MultiSquare

this += factor*whom.

mulAdd(Poly2MultiLinear, Poly2MultiLinear) - Method in class HFE.Poly2MultiSquare

Calculates this += a*b in terms of polynomial multiplication.

mulFactor(Field2_n) - Method in class HFE.Poly2_nMax

multiplies all coefficients by the given factor in GF(2^n) uses static memory to store the result of each step

mulFactor(int) - Method in class HFE.Poly2Max

multiplies all coefficients by the given factor in F_2.

mulMod(Poly2Max, Poly2Max) - Method in class HFE.Poly2Max

Computes this = (a*b)%modul.

mulSlow(AffinePolyVec, AffinePolyVec) - Method in class HFE.SquarePolyVec

res = fac1*fac2 in terms of affine polynomial vector multiplication.

Multi2Mul - class HFE.Multi2Mul.

This class deals with multi-variable polynomials and a general modulus provied to the constructor.

Multi2Mul(Poly2Max) - Constructor for class HFE.Multi2Mul

Initializes the internal field Multi2Mul.reduce

Multi2Power - class HFE.Multi2Power.

This class deals with multi-variable polynomials and a general modulus provied to the constructor.

Multi2Power(Poly2Max, Poly2MultiLinear[], int) - Constructor for class HFE.Multi2Power

Initializes the internal fields

mulTmp1 - Static variable in class HFE.SquarePolyVec

Static register for multiplication of two vectors

mulTmp2 - Static variable in class HFE.SquarePolyVec

mulX() - Method in class HFE.Field2_n

this *= x assumes that there is no reduction necessary

N

n - Variable in class HFE.LUDecomposition2

Row and column dimensions, and pivot sign.

n - Variable in class HFE.Matrix2

Row (m) and column (n) dimensions.

number - Variable in class HFE.Field2_n

Allocats memory for elements of this class

P

padBits - Static variable in class HFE.HFE2_n

Holds the number of bits for a message in terms of a signature.

piv - Variable in class HFE.LUDecomposition2

Internal storage of pivot vector.

Poly2_nMax - class HFE.Poly2_nMax.

This class encapsulates the operations for polynomials over the finite field F_64 which is an extension over F_4.

Poly2_nMax() - Constructor for class HFE.Poly2_nMax

sets all the coefficients to zero and allocates new memory

Poly2_nMax(Poly2_nMax) - Constructor for class HFE.Poly2_nMax

Creates a copy from the given polynomial

Poly2_nMax(Poly2_nMax, int) - Constructor for class HFE.Poly2_nMax

Takes one polynomial and shifts it by the given shift.

Poly2_nMax(Random) - Constructor for class HFE.Poly2_nMax

Generates a polynomial with random coefficients.

Poly2_nMax(Random, int) - Constructor for class HFE.Poly2_nMax

Generates a polynomial with random coefficient.

Poly2Max - class HFE.Poly2Max.

This class provides polynomials of positive degree over the finite field F_2 which is provided in the class Field2.

Poly2Max() - Constructor for class HFE.Poly2Max

sets all the coefficients to zero

Poly2Max(int) - Constructor for class HFE.Poly2Max

Creates a new polynomial.

Poly2Max(int[]) - Constructor for class HFE.Poly2Max

Poly2Max.array2poly(int[])

Poly2Max(Poly2Max) - Constructor for class HFE.Poly2Max

Creates a copy from the given polynomial

Poly2Max(Poly2Max, int) - Constructor for class HFE.Poly2Max

Takes one polynomial and shifts it by the given shift.

Poly2MultiLinear - class HFE.Poly2MultiLinear.

This class provides polynomials of degree one in n independent variables.

Poly2MultiLinear() - Constructor for class HFE.Poly2MultiLinear

sets all the coefficients to zero assumes that the polynomial has no variables

Poly2MultiLinear(int) - Constructor for class HFE.Poly2MultiLinear

Sets all the coefficients to zero by allocating new memory.

Poly2MultiLinear(int[]) - Constructor for class HFE.Poly2MultiLinear

Poly2MultiLinear.array2poly(int[])

Poly2MultiLinear(int, int[]) - Constructor for class HFE.Poly2MultiLinear

Creates a new object by using inArray for the coefficients.

