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The Bouncy Castle Crypto package is a Java implementation of cryptographic algorithms. This jar contains JCE provider and lightweight API for the Bouncy Castle Cryptography APIs for JDK 1.4.
package org.bouncycastle.pqc.crypto.qtesla;
import org.bouncycastle.util.Arrays;
class Polynomial
{
/**
* Size of A Random Number (in Byte)
*/
public static final int RANDOM = 32;
/**
* Size of A Seed (in Byte)
*/
public static final int SEED = 32;
/**
* Size of Hash Value C (in Byte) in the Signature Package
*/
public static final int HASH = 32;
/**
* Size of Hashed Message
*/
public static final int MESSAGE = 64;
/**
* Size of the Signature Package (Z, C) (in Byte) for Heuristic qTESLA Security Category-1.
* Z is A Polynomial Bounded by B and C is the Output of A Hashed String
*/
public static final int SIGNATURE_I = (Parameter.N_I * Parameter.D_I + 7) / 8 + HASH;
/**
* Size of the Signature Package (Z, C) (in Byte) for Heuristic qTESLA Security Category-3 (Option for Size).
* Z is A Polynomial Bounded by B and C is the Output of A Hashed String
*/
public static final int SIGNATURE_III_SIZE = (Parameter.N_III_SIZE * Parameter.D_III_SIZE + 7) / 8 + HASH;
/**
* Size of the Signature Package (Z, C) (in Byte) for Heuristic qTESLA Security Category-3 (Option for Speed).
* Z is A Polynomial Bounded by B and C is the Output of A Hashed String
*/
public static final int SIGNATURE_III_SPEED = (Parameter.N_III_SPEED * Parameter.D_III_SPEED + 7) / 8 + HASH;
/**
* Size of the Signature Package (Z, C) (in Byte) for Provably-Secure qTESLA Security Category-1.
* Z is A Polynomial Bounded by B and C is the Output of A Hashed String
*/
public static final int SIGNATURE_I_P = (Parameter.N_I_P * Parameter.D_I_P + 7) / 8 + HASH;
/**
* Size of the Signature Package (Z, C) (in Byte) for Provably-Secure qTESLA Security Category-3.
* Z is A Polynomial Bounded by B and C is the Output of A Hashed String
*/
public static final int SIGNATURE_III_P = (Parameter.N_III_P * Parameter.D_III_P + 7) / 8 + HASH;
/**
* Size of the Public Key (in Byte) Containing seedA and Polynomial T for Heuristic qTESLA Security Category-1
*/
public static final int PUBLIC_KEY_I = (Parameter.N_I * Parameter.K_I * Parameter.Q_LOGARITHM_I + 7) / 8 + SEED;
/**
* Size of the Public Key (in Byte) Containing seedA and Polynomial T for Heuristic qTESLA Security Category-3 (Option for Size)
*/
public static final int PUBLIC_KEY_III_SIZE = (Parameter.N_III_SIZE * Parameter.K_III_SIZE * Parameter.Q_LOGARITHM_III_SIZE + 7) / 8 + SEED;
/**
* Size of the Public Key (in Byte) Containing seedA and Polynomial T for Heuristic qTESLA Security Category-3 (Option for Speed)
*/
public static final int PUBLIC_KEY_III_SPEED = (Parameter.N_III_SPEED * Parameter.K_III_SPEED * Parameter.Q_LOGARITHM_III_SPEED + 7) / 8 + SEED;
/**
* Size of the Public Key (in Byte) Containing seedA and Polynomial T for Provably-Secure qTESLA Security Category-1
*/
public static final int PUBLIC_KEY_I_P = (Parameter.N_I_P * Parameter.K_I_P * Parameter.Q_LOGARITHM_I_P + 7) / 8 + SEED;
/**
* Size of the Public Key (in Byte) Containing seedA and Polynomial T for Provably-Secure qTESLA Security Category-3
*/
public static final int PUBLIC_KEY_III_P = (Parameter.N_III_P * Parameter.K_III_P * Parameter.Q_LOGARITHM_III_P + 7) / 8 + SEED;
/**
* Size of the Private Key (in Byte) Containing Polynomials (Secret Polynomial and Error Polynomial) and Seeds (seedA and seedY)
* for Heuristic qTESLA Security Category-1
*/
public static final int PRIVATE_KEY_I = Parameter.N_I * Parameter.S_BIT_I / Const.BYTE_SIZE * 2 + SEED * 2;
/**
* Size of the Private Key (in Byte) Containing Polynomials (Secret Polynomial and Error Polynomial) and Seeds (seedA and seedY)
* for Heuristic qTESLA Security Category-3 (Option for Size)
*/
public static final int PRIVATE_KEY_III_SIZE = Parameter.N_III_SIZE * Parameter.S_BIT_III_SIZE / Const.BYTE_SIZE * 2 + SEED * 2;
/**
* Size of the Private Key (in Byte) Containing Polynomials (Secret Polynomial and Error Polynomial) and Seeds (seedA and seedY)
* for Heuristic qTESLA Security Category-3 (Option for Speed)
*/
public static final int PRIVATE_KEY_III_SPEED = Parameter.N_III_SPEED * Parameter.S_BIT_III_SPEED / Const.BYTE_SIZE * 2 + SEED * 2;
/**
* Size of the Private Key (in Byte) Containing Polynomials (Secret Polynomial and Error Polynomial) and Seeds (seedA and seedY)
* for Provably-Secure qTESLA Security Category-1
*/
public static final int PRIVATE_KEY_I_P = Parameter.N_I_P + Parameter.N_I_P * Parameter.K_I_P + SEED * 2;
/**
* Size of the Private Key (in Byte) Containing Polynomials (Secret Polynomial and Error Polynomial) and Seeds (seedA and seedY)
* for Provably-Secure qTESLA Security Category-3
*/
public static final int PRIVATE_KEY_III_P = Parameter.N_III_P + Parameter.N_III_P * Parameter.K_III_P + SEED * 2;
/****************************************************************************
* Description: Montgomery Reduction for Heuristic qTESLA Security Category 1
* and Security Category-3 (Option for Size and Speed)
*
* @param number Number to be Reduced
* @param q Modulus
* @param qInverse
*
* @return Reduced Number
