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package org.bouncycastle.math.ec;
import java.math.BigInteger;
public abstract class WNafUtil
{
public static final String PRECOMP_NAME = "bc_wnaf";
private static final int[] DEFAULT_WINDOW_SIZE_CUTOFFS = new int[]{ 13, 41, 121, 337, 897, 2305 };
private static final int MAX_WIDTH = 16;
private static final byte[] EMPTY_BYTES = new byte[0];
private static final int[] EMPTY_INTS = new int[0];
private static final ECPoint[] EMPTY_POINTS = new ECPoint[0];
public static void configureBasepoint(ECPoint p)
{
final ECCurve c = p.getCurve();
if (null == c)
{
return;
}
BigInteger n = c.getOrder();
int bits = (null == n) ? c.getFieldSize() + 1 : n.bitLength();
final int confWidth = Math.min(MAX_WIDTH, getWindowSize(bits) + 3);
c.precompute(p, PRECOMP_NAME, new PreCompCallback()
{
public PreCompInfo precompute(PreCompInfo existing)
{
WNafPreCompInfo existingWNaf = (existing instanceof WNafPreCompInfo) ? (WNafPreCompInfo)existing : null;
if (null != existingWNaf && existingWNaf.getConfWidth() == confWidth)
{
existingWNaf.setPromotionCountdown(0);
return existingWNaf;
}
WNafPreCompInfo result = new WNafPreCompInfo();
result.setPromotionCountdown(0);
result.setConfWidth(confWidth);
if (null != existingWNaf)
{
result.setPreComp(existingWNaf.getPreComp());
result.setPreCompNeg(existingWNaf.getPreCompNeg());
result.setTwice(existingWNaf.getTwice());
result.setWidth(existingWNaf.getWidth());
}
return result;
}
});
}
public static int[] generateCompactNaf(BigInteger k)
{
if ((k.bitLength() >>> 16) != 0)
{
throw new IllegalArgumentException("'k' must have bitlength < 2^16");
}
if (k.signum() == 0)
{
return EMPTY_INTS;
}
BigInteger _3k = k.shiftLeft(1).add(k);
int bits = _3k.bitLength();
int[] naf = new int[bits >> 1];
BigInteger diff = _3k.xor(k);
int highBit = bits - 1, length = 0, zeroes = 0;
for (int i = 1; i < highBit; ++i)
{
if (!diff.testBit(i))
{
++zeroes;
continue;
}
int digit = k.testBit(i) ? -1 : 1;
naf[length++] = (digit << 16) | zeroes;
zeroes = 1;
++i;
}
naf[length++] = (1 << 16) | zeroes;
if (naf.length > length)
{
naf = trim(naf, length);
}
return naf;
}
public static int[] generateCompactWindowNaf(int width, BigInteger k)
{
if (width == 2)
{
return generateCompactNaf(k);
}
if (width < 2 || width > 16)
{
throw new IllegalArgumentException("'width' must be in the range [2, 16]");
}
if ((k.bitLength() >>> 16) != 0)
{
throw new IllegalArgumentException("'k' must have bitlength < 2^16");
}
if (k.signum() == 0)
{
return EMPTY_INTS;
}
int[] wnaf = new int[k.bitLength() / width + 1];
// 2^width and a mask and sign bit set accordingly
int pow2 = 1 << width;
int mask = pow2 - 1;
int sign = pow2 >>> 1;
boolean carry = false;
int length = 0, pos = 0;
while (pos <= k.bitLength())
{
if (k.testBit(pos) == carry)
{
++pos;
continue;
}
k = k.shiftRight(pos);
int digit = k.intValue() & mask;
if (carry)
{
++digit;
}
carry = (digit & sign) != 0;
if (carry)
{
digit -= pow2;
}
int zeroes = length > 0 ? pos - 1 : pos;
wnaf[length++] = (digit << 16) | zeroes;
pos = width;
}
// Reduce the WNAF array to its actual length
if (wnaf.length > length)
{
wnaf = trim(wnaf, length);
}
return wnaf;
}
public static byte[] generateJSF(BigInteger g, BigInteger h)
{
int digits = Math.max(g.bitLength(), h.bitLength()) + 1;
byte[] jsf = new byte[digits];
BigInteger k0 = g, k1 = h;
int j = 0, d0 = 0, d1 = 0;
int offset = 0;
while ((d0 | d1) != 0 || k0.bitLength() > offset || k1.bitLength() > offset)
