/** @com.intel.drl.spec_ref */
public ECFieldF2m(int m, BigInteger rp) {
this.m = m;
if (this.m <= 0) {
throw new IllegalArgumentException(Messages.getString("security.75")); // $NON-NLS-1$
}
this.rp = rp;
if (this.rp == null) {
throw new NullPointerException(Messages.getString("security.76")); // $NON-NLS-1$
}
// the leftmost bit must be (m+1)-th one,
// set bits count must be 3 or 5,
// bits 0 and m must be set
int rp_bc = this.rp.bitCount();
if ((this.rp.bitLength() != (m + 1))
|| (rp_bc != TPB_LEN && rp_bc != PPB_LEN)
|| (!this.rp.testBit(0) || !this.rp.testBit(m))) {
throw new IllegalArgumentException(Messages.getString("security.77")); // $NON-NLS-1$
}
// setup ks using rp:
// allocate for mid terms only
ks = new int[rp_bc - 2];
// find midterm orders and set ks accordingly
BigInteger rpTmp = rp.clearBit(0);
for (int i = ks.length - 1; i >= 0; i--) {
ks[i] = rpTmp.getLowestSetBit();
rpTmp = rpTmp.clearBit(ks[i]);
}
}
private static BigInteger[] LucasSequence(
BigInteger p, BigInteger X, BigInteger Y, BigInteger k) {
int n = k.bitLength();
int s = k.getLowestSetBit();
BigInteger D = X.multiply(X).subtract(Y.shiftLeft(2));
BigInteger U = BigInteger.ONE;
BigInteger V = X;
for (int j = n - 1; j >= s; j--) {
if (k.testBit(j)) {
BigInteger T = X.multiply(U).add(V).shiftRight(1).mod(p);
V = X.multiply(V).add(D.multiply(U)).shiftRight(1).mod(p);
U = T;
} else {
BigInteger T = U.multiply(V).mod(p);
V = V.multiply(V).add(D.multiply(U.multiply(U))).shiftRight(1).mod(p);
U = T;
}
}
for (int j = 1; j <= s; j++) {
BigInteger T = U.multiply(V).mod(p);
V = V.multiply(V).add(D.multiply(U.multiply(U))).shiftRight(1).mod(p);
U = T;
}
return new BigInteger[] {U, V};
}
/**
* Returns a BigDecimal representation of this fraction. If possible, the returned value will be
* exactly equal to the fraction. If not, the BigDecimal will have a scale large enough to hold
* the same number of significant figures as both numerator and denominator, or the equivalent of
* a double-precision number, whichever is more.
*/
public BigDecimal toBigDecimal() {
// Implementation note: A fraction can be represented exactly in base-10 iff its
// denominator is of the form 2^a * 5^b, where a and b are nonnegative integers.
// (In other words, if there are no prime factors of the denominator except for
// 2 and 5, or if the denominator is 1). So to determine if this denominator is
// of this form, continually divide by 2 to get the number of 2's, and then
// continually divide by 5 to get the number of 5's. Afterward, if the denominator
// is 1 then there are no other prime factors.
// Note: number of 2's is given by the number of trailing 0 bits in the number
int twos = denominator.getLowestSetBit();
BigInteger tmpDen = denominator.shiftRight(twos); // x / 2^n === x >> n
final BigInteger FIVE = BigInteger.valueOf(5);
int fives = 0;
BigInteger[] divMod = null;
// while(tmpDen % 5 == 0) { fives++; tmpDen /= 5; }
while (BigInteger.ZERO.equals((divMod = tmpDen.divideAndRemainder(FIVE))[1])) {
fives++;
tmpDen = divMod[0];
}
if (BigInteger.ONE.equals(tmpDen)) {
// This fraction will terminate in base 10, so it can be represented exactly as
// a BigDecimal. We would now like to make the fraction of the form
// unscaled / 10^scale. We know that 2^x * 5^x = 10^x, and our denominator is
// in the form 2^twos * 5^fives. So use max(twos, fives) as the scale, and
// multiply the numerator and deminator by the appropriate number of 2's or 5's
// such that the denominator is of the form 2^scale * 5^scale. (Of course, we
// only have to actually multiply the numerator, since all we need for the
// BigDecimal constructor is the scale.