****************************************************************************/
private static int montgomery(long number, int q, long qInverse)
{
return (int)((number + ((number * qInverse) & 0xFFFFFFFFL) * q) >> 32);
}
/****************************************************************************
* Description: Montgomery Reduction for Provably-Secure qTESLA
* Security Category-1 and Security Category-3
*
* @param number Number to be Reduced
* @param q Modulus
* @param qInverse
*
* @return Reduced Number
****************************************************************************/
private static long montgomeryP(long number, int q, long qInverse)
{
return (number + ((number * qInverse) & 0xFFFFFFFFL) * q) >> 32;
}
/**********************************************************************************************
* Description: Barrett Reduction for Heuristic qTESLA Security Category-3
* (Option for Size or Speed)
*
* @param number Number to be Reduced
* @param barrettMultiplication
* @param barrettDivision
* @param q Modulus
*
* @return Reduced Number
**********************************************************************************************/
public static int barrett(int number, int q, int barrettMultiplication, int barrettDivision)
{
return number - (int)(((long)number * barrettMultiplication) >> barrettDivision) * q;
}
/*************************************************************************************************
* Description: Barrett Reduction for Provably-Secure qTESLA Security Category-1 and
* Security Category-3
*
* @param number Number to be Reduced
* @param barrettMultiplication
* @param barrettDivision
* @param q Modulus
*
* @return Reduced Number
*************************************************************************************************/
public static long barrett(long number, int q, int barrettMultiplication, int barrettDivision)
{
return number - ((number * barrettMultiplication) >> barrettDivision) * q;
}
/************************************************************************************************************
* Description: Forward Number Theoretic Transform for Heuristic qTESLA Security Category-1,
* Security Category-3 (Option for Size and Speed)
*
* @param destination Destination of Transformation
* @param source Source of Transformation
* @param n Polynomial Degree
* @param q Modulus
* @param qInverse
*
* @return none
************************************************************************************************************/
private static void numberTheoreticTransform(int destination[], int source[], int n, int q, long qInverse)
{
int jTwiddle = 0;
int numberOfProblem = n >> 1;
for (; numberOfProblem > 0; numberOfProblem >>= 1)
{
int j = 0;
int jFirst;
for (jFirst = 0; jFirst < n; jFirst = j + numberOfProblem)
{
long omega = source[jTwiddle++];
for (j = jFirst; j < jFirst + numberOfProblem; j++)
{
int temporary = montgomery(omega * destination[j + numberOfProblem], q, qInverse);
destination[j + numberOfProblem] = destination[j] - temporary;
destination[j] = destination[j] + temporary;
}
}
}
}
/**************************************************************************************************************
* Description: Forward Number Theoretic Transform for Provably-Secure qTESLA Security Category-1
*
* @param destination Destination of Transformation
* @param source Source of Transformation
*
* @return none
**************************************************************************************************************/
private static void numberTheoreticTransformIP(long destination[], long source[])
{
int numberOfProblem = Parameter.N_I_P >> 1;
int jTwiddle = 0;
for (; numberOfProblem > 0; numberOfProblem >>= 1)
{
int j = 0;
int jFirst;
for (jFirst = 0; jFirst < Parameter.N_I_P; jFirst = j + numberOfProblem)
{
long omega = source[jTwiddle++];
for (j = jFirst; j < jFirst + numberOfProblem; j++)
{
long temporary = montgomeryP(
omega * destination[j + numberOfProblem],
Parameter.Q_I_P, Parameter.Q_INVERSE_I_P
);
destination[j + numberOfProblem] = destination[j] + (Parameter.Q_I_P - temporary);
destination[j] = destination[j] + temporary;
}
}
}
}
/**************************************************************************************************************
* Description: Forward Number Theoretic Transform for Provably-Secure qTESLA Security Category-3
*
* @param destination Destination of Transformation
* @param source Source of Transformation
*
* @return none
**************************************************************************************************************/
private static void numberTheoreticTransformIIIP(long destination[], long source[])
{
int jTwiddle = 0;
int numberOfProblem = Parameter.N_III_P >> 1;
for (; numberOfProblem > 0; numberOfProblem >>= 1)
{
int j = 0;
int jFirst;
for (jFirst = 0; jFirst < Parameter.N_III_P; jFirst = j + numberOfProblem)
{
int omega = (int)source[jTwiddle++];
for (j = jFirst; j < jFirst + numberOfProblem; j++)
{
long temporary = barrett(
montgomeryP(
omega * destination[j + numberOfProblem],
Parameter.Q_III_P,
Parameter.Q_INVERSE_III_P
),
Parameter.Q_III_P,
Parameter.BARRETT_MULTIPLICATION_III_P,
Parameter.BARRETT_DIVISION_III_P
);
destination[j + numberOfProblem] = barrett(
