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package org.bouncycastle.math.ec;
import java.math.BigInteger;
/**
* Class implementing the WNAF (Window Non-Adjacent Form) multiplication
* algorithm.
*/
public class WNafL2RMultiplier extends AbstractECMultiplier
{
/**
* Multiplies <code>this</code> by an integer <code>k</code> using the
* Window NAF method.
* @param k The integer by which <code>this</code> is multiplied.
* @return A new <code>ECPoint</code> which equals <code>this</code>
* multiplied by <code>k</code>.
*/
protected ECPoint multiplyPositive(ECPoint p, BigInteger k)
{
// Clamp the window width in the range [2, 16]
int width = Math.max(2, Math.min(16, getWindowSize(k.bitLength())));
WNafPreCompInfo wnafPreCompInfo = WNafUtil.precompute(p, width, true);
ECPoint[] preComp = wnafPreCompInfo.getPreComp();
ECPoint[] preCompNeg = wnafPreCompInfo.getPreCompNeg();
int[] wnaf = WNafUtil.generateCompactWindowNaf(width, k);
ECPoint R = p.getCurve().getInfinity();
int i = wnaf.length;
/*
* NOTE This code optimizes the first window using the precomputed points to substitute an
* addition for 2 or more doublings.
*/
if (i > 1)
{
int wi = wnaf[--i];
int digit = wi >> 16, zeroes = wi & 0xFFFF;
int n = Math.abs(digit);
ECPoint[] table = digit < 0 ? preCompNeg : preComp;
/*
* NOTE: We use this optimization conservatively, since some coordinate systems have
* significantly cheaper doubling relative to addition.
*
* (n << 2) selects precomputed values in the lower half of the table
* (n << 3) selects precomputed values in the lower quarter of the table
*/
//if ((n << 2) < (1 << width))
if ((n << 3) < (1 << width))
{
int highest = LongArray.bitLengths[n];
int lowBits = n ^ (1 << (highest - 1));
int scale = width - highest;
int i1 = ((1 << (width - 1)) - 1);
int i2 = (lowBits << scale) + 1;
R = table[i1 >>> 1].add(table[i2 >>> 1]);
zeroes -= scale;
// System.out.println("Optimized: 2^" + scale + " * " + n + " = " + i1 + " + " + i2);
}
else
{
R = table[n >>> 1];
}
R = R.timesPow2(zeroes);
}
while (i > 0)
{
int wi = wnaf[--i];
int digit = wi >> 16, zeroes = wi & 0xFFFF;
int n = Math.abs(digit);
ECPoint[] table = digit < 0 ? preCompNeg : preComp;
ECPoint r = table[n >>> 1];
R = R.twicePlus(r);
R = R.timesPow2(zeroes);
}
return R;
}
/**
* Determine window width to use for a scalar multiplication of the given size.
*
* @param bits the bit-length of the scalar to multiply by
* @return the window size to use
*/
protected int getWindowSize(int bits)
{
return WNafUtil.getWindowSize(bits);
}
}
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