Poly2MultiLinear(Poly2MultiLinear) - Constructor for class HFE.Poly2MultiLinear

Creates a copy from the given polynomial.

Poly2MultiSquare - class HFE.Poly2MultiSquare.

This class provides polynomials of degree two in n independent variables.

Poly2MultiSquare() - Constructor for class HFE.Poly2MultiSquare

sets all the coefficients to zero assumes that the polynomial has no variables

Poly2MultiSquare(int) - Constructor for class HFE.Poly2MultiSquare

Sets all the coefficients to zero by allocating new memory.

Poly2MultiSquare(int[]) - Constructor for class HFE.Poly2MultiSquare

Poly2MultiSquare.array2poly(int[])

Poly2MultiSquare(int, int[]) - Constructor for class HFE.Poly2MultiSquare

Creates a new object by using inArray for the coefficients.

Poly2MultiSquare(int, Random) - Constructor for class HFE.Poly2MultiSquare

Sets all the coefficients to a random value and also allocates new memory for these coefficients.

Poly2MultiSquare(Poly2MultiLinear) - Constructor for class HFE.Poly2MultiSquare

Creates a copy from the given linear polynomial.

Poly2MultiSquare(Poly2MultiLinear, Poly2MultiLinear) - Constructor for class HFE.Poly2MultiSquare

Multiplies two lineare polynomials and stores the result in a new object.

Poly2MultiSquare(Poly2MultiSquare) - Constructor for class HFE.Poly2MultiSquare

Creates a copy from the given polynomial.

polyInt() - Method in class HFE.Poly2Max

Returns the polynomial as an integer.

pow(Poly2Max, int) - Method in class HFE.Poly2Max

calculates this = base^by.

privatePoly - Variable in class HFE.HFE2_n

Stores the private polynomial over GF(2^n).

publicPoly - Variable in class HFE.HFE2_n

Stores the public key in an array of polynomials.

R

reduce - Variable in class HFE.Multi2Mul

Stores all the reduction steps.

reductionTerm - Static variable in class HFE.Field2_n

Stores the reduction term as bit vector.

reductionTerm - Static variable in class HFE.HFE2_n

Central switch to change the reduction term, i.e.

regNum - Static variable in class HFE.RootFinding

number of registers in this machine.

regUsed - Variable in class HFE.RootFinding

bitvector.

resArray - Variable in class HFE.Multi2Power

Stores all the results.

resVec - Static variable in class HFE.HFE2_n

Message as a vector.

rnd - Variable in class HFE.HFE2_n

Random number generator for signature generation

rnd(Random) - Method in class HFE.AffinePolyVec

Initializes all coefficients with random bits

rnd(Random) - Static method in class HFE.Field2

returns a random element from Field2.

rnd(Random) - Method in class HFE.Field2_n

sets this to a random element from Field2_2.

rnd(Random) - Method in class HFE.Poly2MultiSquare

Sets all the coefficients to a random value without allocating new memory for these coefficients.

rnd(Random) - Method in class HFE.SquarePolyVec

Initializes all coefficients with random bits

rndBit(Random) - Static method in class HFE.Field2_n

returns a random position within current Field2_n

rootFinder - Variable in class HFE.HFE2_n

Root finding algorithm

RootFinding - class HFE.RootFinding.

This class computes root for a given polynomial over GF(2^n).

RootFinding() - Constructor for class HFE.RootFinding

initializes all variables in this class

rootVec - Static variable in class HFE.HFE2_n

Message as a vector.

rowCol - Static variable in class HFE.Transform2

the number of rows and columns, which is taken from the field extension.