destination[j] + (2L * Parameter.Q_III_P - temporary),
Parameter.Q_III_P,
Parameter.BARRETT_MULTIPLICATION_III_P,
Parameter.BARRETT_DIVISION_III_P
);
destination[j] = barrett(
destination[j] + temporary,
Parameter.Q_III_P,
Parameter.BARRETT_MULTIPLICATION_III_P,
Parameter.BARRETT_DIVISION_III_P
);
}
}
}
}
/******************************************************************************************************************
* Description: Inverse Number Theoretic Transform for Heuristic qTESLA Security Category-1
*
* @param destination Destination of Inverse Transformation
* @param source Source of Inverse Transformation
*
* @return none
******************************************************************************************************************/
private static void inverseNumberTheoreticTransformI(int destination[], int source[])
{
int jTwiddle = 0;
for (int numberOfProblem = 1; numberOfProblem < Parameter.N_I; numberOfProblem *= 2)
{
int j = 0;
int jFirst;
for (jFirst = 0; jFirst < Parameter.N_I; jFirst = j + numberOfProblem)
{
long omega = source[jTwiddle++];
for (j = jFirst; j < jFirst + numberOfProblem; j++)
{
int temporary = destination[j];
destination[j] = temporary + destination[j + numberOfProblem];
destination[j + numberOfProblem] = montgomery(
omega * (temporary - destination[j + numberOfProblem]),
Parameter.Q_I, Parameter.Q_INVERSE_I
);
}
}
}
for (int i = 0; i < Parameter.N_I / 2; i++)
{
destination[i] = montgomery((long)Parameter.R_I * destination[i], Parameter.Q_I, Parameter.Q_INVERSE_I);
}
}
/**************************************************************************************************************************************************************************
* Description: Inverse Number Theoretic Transform for Heuristic qTESLA Security Category-3 (Option for Size and Speed)
*
* @param destination Destination of Inverse Transformation
* @param source Source of Inverse Transformation
* @param n Polynomial Degree
* @param q Modulus
* @param qInverse
* @param r
* @param barrettMultiplication
* @param barrettDivision
*
* @return none
**************************************************************************************************************************************************************************/
private static void inverseNumberTheoreticTransform(int destination[], int source[], int n, int q, long qInverse, int r, int barrettMultiplication, int barrettDivision)
{
int jTwiddle = 0;
for (int numberOfProblem = 1; numberOfProblem < n; numberOfProblem *= 2)
{
int j = 0;
for (int jFirst = 0; jFirst < n; jFirst = j + numberOfProblem)
{
long omega = source[jTwiddle++];
for (j = jFirst; j < jFirst + numberOfProblem; j++)
{
int temporary = destination[j];
if (numberOfProblem == 16)
{
destination[j] = barrett(temporary + destination[j + numberOfProblem], q, barrettMultiplication, barrettDivision);
}
else
{
destination[j] = temporary + destination[j + numberOfProblem];
}
destination[j + numberOfProblem] = montgomery(omega * (temporary - destination[j + numberOfProblem]), q, qInverse);
}
}
}
for (int i = 0; i < n / 2; i++)
{
destination[i] = montgomery((long)r * destination[i], q, qInverse);
}
}
/***********************************************************************************************************************************************************************************
* Description: Inverse Number Theoretic Transform for Provably-Secure qTESLA Security Category-1
*
* @param destination Destination of Inverse Transformation
* @param destinationOffset Starting Point of the Destination
* @param source Source of Inverse Transformation
* @param sourceOffset Starting Point of the Source
*
* @return none
***********************************************************************************************************************************************************************************/
private static void inverseNumberTheoreticTransformIP(long destination[], int destinationOffset, long source[], int sourceOffset)
{
int jTwiddle = 0;
for (int numberOfProblem = 1; numberOfProblem < Parameter.N_I_P; numberOfProblem *= 2)
{
int j = 0;
int jFirst;
for (jFirst = 0; jFirst < Parameter.N_I_P; jFirst = j + numberOfProblem)
{
long omega = source[sourceOffset + (jTwiddle++)];
for (j = jFirst; j < jFirst + numberOfProblem; j++)
{
long temporary = destination[destinationOffset + j];
destination[destinationOffset + j] = temporary + destination[destinationOffset + j + numberOfProblem];
destination[destinationOffset + j + numberOfProblem] = montgomeryP(
omega * (temporary + (2L * Parameter.Q_I_P - destination[destinationOffset + j + numberOfProblem])),
Parameter.Q_I_P, Parameter.Q_INVERSE_I_P
);
}
}
numberOfProblem *= 2;
for (jFirst = 0; jFirst < Parameter.N_I_P; jFirst = j + numberOfProblem)
{
long omega = source[sourceOffset + (jTwiddle++)];
for (j = jFirst; j < jFirst + numberOfProblem; j++)
{
long temporary = destination[destinationOffset + j];
destination[destinationOffset + j] = barrett(
temporary + destination[destinationOffset + j + numberOfProblem],
Parameter.Q_I_P, Parameter.BARRETT_MULTIPLICATION_I_P, Parameter.BARRETT_DIVISION_I_P
);
destination[destinationOffset + j + numberOfProblem] = montgomeryP(
