package org.bouncycastle.pqc.math.ntru.polynomial;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.security.SecureRandom;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import org.bouncycastle.util.Arrays;
/**
* A polynomial with {@link BigInteger} coefficients.<br/>
* Some methods (like <code>add</code>) change the polynomial, others (like <code>mult</code>) do
* not but return the result as a new polynomial.
*/
public class BigIntPolynomial
{
private final static double LOG_10_2 = Math.log10(2);
BigInteger[] coeffs;
/**
* Constructs a new polynomial with <code>N</code> coefficients initialized to 0.
*
* @param N the number of coefficients
*/
BigIntPolynomial(int N)
{
coeffs = new BigInteger[N];
for (int i = 0; i < N; i++)
{
coeffs[i] = Constants.BIGINT_ZERO;
}
}
/**
* Constructs a new polynomial with a given set of coefficients.
*
* @param coeffs the coefficients
*/
BigIntPolynomial(BigInteger[] coeffs)
{
this.coeffs = coeffs;
}
/**
* Constructs a <code>BigIntPolynomial</code> from a <code>IntegerPolynomial</code>. The two polynomials are
* independent of each other.
*
* @param p the original polynomial
*/
public BigIntPolynomial(IntegerPolynomial p)
{
coeffs = new BigInteger[p.coeffs.length];
for (int i = 0; i < coeffs.length; i++)
{
coeffs[i] = BigInteger.valueOf(p.coeffs[i]);
}
}
/**
* Generates a random polynomial with <code>numOnes</code> coefficients equal to 1,
* <code>numNegOnes</code> coefficients equal to -1, and the rest equal to 0.
*
* @param N number of coefficients
* @param numOnes number of 1's
* @param numNegOnes number of -1's
* @return
*/
static BigIntPolynomial generateRandomSmall(int N, int numOnes, int numNegOnes)
{
List coeffs = new ArrayList();
for (int i = 0; i < numOnes; i++)
{
coeffs.add(Constants.BIGINT_ONE);
}
for (int i = 0; i < numNegOnes; i++)
{
coeffs.add(BigInteger.valueOf(-1));
}
while (coeffs.size() < N)
{
coeffs.add(Constants.BIGINT_ZERO);
}
Collections.shuffle(coeffs, new SecureRandom());
BigIntPolynomial poly = new BigIntPolynomial(N);
for (int i = 0; i < coeffs.size(); i++)
{
poly.coeffs[i] = (BigInteger)coeffs.get(i);
}
return poly;
}
/**
* Multiplies the polynomial by another, taking the indices mod N. Does not
* change this polynomial but returns the result as a new polynomial.<br/>
* Both polynomials must have the same number of coefficients.
*
* @param poly2 the polynomial to multiply by
* @return a new polynomial
*/
public BigIntPolynomial mult(BigIntPolynomial poly2)
{
int N = coeffs.length;
if (poly2.coeffs.length != N)
{
throw new IllegalArgumentException("Number of coefficients must be the same");
}
BigIntPolynomial c = multRecursive(poly2);
if (c.coeffs.length > N)
{
for (int k = N; k < c.coeffs.length; k++)
{
c.coeffs[k - N] = c.coeffs[k - N].add(c.coeffs[k]);
}
c.coeffs = Arrays.copyOf(c.coeffs, N);
}
return c;
}
/**
* Karazuba multiplication
*/
private BigIntPolynomial multRecursive(BigIntPolynomial poly2)
{
BigInteger[] a = coeffs;
BigInteger[] b = poly2.coeffs;
int n = poly2.coeffs.length;
if (n <= 1)
{
BigInteger[] c = Arrays.clone(coeffs);
for (int i = 0; i < coeffs.length; i++)
{
c[i] = c[i].multiply(poly2.coeffs[0]);
}
return new BigIntPolynomial(c);
}
else
{
int n1 = n / 2;
BigIntPolynomial a1 = new BigIntPolynomial(Arrays.copyOf(a, n1));
BigIntPolynomial a2 = new BigIntPolynomial(Arrays.copyOfRange(a, n1, n));
BigIntPolynomial b1 = new BigIntPolynomial(Arrays.copyOf(b, n1));
BigIntPolynomial b2 = new BigIntPolynomial(Arrays.copyOfRange(b, n1, n));
BigIntPolynomial A = (BigIntPolynomial)a1.clone();
A.add(a2);
BigIntPolynomial B = (BigIntPolynomial)b1.clone();
B.add(b2);
BigIntPolynomial c1 = a1.multRecursive(b1);
BigIntPolynomial c2 = a2.multRecursive(b2);
BigIntPolynomial c3 = A.multRecursive(B);
c3.sub(c1);
c3.sub(c2);
BigIntPolynomial c = new BigIntPolynomial(2 * n - 1);
for (int i = 0; i < c1.coeffs.length; i++)
{
c.coeffs[i] = c1.coeffs[i];
}
for (int i = 0; i < c3.coeffs.length; i++)
{
c.coeffs[n1 + i] = c.coeffs[n1 + i].add(c3.coeffs[i]);
}
for (int i = 0; i < c2.coeffs.length; i++)
{
c.coeffs[2 * n1 + i] = c.coeffs[2 * n1 + i].add(c2.coeffs[i]);
}
return c;
}
}
/**
* Adds another polynomial which can have a different number of coefficients,
* and takes the coefficient values mod <code>modulus</code>.