S

S - Variable in class HFE.RootFinding

registers for root finding algorithm.

set(int, int, int) - Method in class HFE.Matrix2

Set a single element.

set(Random) - Method in class HFE.Matrix2

Generats an m-by-n random matrix.

setBit(int) - Method in class HFE.Field2_n

Sets bit at position where.

setCoeff(Field2_n, int) - Method in class HFE.Poly2_nMax

set coefficient at position pos _with_ copying it

setCoeff(Random, int) - Method in class HFE.Poly2_nMax

set coefficient at position pos with a random value

setCoeffs(Field2_n[]) - Method in class HFE.AffinePolyVec

Sets all the coefficients by the given array.

setCoeffs(Field2_n[]) - Method in class HFE.SquarePolyVec

Sets all the coefficients by the given array.

setCoeffs(int[]) - Method in class HFE.Poly2MultiLinear

Sets all the coefficients by the given array.

setCoeffs(int[]) - Method in class HFE.Poly2MultiSquare

Sets all the coefficients by the given array.

setElement(int[]) - Method in class HFE.Field2_n

sets field element regarding to a bit vector.

setFree(int) - Method in class HFE.RootFinding

Method for register handling.

setMatrix(int[], int[], Matrix2) - Method in class HFE.Matrix2

Set a submatrix.

setMatrix(int[], int, int, Matrix2) - Method in class HFE.Matrix2

Set a submatrix.

setMatrix(int, int, int[], Matrix2) - Method in class HFE.Matrix2

Set a submatrix.

setMatrix(int, int, int, int, Matrix2) - Method in class HFE.Matrix2

Set a submatrix.

setModulus(Poly2_nMax) - Static method in class HFE.Poly2_nMax

Sets the private field modulus.

setModulus(Poly2Max) - Static method in class HFE.Poly2Max

Sets the private field modulus.

setOne() - Method in class HFE.Field2_n

sets this to 1

setRowZero(int) - Method in class HFE.Matrix2

Set a row elementwise zero.

setZero() - Method in class HFE.AffinePolyVec

Sets all the coefficients to zero

setZero() - Method in class HFE.Field2_n

sets this to zero

setZero() - Method in class HFE.Poly2Max

Sets all the coefficients to zero by allocating new memory

setZero() - Method in class HFE.Poly2MultiLinear

Sets all the coefficients to zero

setZero() - Method in class HFE.Poly2MultiSquare

Sets all the coefficients to zero without allocating new memory.

setZero() - Method in class HFE.Poly2_nMax

Sets all the coefficients to zero without allocating new memory

setZero() - Method in class HFE.SquarePolyVec

Sets all the coefficients to zero

shiftL() - Method in class HFE.Field2_n

this <<= 1 - therefore computes a left shift of this by one bit.

shiftL(int) - Method in class HFE.Poly2_nMax

Shifts the current polynomial by the given number of places.

shiftLMod() - Method in class HFE.Field2_n

this <<= 1 % i(t) - therefore computes a left shift of this by one bit and reduces the result by the generating polynomials i(t).

shiftR() - Method in class HFE.Field2_n

this >>= 1 - therefore computes a right shift of this by one bit.

signatureLength - Static variable in class HFE.HFE2_n

Holds the number of bits for a signature.

sigTmpVec - Static variable in class HFE.HFE2_n

Hash of message as a vector.

size - Static variable in class HFE.Field2_n

determinates the size of elements of this class.

solve(int[], int[]) - Method in class HFE.LUDecomposition2

Solve A*x = b, i.e.

solve(Matrix2) - Method in class HFE.LUDecomposition2

Solve A*X = B

speedIt() - Static method in class HFE.HFE2_n

Tests how fast the package runs on the current hardware.

speedIt() - Static method in class HFE.Multi2Mul

Tests how fast the package runs on the current hardware.

speedIt() - Static method in class HFE.Poly2_nMax

speedIt() - Static method in class HFE.SquarePolyVec

Tests how fast the package runs on the current hardware.

speedSignatureSHA_1() - Static method in class HFE.SpeedTest

Tests how fast message signature runs on the current hardware.

SpeedTest - class HFE.SpeedTest.