omega * (temporary + (2L * Parameter.Q_I_P - destination[destinationOffset + j + numberOfProblem])),
Parameter.Q_I_P, Parameter.Q_INVERSE_I_P
);
}
}
}
}
/******************************************************************************************************************************************************************************************
* Description: Inverse Number Theoretic Transform for Provably-Secure qTESLA Security Category-3
*
* @param destination Destination of Inverse Transformation
* @param destinationOffset Starting Point of the Destination
* @param source Source of Inverse Transformation
* @param sourceOffset Starting Point of the Source
*
* @return none
******************************************************************************************************************************************************************************************/
private static void inverseNumberTheoreticTransformIIIP(long destination[], int destinationOffset, long source[], int sourceOffset)
{
int jTwiddle = 0;
for (int numberOfProblem = 1; numberOfProblem < Parameter.N_III_P; numberOfProblem *= 2)
{
int j = 0;
int jFirst;
for (jFirst = 0; jFirst < Parameter.N_III_P; jFirst = j + numberOfProblem)
{
long omega = source[sourceOffset + (jTwiddle++)];
for (j = jFirst; j < jFirst + numberOfProblem; j++)
{
long temporary = destination[destinationOffset + j];
destination[destinationOffset + j] = barrett(
temporary + destination[destinationOffset + j + numberOfProblem],
Parameter.Q_III_P, Parameter.BARRETT_MULTIPLICATION_III_P, Parameter.BARRETT_DIVISION_III_P
);
destination[destinationOffset + j + numberOfProblem] = barrett(
montgomeryP(
omega * (temporary + (2L * Parameter.Q_III_P - destination[destinationOffset + j + numberOfProblem])),
Parameter.Q_III_P, Parameter.Q_INVERSE_III_P
),
Parameter.Q_III_P, Parameter.BARRETT_MULTIPLICATION_III_P, Parameter.BARRETT_DIVISION_III_P
);
}
}
}
}
/****************************************************************************************************************************************************
* Description: Component Wise Polynomial Multiplication for Heuristic qTESLA Security Category-1 and Security Category-3 (Option for Size and Speed)
*
* @param product Product = Multiplicand (*) Multiplier
* @param multiplicand Multiplicand Array
* @param multiplier Multiplier Array
* @param n Polynomial Degree
* @param q Modulus
* @param qInverse
*
* @return none
****************************************************************************************************************************************************/
private static void componentWisePolynomialMultiplication(int[] product, int[] multiplicand, int[] multiplier, int n, int q, long qInverse)
{
for (int i = 0; i < n; i++)
{
product[i] = montgomery((long)multiplicand[i] * multiplier[i], q, qInverse);
}
}
/******************************************************************************************************************************************************************************************************************
* Description: Component Wise Polynomial Multiplication for Provably-Secure qTESLA Security Category-1 and Security Category-3
*
* @param product Product = Multiplicand (*) Multiplier
* @param productOffset Starting Point of the Product Array
* @param multiplicand Multiplicand Array
* @param multiplicandOffset Starting Point of the Multiplicand Array
* @param multiplier Multiplier Array
* @param multiplierOffset Starting Point of the Multiplier Array
* @param n Polynomial Degree
* @param q Modulus
* @param qInverse
*
* @return none
******************************************************************************************************************************************************************************************************************/
private static void componentWisePolynomialMultiplication(long[] product, int productOffset, long[] multiplicand, int multiplicandOffset, long[] multiplier, int multiplierOffset, int n, int q, long qInverse)
{
for (int i = 0; i < n; i++)
{
product[productOffset + i] = montgomeryP(multiplicand[multiplicandOffset + i] * multiplier[multiplierOffset + i], q, qInverse);
}
}
/***********************************************************************************************************************************************
* Description: Polynomial Number Theoretic Transform for Provably-Secure qTESLA Security Category-1 and Category-3
*
* @param arrayNumberTheoreticTransform Transformed Array
* @param array Array to be Transformed
* @param n Polynomial Degree
*
* @return none
***********************************************************************************************************************************************/
public static void polynomialNumberTheoreticTransform(long[] arrayNumberTheoreticTransform, long[] array, int n)
{
for (int i = 0; i < n; i++)
{
arrayNumberTheoreticTransform[i] = array[i];
}
if (n == Parameter.N_I_P)
{
numberTheoreticTransformIP(arrayNumberTheoreticTransform, PolynomialProvablySecure.ZETA_I_P);
}
if (n == Parameter.N_III_P)
{
numberTheoreticTransformIIIP(arrayNumberTheoreticTransform, PolynomialProvablySecure.ZETA_III_P);
}
}