{
int n0 = ((k0.intValue() >>> offset) + d0) & 7, n1 = ((k1.intValue() >>> offset) + d1) & 7;
int u0 = n0 & 1;
if (u0 != 0)
{
u0 -= (n0 & 2);
if ((n0 + u0) == 4 && (n1 & 3) == 2)
{
u0 = -u0;
}
}
int u1 = n1 & 1;
if (u1 != 0)
{
u1 -= (n1 & 2);
if ((n1 + u1) == 4 && (n0 & 3) == 2)
{
u1 = -u1;
}
}
if ((d0 << 1) == 1 + u0)
{
d0 ^= 1;
}
if ((d1 << 1) == 1 + u1)
{
d1 ^= 1;
}
if (++offset == 30)
{
offset = 0;
k0 = k0.shiftRight(30);
k1 = k1.shiftRight(30);
}
jsf[j++] = (byte)((u0 << 4) | (u1 & 0xF));
}
// Reduce the JSF array to its actual length
if (jsf.length > j)
{
jsf = trim(jsf, j);
}
return jsf;
}
public static byte[] generateNaf(BigInteger k)
{
if (k.signum() == 0)
{
return EMPTY_BYTES;
}
BigInteger _3k = k.shiftLeft(1).add(k);
int digits = _3k.bitLength() - 1;
byte[] naf = new byte[digits];
BigInteger diff = _3k.xor(k);
for (int i = 1; i < digits; ++i)
{
if (diff.testBit(i))
{
naf[i - 1] = (byte)(k.testBit(i) ? -1 : 1);
++i;
}
}
naf[digits - 1] = 1;
return naf;
}
/**
* Computes the Window NAF (non-adjacent Form) of an integer.
* @param width The width w of the Window NAF. The width is
* defined as the minimal number w, such that for any
* w consecutive digits in the resulting representation, at
* most one is non-zero.
* @param k The integer of which the Window NAF is computed.
* @return The Window NAF of the given width, such that the following holds:
* k = ∑i=0l-1 ki2i
* , where the ki denote the elements of the
* returned byte[].
*/
public static byte[] generateWindowNaf(int width, BigInteger k)
{
if (width == 2)
{
return generateNaf(k);
}
if (width < 2 || width > 8)
{
throw new IllegalArgumentException("'width' must be in the range [2, 8]");
}
if (k.signum() == 0)
{
return EMPTY_BYTES;
}
byte[] wnaf = new byte[k.bitLength() + 1];
// 2^width and a mask and sign bit set accordingly
int pow2 = 1 << width;
int mask = pow2 - 1;
int sign = pow2 >>> 1;
boolean carry = false;
int length = 0, pos = 0;
while (pos <= k.bitLength())
{
if (k.testBit(pos) == carry)
{
++pos;
continue;
}
k = k.shiftRight(pos);
int digit = k.intValue() & mask;
if (carry)
{
++digit;
}
carry = (digit & sign) != 0;
if (carry)
{
digit -= pow2;
}
length += (length > 0) ? pos - 1 : pos;
wnaf[length++] = (byte)digit;
pos = width;
}
// Reduce the WNAF array to its actual length
if (wnaf.length > length)
{
wnaf = trim(wnaf, length);
}
return wnaf;
}
public static int getNafWeight(BigInteger k)
{
if (k.signum() == 0)
{
return 0;
}
BigInteger _3k = k.shiftLeft(1).add(k);
BigInteger diff = _3k.xor(k);
return diff.bitCount();
}
public static WNafPreCompInfo getWNafPreCompInfo(ECPoint p)
{
return getWNafPreCompInfo(p.getCurve().getPreCompInfo(p, PRECOMP_NAME));
}
public static WNafPreCompInfo getWNafPreCompInfo(PreCompInfo preCompInfo)
{
return (preCompInfo instanceof WNafPreCompInfo) ? (WNafPreCompInfo)preCompInfo : null;
}
/**
* 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
*/
public static int getWindowSize(int bits)
{
return getWindowSize(bits, DEFAULT_WINDOW_SIZE_CUTOFFS, MAX_WIDTH);
}
/**
* Determine window width to use for a scalar multiplication of the given size.
*
* @param bits the bit-length of the scalar to multiply by
* @param maxWidth the maximum window width to return
* @return the window size to use
*/
public static int getWindowSize(int bits, int maxWidth)
{
return getWindowSize(bits, DEFAULT_WINDOW_SIZE_CUTOFFS, maxWidth);
}
/**
* Determine window width to use for a scalar multiplication of the given size.