Holds speed test routines for QuartzLight

SpeedTest() - Constructor for class HFE.SpeedTest

sqr() - Method in class HFE.AffinePolyVec

Computes an affine polynomial vector which is exactly a squaring of the original one.

sqr(Field2_n) - Method in class HFE.Field2_n

this = fac^2 This algorithm is not very fast, but will be replaced by a faster algorithm in the next version

square - Variable in class HFE.RootFinding

array of squares mod Poly.

squareMod(Poly2_nMax, Poly2_nMax, int) - Method in class HFE.Poly2_nMax

Calculates this = in^2 mod modul and used the fact that characteristic p=2 for GF(2^n) which means that squaring in GF(2^n) is cheaper than multiplication.

squareMul_tmp - Static variable in class HFE.Poly2_nMax

local variable for squareMod.

squareMul_tmpCoeff - Static variable in class HFE.Poly2_nMax

local variable for squareMod.

SquarePolyVec - class HFE.SquarePolyVec.

This class provides a vector of polynomials of degree one in n independent variables.

SquarePolyVec() - Constructor for class HFE.SquarePolyVec

Initializes all coefficients to zero.

SquarePolyVec(AffinePolyVec) - Constructor for class HFE.SquarePolyVec

Creates a copy from the given affine polynomial.

SquarePolyVec(AffinePolyVec, AffinePolyVec) - Constructor for class HFE.SquarePolyVec

Creates a new object as the product of two given affine polynomials

SquarePolyVec(SquarePolyVec) - Constructor for class HFE.SquarePolyVec

Creates a copy from the given polynomial.

stringIt() - Method in class HFE.Field2_n

converts this to a string

stringIt() - Method in class HFE.Poly2_nMax

transfer the polynomial to a string

sub(AffinePolyVec) - Method in class HFE.AffinePolyVec

calculate this -= whom as polynomial subtraction

sub(AffinePolyVec, AffinePolyVec) - Method in class HFE.AffinePolyVec

calculates this = a - b as polynomial subtraction

sub(Field2_n) - Method in class HFE.Field2_n

this -= ter Adds two numbers using the xor function for intergers.

sub(Field2_n, Field2_n) - Method in class HFE.Field2_n

this = ter1 - ter2 Subtracts two numbers using the xor function for intergers.

sub(int, int) - Static method in class HFE.Field2

Subtracts two numbers using the xor function for intergers.

sub(Matrix2) - Method in class HFE.Matrix2

C = A - B

sub(Poly2MultiLinear) - Method in class HFE.Poly2MultiLinear

calculate this -= whom as polynomial subtraction

sub(Poly2MultiLinear, Poly2MultiLinear) - Method in class HFE.Poly2MultiLinear

calculates this = a - b as polynomial subtraction

sub(Poly2MultiSquare) - Method in class HFE.Poly2MultiSquare

calculate this -= whom as polynomial subtraction

sub(Poly2MultiSquare, Poly2MultiSquare) - Method in class HFE.Poly2MultiSquare

calculates this = a - b as polynomial subtraction

sub(SquarePolyVec) - Method in class HFE.SquarePolyVec

calculate this -= whom as polynomial subtraction

sub(SquarePolyVec, SquarePolyVec) - Method in class HFE.SquarePolyVec

calculates this = a - b as polynomial subtraction

subEquals(Matrix2) - Method in class HFE.Matrix2

A -= B

T

tau_inverse(int) - Static method in class HFE.Poly2MultiSquare

Calulates the number of variables for a given number of terms t.

tau(int) - Static method in class HFE.Poly2MultiSquare

Calulates the number of terms for a given number of variables n by using the formula ((n+1)*(n+2))/2.

testIt() - Static method in class HFE.AffinePolyVec

Tests the functionality for the whole class.

testIt() - Static method in class HFE.Field2

Tests the functionality of the whole class.

testIt() - Static method in class HFE.Field2_n

Tests the functionality of the whole class.

testIt() - Static method in class HFE.HFE2_n

Tests the functionality of the whole class.

testIt() - Static method in class HFE.LUDecomposition2

Tests the functionality of the whole class.

testIt() - Static method in class HFE.Matrix2

Tests the functionality of the whole class.

testIt() - Static method in class HFE.Multi2Mul

Tests the functionality of the class.

testIt() - Static method in class HFE.Multi2Power

Tests the functionality of the class.

