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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 1.5 and up.
package org.bouncycastle.pqc.math.ntru.polynomial;
import org.bouncycastle.util.Arrays;
/**
* A polynomial class that combines two coefficients into one long value for
* faster multiplication in 64 bit environments.
* Coefficients can be between 0 and 2047 and are stored in pairs in the bits 0..10 and 24..34 of a long number.
*/
public class LongPolynomial2
{
private long[] coeffs; // each representing two coefficients in the original IntegerPolynomial
private int numCoeffs;
/**
* Constructs a LongPolynomial2 from a IntegerPolynomial. The two polynomials are independent of each other.
*
* @param p the original polynomial. Coefficients must be between 0 and 2047.
*/
public LongPolynomial2(IntegerPolynomial p)
{
numCoeffs = p.coeffs.length;
coeffs = new long[(numCoeffs + 1) / 2];
int idx = 0;
for (int pIdx = 0; pIdx < numCoeffs; )
{
int c0 = p.coeffs[pIdx++];
while (c0 < 0)
{
c0 += 2048;
}
long c1 = pIdx < numCoeffs ? p.coeffs[pIdx++] : 0;
while (c1 < 0)
{
c1 += 2048;
}
coeffs[idx] = c0 + (c1 << 24);
idx++;
}
}
private LongPolynomial2(long[] coeffs)
{
this.coeffs = coeffs;
}
private LongPolynomial2(int N)
{
coeffs = new long[N];
}
/**
* Multiplies the polynomial with another, taking the indices mod N and the values mod 2048.
*/
public LongPolynomial2 mult(LongPolynomial2 poly2)
{
int N = coeffs.length;
if (poly2.coeffs.length != N || numCoeffs != poly2.numCoeffs)
{
throw new IllegalArgumentException("Number of coefficients must be the same");
}
LongPolynomial2 c = multRecursive(poly2);
if (c.coeffs.length > N)
{
if (numCoeffs % 2 == 0)
{
for (int k = N; k < c.coeffs.length; k++)
{
c.coeffs[k - N] = (c.coeffs[k - N] + c.coeffs[k]) & 0x7FF0007FFL;
}
c.coeffs = Arrays.copyOf(c.coeffs, N);
}
else
{
for (int k = N; k < c.coeffs.length; k++)
{
c.coeffs[k - N] = c.coeffs[k - N] + (c.coeffs[k - 1] >> 24);
c.coeffs[k - N] = c.coeffs[k - N] + ((c.coeffs[k] & 2047) << 24);
c.coeffs[k - N] &= 0x7FF0007FFL;
}
c.coeffs = Arrays.copyOf(c.coeffs, N);
c.coeffs[c.coeffs.length - 1] &= 2047;
}
}
c = new LongPolynomial2(c.coeffs);
c.numCoeffs = numCoeffs;
return c;
}
public IntegerPolynomial toIntegerPolynomial()
{
int[] intCoeffs = new int[numCoeffs];
int uIdx = 0;
for (int i = 0; i < coeffs.length; i++)
{
intCoeffs[uIdx++] = (int)(coeffs[i] & 2047);
if (uIdx < numCoeffs)
{
intCoeffs[uIdx++] = (int)((coeffs[i] >> 24) & 2047);
}
}
return new IntegerPolynomial(intCoeffs);
}
/**
* Karazuba multiplication
*/
private LongPolynomial2 multRecursive(LongPolynomial2 poly2)
{
long[] a = coeffs;
long[] b = poly2.coeffs;
int n = poly2.coeffs.length;
if (n <= 32)
{
int cn = 2 * n;
LongPolynomial2 c = new LongPolynomial2(new long[cn]);
for (int k = 0; k < cn; k++)
{
for (int i = Math.max(0, k - n + 1); i <= Math.min(k, n - 1); i++)
{
long c0 = a[k - i] * b[i];
long cu = c0 & 0x7FF000000L + (c0 & 2047);