BigInteger unscaled = numerator;
int scale = Math.max(twos, fives);
if (twos < fives) unscaled = unscaled.shiftLeft(fives - twos); // x * 2^n === x << n
else if (fives < twos) unscaled = unscaled.multiply(FIVE.pow(twos - fives));
return new BigDecimal(unscaled, scale);
}
// else: this number will repeat infinitely in base-10. So try to figure out
// a good number of significant digits. Start with the number of digits required
// to represent the numerator and denominator in base-10, which is given by
// bitLength / log[2](10). (bitLenth is the number of digits in base-2).
final double LG10 = 3.321928094887362; // Precomputed ln(10)/ln(2), a.k.a. log[2](10)
int precision = Math.max(numerator.bitLength(), denominator.bitLength());
precision = (int) Math.ceil(precision / LG10);
// If the precision is less than 18 digits, use 18 digits so that the number
// will be at least as accurate as a cast to a double. For example, with
// the fraction 1/3, precision will be 1, giving a result of 0.3. This is
// quite a bit different from what a user would expect.
if (precision < 18) precision = 18;
return toBigDecimal(precision);
}
public BigInteger fastPower(BigInteger a, BigInteger t) {
BigInteger result = BigInteger.ONE;
while (t.compareTo(BigInteger.ZERO) == 1) {
if (t.getLowestSetBit() == 0) {
result = result.multiply(a);
}
a = a.multiply(a);
t = t.shiftRight(1);
a = a.mod(n);
result = result.mod(n);
}
return result;
}
/**
* Encodes a string using arithmetic encoding.
*
* @param message the message to encode
* @return the encoded value as a byte array
*/
@Override
public byte[] encode(String message) {
// Remove invalid UTF-8 symbols.
message = message.replace(Character.toString((char) 0xFFFD), "");
// Set up encoding process.
BigInteger lowValue = BigInteger.valueOf(0);
BigInteger highValue = BigInteger.valueOf(0);
BigInteger length = BigInteger.valueOf(message.length());
BigInteger totalProduct = BigInteger.valueOf(1);
// Make the key based on the current string.
CharMap key = makeKey(message);
// Calculate the lowValue (the lowest possible encoding).
for (Character c : message.toCharArray()) {
lowValue = lowValue.add(totalProduct.multiply(BigInteger.valueOf(key.get(c))));
lowValue = lowValue.multiply(length);
totalProduct = totalProduct.multiply(BigInteger.valueOf(key.getProbability(c)));
}
lowValue = lowValue.divide(length);
// Calculate the highValue based on the lowValue.
highValue = lowValue.add(totalProduct);
// Create a value for the final encoding
BigInteger value = lowValue;
value = maxZeroes(value, highValue);
int zeroes = value.getLowestSetBit();
value = value.shiftRight(zeroes);
// Output the resulting number to a byte array.
ByteArrayOutputStream outputBytes = new ByteArrayOutputStream();
DataOutputStream output = new DataOutputStream(outputBytes);
try {
output.writeInt(key.size());
output.writeInt(zeroes);
for (Map.Entry<Character, Integer> e : key.entrySet()) {
output.writeChar(e.getKey());
output.writeInt(e.getValue());
}
output.write(value.toByteArray());
} catch (java.io.IOException e) {
System.err.println("There was an IOException.");
return null;
}
// Return the output bytes.
return outputBytes.toByteArray();
}
/** Constructs a new BigFraction from the given BigDecimal object. */
private static BigFraction valueOfHelper(final BigDecimal d) {
// BigDecimal format: unscaled / 10^scale.
BigInteger tmpNumerator = d.unscaledValue();
BigInteger tmpDenominator = BigInteger.ONE;
// Special case for d == 0 (math below won't work right)
// Note: Cannot use d.equals(BigDecimal.ZERO), because
// BigDecimal.equals()
// does not consider numbers equal if they have different scales. So,
// 0.00 is not equal to BigDecimal.ZERO.
if (tmpNumerator.equals(BigInteger.ZERO)) {
return BigFraction.ZERO;
}
if (d.scale() < 0) {
tmpNumerator = tmpNumerator.multiply(BigInteger.TEN.pow(-d.scale()));
} else if (d.scale() > 0) {
// Now we have the form: unscaled / 10^scale = unscaled / (2^scale *
// 5^scale)
// We know then that gcd(unscaled, 2^scale * 5^scale) = 2^commonTwos
// * 5^commonFives
// Easy to determine commonTwos
final int commonTwos = Math.min(d.scale(), tmpNumerator.getLowestSetBit());
tmpNumerator = tmpNumerator.shiftRight(commonTwos);
tmpDenominator = tmpDenominator.shiftLeft(d.scale() - commonTwos);
// Determining commonFives is a little trickier..