/*******************************************************************************************************************************************
* Description: Polynomial Multiplication for Heuristic qTESLA Security Category-1 and Category-3 (Option for Size and Speed)
*
* @param product Product = Multiplicand * Multiplier
* @param multiplicand Multiplicand Array
* @param multiplier Multiplier Array
* @param n Polynomial Degree
* @param q Modulus
* @param qInverse
* @param zeta
*
* @return none
*******************************************************************************************************************************************/
public static void polynomialMultiplication(int[] product, int[] multiplicand, int[] multiplier, int n, int q, long qInverse, int[] zeta)
{
int[] multiplierNumberTheoreticTransform = new int[n];
for (int i = 0; i < n; i++)
{
multiplierNumberTheoreticTransform[i] = multiplier[i];
}
numberTheoreticTransform(multiplierNumberTheoreticTransform, zeta, n, q, qInverse);
componentWisePolynomialMultiplication(product, multiplicand, multiplierNumberTheoreticTransform, n, q, qInverse);
if (q == Parameter.Q_I)
{
inverseNumberTheoreticTransformI(product, PolynomialHeuristic.ZETA_INVERSE_I);
}
if (q == Parameter.Q_III_SIZE)
{
inverseNumberTheoreticTransform(
product, PolynomialHeuristic.ZETA_INVERSE_III_SIZE,
Parameter.N_III_SIZE, Parameter.Q_III_SIZE, Parameter.Q_INVERSE_III_SIZE, Parameter.R_III_SIZE,
Parameter.BARRETT_MULTIPLICATION_III_SIZE, Parameter.BARRETT_DIVISION_III_SIZE
);
}
if (q == Parameter.Q_III_SPEED)
{
inverseNumberTheoreticTransform(
product, PolynomialHeuristic.ZETA_INVERSE_III_SPEED,
Parameter.N_III_SPEED, Parameter.Q_III_SPEED, Parameter.Q_INVERSE_III_SPEED, Parameter.R_III_SPEED,
Parameter.BARRETT_MULTIPLICATION_III_SPEED, Parameter.BARRETT_DIVISION_III_SPEED
);
}
}
/***************************************************************************************************************************************************************************************************
* Description: Polynomial Multiplication for Provably-Secure qTESLA Security Category-1 and Category-3
*
* @param product Product = Multiplicand * Multiplier
* @param productOffset Starting Point of the Product Array
* @param multiplicand Multiplicand Array
* @param multiplicandOffset Starting Point of the Multiplicand Array
* @param multiplier Multiplier Array
* @param multiplierOffset Starting Point of the Multiplier Array
* @param n Polynomial Degree
* @param q Modulus
* @param qInverse
*
* @return none
***************************************************************************************************************************************************************************************************/
public static void polynomialMultiplication(long[] product, int productOffset, long[] multiplicand, int multiplicandOffset, long[] multiplier, int multiplierOffset, int n, int q, long qInverse)
{
componentWisePolynomialMultiplication(product, productOffset, multiplicand, multiplicandOffset, multiplier, multiplierOffset, n, q, qInverse);
if (q == Parameter.Q_I_P)
{
inverseNumberTheoreticTransformIP(product, productOffset, PolynomialProvablySecure.ZETA_INVERSE_I_P, 0);
}
if (q == Parameter.Q_III_P)
{
inverseNumberTheoreticTransformIIIP(product, productOffset, PolynomialProvablySecure.ZETA_INVERSE_III_P, 0);
}
}
/****************************************************************************************************************************************************
* Description: Polynomial Addition for Heuristic qTESLA Security Category-1 and Category-3 (Option for Size or Speed)
* Q + L_E < 2 ^ (CEIL (LOGARITHM (Q, 2)))
* No Necessary Reduction for Y + SC
*
* @param summation Summation = Augend + Addend
* @param augend Augend Array
* @param addend Addend Array
* @param n Polynomial Degree
*
* @return none
****************************************************************************************************************************************************/
public static void polynomialAddition(int[] summation, int[] augend, int[] addend, int n)
{
for (int i = 0; i < n; i++)
{
summation[i] = augend[i] + addend[i];
}
}
/********************************************************************************************************************************************************
* Description: Polynomial Addition for Provably-Secure qTESLA Security Category-1 and Category-3
* Q + L_E < 2 ^ (CEIL (LOGARITHM (Q, 2)))
* No Necessary Reduction for Y + SC
*
* @param summation Summation = Augend + Addend
* @param summationOffset Starting Point of the Summation Array
* @param augend Augend Array
* @param augendOffset Starting Point of the Augend Array
* @param addend Addend Array
* @param addendOffset Starting Point of the Addend Array
* @param n Polynomial Degree
*
* @return none
********************************************************************************************************************************************************/
public static void polynomialAddition(long[] summation, int summationOffset, long[] augend, int augendOffset, long[] addend, int addendOffset, int n)
{
for (int i = 0; i < n; i++)
{
summation[summationOffset + i] = augend[augendOffset + i] + addend[addendOffset + i];