long co = (c0 >>> 48) & 2047;
c.coeffs[k] = (c.coeffs[k] + cu) & 0x7FF0007FFL;
c.coeffs[k + 1] = (c.coeffs[k + 1] + co) & 0x7FF0007FFL;
}
}
return c;
}
else
{
int n1 = n / 2;
LongPolynomial2 a1 = new LongPolynomial2(Arrays.copyOf(a, n1));
LongPolynomial2 a2 = new LongPolynomial2(Arrays.copyOfRange(a, n1, n));
LongPolynomial2 b1 = new LongPolynomial2(Arrays.copyOf(b, n1));
LongPolynomial2 b2 = new LongPolynomial2(Arrays.copyOfRange(b, n1, n));
LongPolynomial2 A = (LongPolynomial2)a1.clone();
A.add(a2);
LongPolynomial2 B = (LongPolynomial2)b1.clone();
B.add(b2);
LongPolynomial2 c1 = a1.multRecursive(b1);
LongPolynomial2 c2 = a2.multRecursive(b2);
LongPolynomial2 c3 = A.multRecursive(B);
c3.sub(c1);
c3.sub(c2);
LongPolynomial2 c = new LongPolynomial2(2 * n);
for (int i = 0; i < c1.coeffs.length; i++)
{
c.coeffs[i] = c1.coeffs[i] & 0x7FF0007FFL;
}
for (int i = 0; i < c3.coeffs.length; i++)
{
c.coeffs[n1 + i] = (c.coeffs[n1 + i] + c3.coeffs[i]) & 0x7FF0007FFL;
}
for (int i = 0; i < c2.coeffs.length; i++)
{
c.coeffs[2 * n1 + i] = (c.coeffs[2 * n1 + i] + c2.coeffs[i]) & 0x7FF0007FFL;
}
return c;
}
}
/**
* Adds another polynomial which can have a different number of coefficients.
*
* @param b another polynomial
*/
private void add(LongPolynomial2 b)
{
if (b.coeffs.length > coeffs.length)
{
coeffs = Arrays.copyOf(coeffs, b.coeffs.length);
}
for (int i = 0; i < b.coeffs.length; i++)
{
coeffs[i] = (coeffs[i] + b.coeffs[i]) & 0x7FF0007FFL;
}
}
/**
* Subtracts another polynomial which can have a different number of coefficients.
*
* @param b another polynomial
*/
private void sub(LongPolynomial2 b)
{
if (b.coeffs.length > coeffs.length)
{
coeffs = Arrays.copyOf(coeffs, b.coeffs.length);
}
for (int i = 0; i < b.coeffs.length; i++)
{
coeffs[i] = (0x0800000800000L + coeffs[i] - b.coeffs[i]) & 0x7FF0007FFL;
}
}
/**
* Subtracts another polynomial which must have the same number of coefficients,
* and applies an AND mask to the upper and lower halves of each coefficients.
*
* @param b another polynomial
* @param mask a bit mask less than 2048 to apply to each 11-bit coefficient
*/
public void subAnd(LongPolynomial2 b, int mask)
{
long longMask = (((long)mask) << 24) + mask;
for (int i = 0; i < b.coeffs.length; i++)
{
coeffs[i] = (0x0800000800000L + coeffs[i] - b.coeffs[i]) & longMask;
}
}
/**
* Multiplies this polynomial by 2 and applies an AND mask to the upper and
* lower halves of each coefficients.
*
* @param mask a bit mask less than 2048 to apply to each 11-bit coefficient
*/
public void mult2And(int mask)
{
long longMask = (((long)mask) << 24) + mask;
for (int i = 0; i < coeffs.length; i++)
{
coeffs[i] = (coeffs[i] << 1) & longMask;
}
}
public Object clone()
{
LongPolynomial2 p = new LongPolynomial2(coeffs.clone());
p.numCoeffs = numCoeffs;
return p;
}
public boolean equals(Object obj)
{
if (obj instanceof LongPolynomial2)
{
return Arrays.areEqual(coeffs, ((LongPolynomial2)obj).coeffs);
}
else
{
return false;
}
}
}