*
* @param bits the bit-length of the scalar to multiply by
* @param windowSizeCutoffs a monotonically increasing list of bit sizes at which to increment the window width
* @return the window size to use
*/
public static int getWindowSize(int bits, int[] windowSizeCutoffs)
{
return getWindowSize(bits, windowSizeCutoffs, MAX_WIDTH);
}
/**
* Determine window width to use for a scalar multiplication of the given size.
*
* @param bits the bit-length of the scalar to multiply by
* @param windowSizeCutoffs a monotonically increasing list of bit sizes at which to increment the window width
* @param maxWidth the maximum window width to return
* @return the window size to use
*/
public static int getWindowSize(int bits, int[] windowSizeCutoffs, int maxWidth)
{
int w = 0;
for (; w < windowSizeCutoffs.length; ++w)
{
if (bits < windowSizeCutoffs[w])
{
break;
}
}
return Math.max(2, Math.min(maxWidth, w + 2));
}
public static WNafPreCompInfo precompute(final ECPoint p, final int minWidth, final boolean includeNegated)
{
final ECCurve c = p.getCurve();
return (WNafPreCompInfo)c.precompute(p, PRECOMP_NAME, new PreCompCallback()
{
public PreCompInfo precompute(PreCompInfo existing)
{
WNafPreCompInfo existingWNaf = (existing instanceof WNafPreCompInfo) ? (WNafPreCompInfo)existing : null;
int width = Math.max(2, Math.min(MAX_WIDTH, minWidth));
int reqPreCompLen = 1 << (width - 2);
if (checkExisting(existingWNaf, width, reqPreCompLen, includeNegated))
{
existingWNaf.decrementPromotionCountdown();
return existingWNaf;
}
WNafPreCompInfo result = new WNafPreCompInfo();
ECPoint[] preComp = null, preCompNeg = null;
ECPoint twiceP = null;
if (null != existingWNaf)
{
int promotionCountdown = existingWNaf.decrementPromotionCountdown();
result.setPromotionCountdown(promotionCountdown);
int confWidth = existingWNaf.getConfWidth();
result.setConfWidth(confWidth);
preComp = existingWNaf.getPreComp();
preCompNeg = existingWNaf.getPreCompNeg();
twiceP = existingWNaf.getTwice();
}
width = Math.min(MAX_WIDTH, Math.max(result.getConfWidth(), width));
reqPreCompLen = 1 << (width - 2);
int iniPreCompLen = 0;
if (null == preComp)
{
preComp = EMPTY_POINTS;
}
else
{
iniPreCompLen = preComp.length;
}
if (iniPreCompLen < reqPreCompLen)
{
preComp = resizeTable(preComp, reqPreCompLen);
if (reqPreCompLen == 1)
{
preComp[0] = p.normalize();
}
else
{
int curPreCompLen = iniPreCompLen;
if (curPreCompLen == 0)
{
preComp[0] = p;
curPreCompLen = 1;
}
ECFieldElement iso = null;
if (reqPreCompLen == 2)
{
preComp[1] = p.threeTimes();
}
else
{
ECPoint isoTwiceP = twiceP, last = preComp[curPreCompLen - 1];
if (null == isoTwiceP)
{
isoTwiceP = preComp[0].twice();
twiceP = isoTwiceP;
/*
* For Fp curves with Jacobian projective coordinates, use a (quasi-)isomorphism
* where 'twiceP' is "affine", so that the subsequent additions are cheaper. This
* also requires scaling the initial point's X, Y coordinates, and reversing the
* isomorphism as part of the subsequent normalization.
*
* NOTE: The correctness of this optimization depends on:
* 1) additions do not use the curve's A, B coefficients.
* 2) no special cases (i.e. Q +/- Q) when calculating 1P, 3P, 5P, ...
*/
if (!twiceP.isInfinity() && ECAlgorithms.isFpCurve(c) && c.getFieldSize() >= 64)
{
switch (c.getCoordinateSystem())
{
case ECCurve.COORD_JACOBIAN:
case ECCurve.COORD_JACOBIAN_CHUDNOVSKY:
case ECCurve.COORD_JACOBIAN_MODIFIED:
{
iso = twiceP.getZCoord(0);
isoTwiceP = c.createPoint(twiceP.getXCoord().toBigInteger(), twiceP.getYCoord()
.toBigInteger());
ECFieldElement iso2 = iso.square(), iso3 = iso2.multiply(iso);
last = last.scaleX(iso2).scaleY(iso3);
if (iniPreCompLen == 0)
{
preComp[0] = last;
}
break;
}
}
}
}
while (curPreCompLen < reqPreCompLen)
{
/*
* Compute the new ECPoints for the precomputation array. The values 1, 3,
* 5, ..., 2^(width-1)-1 times p are computed
*/
preComp[curPreCompLen++] = last = last.add(isoTwiceP);
}
}
/*
* Having oft-used operands in affine form makes operations faster.