}
}
/*************************************************************************************************************
* Description: Polynomial Addition with Correction for Heuristic qTESLA Security Category-1 and Category-3
* (Option for Size or Speed)
* Q + L_E < 2 ^ (CEIL (LOGARITHM (Q, 2)))
* No Necessary Reduction for Y + SC
*
* @param summation Summation = Augend + Addend
* @param augend Augend Array
* @param addend Addend Array
* @param n Polynomial Degree
*
* @return none
************************************************************************************************************/
public static void polynomialAdditionCorrection(int[] summation, int[] augend, int[] addend, int n, int q)
{
for (int i = 0; i < n; i++)
{
summation[i] = augend[i] + addend[i];
/* If summation[i] < 0 Then Add Q */
summation[i] += (summation[i] >> 31) & q;
summation[i] -= q;
/* If summation[i] >= Q Then Subtract Q */
summation[i] += (summation[i] >> 31) & q;
}
}
/**********************************************************************************************************************
* Description: Polynomial Subtraction with Correction for Heuristic qTESLA Security Category-1 and Security Category-3
* (Option for Size or Speed)
*
* @param difference Difference = Minuend (-) Subtrahend
* @param minuend Minuend Array
* @param subtrahend Subtrahend Array
* @param n Polynomial Degree
* @param q Modulus
*
* @return none
***********************************************************************************************************************/
public static void polynomialSubtractionCorrection(int[] difference, int[] minuend, int[] subtrahend, int n, int q)
{
for (int i = 0; i < n; i++)
{
difference[i] = minuend[i] - subtrahend[i];
/* If difference[i] < 0 Then Add Q */
difference[i] += (difference[i] >> 31) & q;
}
}
/*******************************************************************************************************************************************
* Description: Polynomial Subtraction with Montgomery Reduction for Heuristic qTESLA Security Category-1 and Security Category-3
* (Option for Size or Speed)
*
* @param difference Difference = Minuend (-) Subtrahend
* @param minuend Minuend Array
* @param subtrahend Subtrahend Array
* @param n Polynomial Degree
* @param q Modulus
* @param qInverse
* @param r
*
* @return none
*******************************************************************************************************************************************/
public static void polynomialSubtractionMontgomery(int[] difference, int[] minuend, int[] subtrahend, int n, int q, long qInverse, int r)
{
for (int i = 0; i < n; i++)
{
difference[i] = montgomery((long)r * (minuend[i] - subtrahend[i]), q, qInverse);
}
}
/******************************************************************************************************************************************************************************************************************************
* Description: Polynomial Subtraction for Provably-Secure qTESLA Security Category-1 and Security Category-3
*
* @param difference Difference = Minuend (-) Subtrahend
* @param differenceOffset Starting Point of the Difference Array
* @param minuend Minuend Array
* @param minuendOffset Starting Point of the Minuend Array
* @param subtrahend Subtrahend Array
* @param subtrahendOffset Starting Point of the Subtrahend Array
* @param n Polynomial Degree
* @param q Modulus
* @param barrettMultiplication
* @param barrettDivision
*
* @return none
******************************************************************************************************************************************************************************************************************************/
public static void polynomialSubtraction(long[] difference, int differenceOffset, long[] minuend, int minuendOffset, long[] subtrahend, int subtrahendOffset, int n, int q, int barrettMultiplication, int barrettDivision)
{
for (int i = 0; i < n; i++)
{
difference[differenceOffset + i] = barrett(minuend[minuendOffset + i] - subtrahend[subtrahendOffset + i], q, barrettMultiplication, barrettDivision);
}
}
/******************************************************************************************************************************************************************************
* Description: Generation of Polynomial A for Heuristic qTESLA Security Category-1 and Security Category-3 (Option for Size or Speed)
*
* @param A Polynomial to be Generated
* @param seed Kappa-Bit Seed
* @param seedOffset Starting Point of the Kappa-Bit Seed
* @param n Polynomial Degree
* @param q Modulus
* @param qInverse
* @param qLogarithm q <= 2 ^ qLogarithm
* @param generatorA
* @param inverseNumberTheoreticTransform
*
* @return none
******************************************************************************************************************************************************************************/
public static void polynomialUniform(int[] A, byte[] seed, int seedOffset, int n, int q, long qInverse, int qLogarithm, int generatorA, int inverseNumberTheoreticTransform)
{
int position = 0;
int i = 0;
int numberOfByte = (qLogarithm + 7) / 8;
int numberOfBlock = generatorA;
