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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.math.ec;
import java.math.BigInteger;
public abstract class WNafUtil
{
private static int[] DEFAULT_WINDOW_SIZE_CUTOFFS = new int[]{ 13, 41, 121, 337, 897, 2305 };
public static int[] generateCompactNaf(BigInteger k)
{
if ((k.bitLength() >>> 16) != 0)
{
throw new IllegalArgumentException("'k' must have bitlength < 2^16");
}
BigInteger _3k = k.shiftLeft(1).add(k);
int digits = _3k.bitLength() - 1;
int[] naf = new int[(digits + 1) >> 1];
int length = 0, zeroes = 0;
for (int i = 1; i <= digits; ++i)
{
boolean _3kBit = _3k.testBit(i);
boolean kBit = k.testBit(i);
if (_3kBit == kBit)
{
++zeroes;
}
else
{
int digit = kBit ? -1 : 1;
naf[length++] = (digit << 16) | zeroes;
zeroes = 0;
}
}
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");
}
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;
while (k0.signum() > 0 || k1.signum() > 0 || d0 > 0 || d1 > 0)
{
int n0 = (k0.intValue() + d0) & 7, n1 = (k1.intValue() + 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 - d0;
}
if ((d1 << 1) == 1 + u1)
{
d1 = 1 - d1;
}
k0 = k0.shiftRight(1);
k1 = k1.shiftRight(1);
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)
{
BigInteger _3k = k.shiftLeft(1).add(k);
int digits = _3k.bitLength() - 1;
byte[] naf = new byte[digits];
for (int i = 1; i <= digits; ++i)
{
boolean _3kBit = _3k.testBit(i);
boolean kBit = k.testBit(i);
naf[i - 1] = (byte)(_3kBit == kBit ? 0 : kBit ? -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]");
}
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 WNafPreCompInfo getWNafPreCompInfo(PreCompInfo preCompInfo)
{
if ((preCompInfo != null) && (preCompInfo instanceof WNafPreCompInfo))
{
return (WNafPreCompInfo)preCompInfo;
}
return new WNafPreCompInfo();
}
/**
* 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);
}
/**
* 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)
{
int w = 0;
for (; w < windowSizeCutoffs.length; ++w)
{
if (bits < windowSizeCutoffs[w])
{
break;
}
}
return w + 2;
}
public static WNafPreCompInfo precompute(ECPoint p, int width, boolean includeNegated)
{
ECCurve c = p.getCurve();
WNafPreCompInfo wnafPreCompInfo = getWNafPreCompInfo(c.getPreCompInfo(p));
ECPoint[] preComp = wnafPreCompInfo.getPreComp();
if (preComp == null)
{
preComp = new ECPoint[]{ p };
}
int preCompLen = preComp.length;
int reqPreCompLen = 1 << Math.max(0, width - 2);
if (preCompLen < reqPreCompLen)
{
ECPoint twiceP = wnafPreCompInfo.getTwiceP();
if (twiceP == null)
{
twiceP = preComp[0].twice().normalize();
wnafPreCompInfo.setTwiceP(twiceP);
}
preComp = resizeTable(preComp, reqPreCompLen);
/*
* TODO Okeya/Sakurai paper has precomputation trick and "Montgomery's Trick" to speed this up.
* Also, co-Z arithmetic could avoid the subsequent normalization too.
*/
for (int i = preCompLen; i < reqPreCompLen; i++)
{
/*
* Compute the new ECPoints for the precomputation array. The values 1, 3, 5, ...,
* 2^(width-1)-1 times p are computed
*/
preComp[i] = twiceP.add(preComp[i - 1]);
}
/*
* Having oft-used operands in affine form makes operations faster.
*/
c.normalizeAll(preComp);
}
wnafPreCompInfo.setPreComp(preComp);
if (includeNegated)
{
ECPoint[] preCompNeg = wnafPreCompInfo.getPreCompNeg();
int pos;
if (preCompNeg == null)
{
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;
}
wnafPreCompInfo.setPreCompNeg(preCompNeg);
}
c.setPreCompInfo(p, wnafPreCompInfo);
return wnafPreCompInfo;
}
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;
}
}
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