*/
c.normalizeAll(preComp, iniPreCompLen, reqPreCompLen - iniPreCompLen, iso);
}
}
if (includeNegated)
{
int pos;
if (null == preCompNeg)
{
pos = 0;
preCompNeg = new ECPoint[reqPreCompLen];
}
else
{
pos = preCompNeg.length;
if (pos < reqPreCompLen)
{
preCompNeg = resizeTable(preCompNeg, reqPreCompLen);
}
}
while (pos < reqPreCompLen)
{
preCompNeg[pos] = preComp[pos].negate();
++pos;
}
}
result.setPreComp(preComp);
result.setPreCompNeg(preCompNeg);
result.setTwice(twiceP);
result.setWidth(width);
return result;
}
private boolean checkExisting(WNafPreCompInfo existingWNaf, int width, int reqPreCompLen, boolean includeNegated)
{
return null != existingWNaf
&& existingWNaf.getWidth() >= Math.max(existingWNaf.getConfWidth(), width)
&& checkTable(existingWNaf.getPreComp(), reqPreCompLen)
&& (!includeNegated || checkTable(existingWNaf.getPreCompNeg(), reqPreCompLen));
}
private boolean checkTable(ECPoint[] table, int reqLen)
{
return null != table && table.length >= reqLen;
}
});
}
public static WNafPreCompInfo precomputeWithPointMap(final ECPoint p, final ECPointMap pointMap, final WNafPreCompInfo fromWNaf,
final boolean includeNegated)
{
final ECCurve c = p.getCurve();
return (WNafPreCompInfo)c.precompute(p, PRECOMP_NAME, new PreCompCallback()
{
public PreCompInfo precompute(PreCompInfo existing)
{
WNafPreCompInfo existingWNaf = (existing instanceof WNafPreCompInfo) ? (WNafPreCompInfo)existing : null;
int width = fromWNaf.getWidth();
int reqPreCompLen = fromWNaf.getPreComp().length;
if (checkExisting(existingWNaf, width, reqPreCompLen, includeNegated))
{
existingWNaf.decrementPromotionCountdown();
return existingWNaf;
}
/*
* TODO Ideally this method would support incremental calculation, but given the
* existing use-cases it would be of little-to-no benefit.
*/
WNafPreCompInfo result = new WNafPreCompInfo();
result.setPromotionCountdown(fromWNaf.getPromotionCountdown());
ECPoint twiceFrom = fromWNaf.getTwice();
if (null != twiceFrom)
{
ECPoint twice = pointMap.map(twiceFrom);
result.setTwice(twice);
}
ECPoint[] preCompFrom = fromWNaf.getPreComp();
ECPoint[] preComp = new ECPoint[preCompFrom.length];
for (int i = 0; i < preCompFrom.length; ++i)
{
preComp[i] = pointMap.map(preCompFrom[i]);
}
result.setPreComp(preComp);
result.setWidth(width);
if (includeNegated)
{
ECPoint[] preCompNeg = new ECPoint[preComp.length];
for (int i = 0; i < preCompNeg.length; ++i)
{
preCompNeg[i] = preComp[i].negate();
}
result.setPreCompNeg(preCompNeg);
}
return result;
}
private boolean checkExisting(WNafPreCompInfo existingWNaf, int width, int reqPreCompLen, boolean includeNegated)
{
return null != existingWNaf
&& existingWNaf.getWidth() >= width
&& checkTable(existingWNaf.getPreComp(), reqPreCompLen)
&& (!includeNegated || checkTable(existingWNaf.getPreCompNeg(), reqPreCompLen));
}
private boolean checkTable(ECPoint[] table, int reqLen)
{
return null != table && table.length >= reqLen;
}
});
}
private static byte[] trim(byte[] a, int length)
{
byte[] result = new byte[length];
System.arraycopy(a, 0, result, 0, result.length);
return result;
}
private static int[] trim(int[] a, int length)
{
int[] result = new int[length];
System.arraycopy(a, 0, result, 0, result.length);
return result;
}
private static ECPoint[] resizeTable(ECPoint[] a, int length)
{
ECPoint[] result = new ECPoint[length];
System.arraycopy(a, 0, result, 0, a.length);
return result;
}
}