short dualModeSampler = 0;
int value1;
int value2;
int value3;
int value4;
int mask = (1 << qLogarithm) - 1;
byte[] buffer = new byte[HashUtils.SECURE_HASH_ALGORITHM_KECCAK_128_RATE * generatorA];
HashUtils.customizableSecureHashAlgorithmKECCAK128Simple(
buffer, 0, HashUtils.SECURE_HASH_ALGORITHM_KECCAK_128_RATE * generatorA,
dualModeSampler++,
seed, seedOffset, RANDOM
);
while (i < n)
{
if (position > (HashUtils.SECURE_HASH_ALGORITHM_KECCAK_128_RATE * numberOfBlock - Const.INT_SIZE / Const.BYTE_SIZE * numberOfByte))
{
numberOfBlock = 1;
HashUtils.customizableSecureHashAlgorithmKECCAK128Simple(
buffer, 0, HashUtils.SECURE_HASH_ALGORITHM_KECCAK_128_RATE * numberOfBlock,
dualModeSampler++,
seed, seedOffset, RANDOM
);
position = 0;
}
value1 = CommonFunction.load32(buffer, position) & mask;
position += numberOfByte;
value2 = CommonFunction.load32(buffer, position) & mask;
position += numberOfByte;
value3 = CommonFunction.load32(buffer, position) & mask;
position += numberOfByte;
value4 = CommonFunction.load32(buffer, position) & mask;
position += numberOfByte;
if (value1 < q && i < n)
{
A[i++] = montgomery((long)value1 * inverseNumberTheoreticTransform, q, qInverse);
}
if (value2 < q && i < n)
{
A[i++] = montgomery((long)value2 * inverseNumberTheoreticTransform, q, qInverse);
}
if (value3 < q && i < n)
{
A[i++] = montgomery((long)value3 * inverseNumberTheoreticTransform, q, qInverse);
}
if (value4 < q && i < n)
{
A[i++] = montgomery((long)value4 * inverseNumberTheoreticTransform, q, qInverse);
}
}
}
/**************************************************************************************************************************************************************************************
* Description: Generation of Polynomial A for Provably-Secure qTESLA Security Category-1 and Security Category-3
*
* @param A Polynomial to be Generated
* @param seed Kappa-Bit Seed
* @param seedOffset Starting Point of the Kappa-Bit Seed
* @param n Polynomial Degree
* @param k Number of Ring-Learning-With-Errors Samples
* @param q Modulus
* @param qInverse
* @param qLogarithm q <= 2 ^ qLogarithm
* @param generatorA
* @param inverseNumberTheoreticTransform
*
* @return none
**************************************************************************************************************************************************************************************/
public static void polynomialUniform(long[] A, byte[] seed, int seedOffset, int n, int k, int q, long qInverse, int qLogarithm, int generatorA, int inverseNumberTheoreticTransform)
{
int position = 0;
int i = 0;
int numberOfByte = (qLogarithm + 7) / 8;
int numberOfBlock = generatorA;
short dualModeSampler = 0;
int value1;
int value2;
int value3;
int value4;
int mask = (1 << qLogarithm) - 1;
byte[] buffer = new byte[HashUtils.SECURE_HASH_ALGORITHM_KECCAK_128_RATE * numberOfBlock];
HashUtils.customizableSecureHashAlgorithmKECCAK128Simple(
buffer, 0, HashUtils.SECURE_HASH_ALGORITHM_KECCAK_128_RATE * numberOfBlock,
dualModeSampler++,
seed, seedOffset, RANDOM
);
while (i < n * k)
{
if (position > (HashUtils.SECURE_HASH_ALGORITHM_KECCAK_128_RATE * numberOfBlock - Const.INT_SIZE / Const.BYTE_SIZE * numberOfByte))
{
numberOfBlock = 1;
HashUtils.customizableSecureHashAlgorithmKECCAK128Simple(
buffer, 0, HashUtils.SECURE_HASH_ALGORITHM_KECCAK_128_RATE * numberOfBlock,
dualModeSampler++,
seed, seedOffset, RANDOM
);
position = 0;
}
value1 = CommonFunction.load32(buffer, position) & mask;
position += numberOfByte;
value2 = CommonFunction.load32(buffer, position) & mask;
position += numberOfByte;
value3 = CommonFunction.load32(buffer, position) & mask;
position += numberOfByte;
value4 = CommonFunction.load32(buffer, position) & mask;
position += numberOfByte;
if (value1 < q && i < n * k)
{
A[i++] = montgomeryP((long)value1 * inverseNumberTheoreticTransform, q, qInverse);
}
if (value2 < q && i < n * k)
{
A[i++] = montgomeryP((long)value2 * inverseNumberTheoreticTransform, q, qInverse);
}
if (value3 < q && i < n * k)
{
A[i++] = montgomeryP((long)value3 * inverseNumberTheoreticTransform, q, qInverse);
}
if (value4 < q && i < n * k)
{
A[i++] = montgomeryP((long)value4 * inverseNumberTheoreticTransform, q, qInverse);
}
}
}
/**************************************************************************************************************************************************************
* Description: Performs Sparse Polynomial Multiplication for A Value Needed During Message Signification for Heuristic qTESLA Security Category-1 and
* SecurityCategory-3 (Option for Size or Speed)
*
* @param product Product of Two Polynomials
* @param privateKey Part of the Private Key
* @param positionList List of Indices of Non-Zero Elements in C
* @param signList List of Signs of Non-Zero Elements in C
* @param n Polynomial Degree
* @param h Number of Non-Zero Entries of Output Elements of Encryption
*
* @return none
**************************************************************************************************************************************************************/
public static void sparsePolynomialMultiplication16(int[] product, final short[] privateKey, final int[] positionList, final short[] signList, int n, int h)