testIt() - Static method in class HFE.Poly2Max

Tests the functionality for the whole class.

testIt() - Static method in class HFE.Poly2MultiLinear

Tests the functionality for the whole class.

testIt() - Static method in class HFE.Poly2MultiSquare

Tests the functionality for the whole class.

testIt() - Static method in class HFE.Poly2_nMax

Tests the functionality for the whole class.

testIt() - Static method in class HFE.RootFinding

Tests the functionality of the whole class.

testIt() - Static method in class HFE.SquarePolyVec

Tests the functionality for the whole class.

testIt() - Static method in class HFE.Transform2

Tests the functionality of the class.

textVec - Static variable in class HFE.HFE2_n

Message as a vector.

tmpElem1 - Static variable in class HFE.HFE2_n

Temporary register [element of GF(2^n)].

tmpElem2 - Static variable in class HFE.HFE2_n

Temporary register [element of GF(2^n)].

tmpRoot - Variable in class HFE.RootFinding

temporary register for roots

tmpSqr - Static variable in class HFE.Field2_n

static values for squaring.

transform(int[], int[]) - Method in class HFE.Transform2

applies the transformation to a given vector, i.e.

transform(Poly2MultiSquare[]) - Method in class HFE.Transform2

Applies the transformation to a given vector of polynomials, i.e.

transform(Poly2MultiSquare[], SquarePolyVec) - Method in class HFE.Transform2

Applies the transformation to a given vector of polynomials, i.e.

transform(SquarePolyVec) - Method in class HFE.Transform2

Applies the transformation to a given vector of polynomials, i.e.

Transform2 - class HFE.Transform2.

Transform2 provides a affine transformation (i.e.

Transform2() - Constructor for class HFE.Transform2

Generates a affine transformation which is the identity, i.e.

Transform2(Random) - Constructor for class HFE.Transform2

Generates a affine transformation using a PRNG

transform2poly(Transform2) - Method in class HFE.AffinePolyVec

Transforms an affine transformation into an affine polynomial vector.

transform2poly(Transform2) - Method in class HFE.SquarePolyVec

Transforms an affine transformation into an affine polynomial vector.

transpose() - Method in class HFE.Matrix2

Matrix transpose.

transS - Variable in class HFE.HFE2_n

Transformation S in HFE

transSpoly - Variable in class HFE.HFE2_n

Transform S in HFE in terms of affine polynomials

transT - Variable in class HFE.HFE2_n

Transformation T in HFE

transTpoly - Variable in class HFE.HFE2_n

Transform T in HFE in terms of affine polynomials

U

untransform(int[], int[]) - Method in class HFE.Transform2

reverts the transformation to a given vector, i.e.

V

valSign(int[], int[]) - Method in class HFE.HFE2_n

Validates if given signature sig is valid or not.

value - Variable in class HFE.Poly2Max

Current value of the polynomial.

value - Variable in class HFE.Poly2_nMax

Current value of the polynomial.

valueVec - Static variable in class HFE.HFE2_n

Message in a special format as a vector.

varNum - Static variable in class HFE.AffinePolyVec

The number of variables in this polynomial.

varNum - Variable in class HFE.Poly2MultiLinear

The number of variables in this polynomial.

varNum - Variable in class HFE.Poly2MultiSquare

The number of variables in this polynomial.

varNum - Static variable in class HFE.SquarePolyVec

The number of variables in this polynomial.

W

writeString() - Method in class HFE.AffinePolyVec

Writes the polynomials as a string to stdout

writeString() - Method in class HFE.Poly2Max

Writes the polynomial as a string to stdout

writeString() - Method in class HFE.Poly2MultiLinear

Writes the polynomial as a string to stdout

writeString() - Method in class HFE.Poly2MultiSquare

Writes the polynomial as a string to stdout

writeString() - Method in class HFE.SquarePolyVec

Writes the polynomials as a string to stdout

writeString() - Method in class HFE.Transform2

Writes the current transformation to stdout

X

xorBit(int) - Method in class HFE.Field2_n

xors the bit at position where.

A C D E F G H I L M N P R S T U V W X