*
* @param b another polynomial
*/
void add(BigIntPolynomial b, BigInteger modulus)
{
add(b);
mod(modulus);
}
/**
* Adds another polynomial which can have a different number of coefficients.
*
* @param b another polynomial
*/
public void add(BigIntPolynomial b)
{
if (b.coeffs.length > coeffs.length)
{
int N = coeffs.length;
coeffs = Arrays.copyOf(coeffs, b.coeffs.length);
for (int i = N; i < coeffs.length; i++)
{
coeffs[i] = Constants.BIGINT_ZERO;
}
}
for (int i = 0; i < b.coeffs.length; i++)
{
coeffs[i] = coeffs[i].add(b.coeffs[i]);
}
}
/**
* Subtracts another polynomial which can have a different number of coefficients.
*
* @param b another polynomial
*/
public void sub(BigIntPolynomial b)
{
if (b.coeffs.length > coeffs.length)
{
int N = coeffs.length;
coeffs = Arrays.copyOf(coeffs, b.coeffs.length);
for (int i = N; i < coeffs.length; i++)
{
coeffs[i] = Constants.BIGINT_ZERO;
}
}
for (int i = 0; i < b.coeffs.length; i++)
{
coeffs[i] = coeffs[i].subtract(b.coeffs[i]);
}
}
/**
* Multiplies each coefficient by a <code>BigInteger</code>. Does not return a new polynomial but modifies this polynomial.
*
* @param factor
*/
public void mult(BigInteger factor)
{
for (int i = 0; i < coeffs.length; i++)
{
coeffs[i] = coeffs[i].multiply(factor);
}
}
/**
* Multiplies each coefficient by a <code>int</code>. Does not return a new polynomial but modifies this polynomial.
*
* @param factor
*/
void mult(int factor)
{
mult(BigInteger.valueOf(factor));
}
/**
* Divides each coefficient by a <code>BigInteger</code> and rounds the result to the nearest whole number.<br/>
* Does not return a new polynomial but modifies this polynomial.
*
* @param divisor the number to divide by
*/
public void div(BigInteger divisor)
{
BigInteger d = divisor.add(Constants.BIGINT_ONE).divide(BigInteger.valueOf(2));
for (int i = 0; i < coeffs.length; i++)
{
coeffs[i] = coeffs[i].compareTo(Constants.BIGINT_ZERO) > 0 ? coeffs[i].add(d) : coeffs[i].add(d.negate());
coeffs[i] = coeffs[i].divide(divisor);
}
}
/**
* Divides each coefficient by a <code>BigDecimal</code> and rounds the result to <code>decimalPlaces</code> places.
*
* @param divisor the number to divide by
* @param decimalPlaces the number of fractional digits to round the result to
* @return a new <code>BigDecimalPolynomial</code>
*/
public BigDecimalPolynomial div(BigDecimal divisor, int decimalPlaces)
{
BigInteger max = maxCoeffAbs();
int coeffLength = (int)(max.bitLength() * LOG_10_2) + 1;
// factor = 1/divisor
BigDecimal factor = Constants.BIGDEC_ONE.divide(divisor, coeffLength + decimalPlaces + 1, BigDecimal.ROUND_HALF_EVEN);
// multiply each coefficient by factor
BigDecimalPolynomial p = new BigDecimalPolynomial(coeffs.length);
for (int i = 0; i < coeffs.length; i++)
// multiply, then truncate after decimalPlaces so subsequent operations aren't slowed down
{
p.coeffs[i] = new BigDecimal(coeffs[i]).multiply(factor).setScale(decimalPlaces, BigDecimal.ROUND_HALF_EVEN);
}
return p;
}
/**
* Returns the base10 length of the largest coefficient.
*
* @return length of the longest coefficient
*/
public int getMaxCoeffLength()
{
return (int)(maxCoeffAbs().bitLength() * LOG_10_2) + 1;
}
private BigInteger maxCoeffAbs()
{
BigInteger max = coeffs[0].abs();
for (int i = 1; i < coeffs.length; i++)
{
BigInteger coeff = coeffs[i].abs();
if (coeff.compareTo(max) > 0)
{
max = coeff;
}
}
return max;
}
/**
* Takes each coefficient modulo a number.
*
* @param modulus
*/
public void mod(BigInteger modulus)
{
for (int i = 0; i < coeffs.length; i++)
{
coeffs[i] = coeffs[i].mod(modulus);
}
}
/**
* Returns the sum of all coefficients, i.e. evaluates the polynomial at 0.
*
* @return the sum of all coefficients
*/
BigInteger sumCoeffs()
{
BigInteger sum = Constants.BIGINT_ZERO;
for (int i = 0; i < coeffs.length; i++)
{
sum = sum.add(coeffs[i]);
}
return sum;
}
/**
* Makes a copy of the polynomial that is independent of the original.
*/
public Object clone()
{
return new BigIntPolynomial(coeffs.clone());
}
public int hashCode()
{
final int prime = 31;
int result = 1;
result = prime * result + Arrays.hashCode(coeffs);
return result;
}
public boolean equals(Object obj)
{
if (this == obj)
{
return true;
}
if (obj == null)
{
return false;
}
if (getClass() != obj.getClass())
{
return false;
}
BigIntPolynomial other = (BigIntPolynomial)obj;
if (!Arrays.areEqual(coeffs, other.coeffs))
{
return false;
}
return true;
}
public BigInteger[] getCoeffs()
{
return Arrays.clone(coeffs);
}
}