{
int position;
Arrays.fill(product, 0);
for (int i = 0; i < h; i++)
{
position = positionList[i];
for (int j = 0; j < position; j++)
{
product[j] -= signList[i] * privateKey[n + j - position];
}
for (int j = position; j < n; j++)
{
product[j] += signList[i] * privateKey[j - position];
}
}
}
/*****************************************************************************************************************************************************************************************************
* Description: Performs Sparse Polynomial Multiplication for A Value Needed During Message Signification for Provably-Secure qTESLA Security Category-1 and Category-3
*
* @param product Product of Two Polynomials
* @param productOffset Starting Point of the Product of Two Polynomials
* @param privateKey Part of the Private Key
* @param privateKeyOffset Starting Point of the Private Key
* @param positionList List of Indices of Non-Zero Elements in C
* @param signList List of Signs of Non-Zero Elements in C
* @param n Polynomial Degree
* @param h Number of Non-Zero Entries of Output Elements of Encryption
*
* @return none
******************************************************************************************************************************************************************************************************/
public static void sparsePolynomialMultiplication8(long[] product, int productOffset, final byte[] privateKey, int privateKeyOffset, final int[] positionList, final short[] signList, int n, int h)
{
int position;
Arrays.fill(product, 0L);
for (int i = 0; i < h; i++)
{
position = positionList[i];
for (int j = 0; j < position; j++)
{
product[productOffset + j] -= signList[i] * privateKey[privateKeyOffset + n + j - position];
}
for (int j = position; j < n; j++)
{
product[productOffset + j] += signList[i] * privateKey[privateKeyOffset + j - position];
}
}
}
/***********************************************************************************************************************************************************
* Description: Performs Sparse Polynomial Multiplication for A Value Needed During Message Signification for Heuristic qTESLA Security Category-1 and
* Security Category-3 (Option for Size or Speed)
*
* @param product Product of Two Polynomials
* @param publicKey Part of the Public Key
* @param positionList List of Indices of Non-Zero Elements in C
* @param signList List of Signs of Non-Zero Elements in C
* @param n Polynomial Degree
* @param h Number of Non-Zero Entries of Output Elements of Encryption
*
* @return none
***********************************************************************************************************************************************************/
public static void sparsePolynomialMultiplication32(int[] product, final int[] publicKey, final int[] positionList, final short[] signList, int n, int h)
{
int position;
Arrays.fill(product, 0);
for (int i = 0; i < h; i++)
{
position = positionList[i];
for (int j = 0; j < position; j++)
{
product[j] -= signList[i] * publicKey[n + j - position];
}
for (int j = position; j < n; j++)
{
product[j] += signList[i] * publicKey[j - position];
}
}
}
/***********************************************************************************************************************************************************************************************************************************************************
* Description: Performs Sparse Polynomial Multiplication for A Value Needed During Message Signification for Provably-Secure qTESLA Security Category-1 and Security Category-3
*
* @param product Product of Two Polynomials
* @param productOffset Starting Point of the Product of Two Polynomials
* @param publicKey Part of the Public Key
* @param publicKeyOffset Starting Point of the Public Key
* @param positionList List of Indices of Non-Zero Elements in C
* @param signList List of Signs of Non-Zero Elements in C
* @param n Polynomial Degree
* @param h Number of Non-Zero Entries of Output Elements of Encryption
* @param q Modulus
* @param barrettMultiplication
* @param barrettDivision
*
* @return none
***********************************************************************************************************************************************************************************************************************************************************/
public static void sparsePolynomialMultiplication32(long[] product, int productOffset, final int[] publicKey, int publicKeyOffset, final int[] positionList, final short[] signList, int n, int h, int q, int barrettMultiplication, int barrettDivision)
{
int position;
Arrays.fill(product, 0L);
for (int i = 0; i < h; i++)
{
position = positionList[i];
for (int j = 0; j < position; j++)
{
product[productOffset + j] -= signList[i] * publicKey[publicKeyOffset + n + j - position];
}
for (int j = position; j < n; j++)
{
product[productOffset + j] += signList[i] * publicKey[publicKeyOffset + j - position];
}
}
for (int i = 0; i < n; i++)
{
product[productOffset + i] = barrett(product[productOffset + i], q, barrettMultiplication, barrettDivision);
}
}
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