int commonFives = 0;
BigInteger[] divMod = null;
// while(commonFives < d.scale() && tmpNumerator % 5 == 0) {
// tmpNumerator /= 5; commonFives++; }
while (commonFives < d.scale()
&& BigInteger.ZERO.equals((divMod = tmpNumerator.divideAndRemainder(BIGINT_FIVE))[1])) {
tmpNumerator = divMod[0];
commonFives++;
}
if (commonFives < d.scale()) {
tmpDenominator = tmpDenominator.multiply(BIGINT_FIVE.pow(d.scale() - commonFives));
}
}
// else: d.scale() == 0: do nothing
// Guaranteed there is no gcd, so fraction is in lowest terms
return new BigFraction(tmpNumerator, tmpDenominator, Reduced.YES);
}
private BigInteger[] lucasSequence(BigInteger P, BigInteger Q, BigInteger k) {
// TODO Research and apply "common-multiplicand multiplication here"
int n = k.bitLength();
int s = k.getLowestSetBit();
// assert k.testBit(s);
BigInteger Uh = ECConstants.ONE;
BigInteger Vl = ECConstants.TWO;
BigInteger Vh = P;
BigInteger Ql = ECConstants.ONE;
BigInteger Qh = ECConstants.ONE;
for (int j = n - 1; j >= s + 1; --j) {
Ql = modMult(Ql, Qh);
if (k.testBit(j)) {
Qh = modMult(Ql, Q);
Uh = modMult(Uh, Vh);
Vl = modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql)));
Vh = modReduce(Vh.multiply(Vh).subtract(Qh.shiftLeft(1)));
} else {
Qh = Ql;
Uh = modReduce(Uh.multiply(Vl).subtract(Ql));
Vh = modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql)));
Vl = modReduce(Vl.multiply(Vl).subtract(Ql.shiftLeft(1)));
}
}
Ql = modMult(Ql, Qh);
Qh = modMult(Ql, Q);
Uh = modReduce(Uh.multiply(Vl).subtract(Ql));
Vl = modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql)));
Ql = modMult(Ql, Qh);
for (int j = 1; j <= s; ++j) {
Uh = modMult(Uh, Vl);
Vl = modReduce(Vl.multiply(Vl).subtract(Ql.shiftLeft(1)));
Ql = modMult(Ql, Ql);
}
return new BigInteger[] {Uh, Vl};
}
private static BigInteger[] lucasSequence(
BigInteger p, BigInteger P, BigInteger Q, BigInteger k) {
int n = k.bitLength();
int s = k.getLowestSetBit();
BigInteger Uh = ECConstants.ONE;
BigInteger Vl = ECConstants.TWO;
BigInteger Vh = P;
BigInteger Ql = ECConstants.ONE;
BigInteger Qh = ECConstants.ONE;
for (int j = n - 1; j >= s + 1; --j) {
Ql = Ql.multiply(Qh).mod(p);
if (k.testBit(j)) {
Qh = Ql.multiply(Q).mod(p);
Uh = Uh.multiply(Vh).mod(p);
Vl = Vh.multiply(Vl).subtract(P.multiply(Ql)).mod(p);
Vh = Vh.multiply(Vh).subtract(Qh.shiftLeft(1)).mod(p);
} else {
Qh = Ql;
Uh = Uh.multiply(Vl).subtract(Ql).mod(p);
Vh = Vh.multiply(Vl).subtract(P.multiply(Ql)).mod(p);
Vl = Vl.multiply(Vl).subtract(Ql.shiftLeft(1)).mod(p);
}
}
Ql = Ql.multiply(Qh).mod(p);
Qh = Ql.multiply(Q).mod(p);
Uh = Uh.multiply(Vl).subtract(Ql).mod(p);
Vl = Vh.multiply(Vl).subtract(P.multiply(Ql)).mod(p);
Ql = Ql.multiply(Qh).mod(p);
for (int j = 1; j <= s; ++j) {
Uh = Uh.multiply(Vl).mod(p);
Vl = Vl.multiply(Vl).subtract(Ql.shiftLeft(1)).mod(p);
Ql = Ql.multiply(Ql).mod(p);
}
return new BigInteger[] {Uh, Vl};
}
public static void bitOps(int order) {
int failCount1 = 0, failCount2 = 0, failCount3 = 0;
for (int i = 0; i < size * 5; i++) {
BigInteger x = fetchNumber(order);
BigInteger y;
/* Test setBit and clearBit (and testBit) */
if (x.signum() < 0) {
y = BigInteger.valueOf(-1);
for (int j = 0; j < x.bitLength(); j++) if (!x.testBit(j)) y = y.clearBit(j);
} else {
y = BigInteger.ZERO;
for (int j = 0; j < x.bitLength(); j++) if (x.testBit(j)) y = y.setBit(j);
}
if (!x.equals(y)) failCount1++;
/* Test flipBit (and testBit) */
y = BigInteger.valueOf(x.signum() < 0 ? -1 : 0);
for (int j = 0; j < x.bitLength(); j++) if (x.signum() < 0 ^ x.testBit(j)) y = y.flipBit(j);
if (!x.equals(y)) failCount2++;
}
report("clearBit/testBit", failCount1);
report("flipBit/testBit", failCount2);
for (int i = 0; i < size * 5; i++) {
BigInteger x = fetchNumber(order);
/* Test getLowestSetBit() */
int k = x.getLowestSetBit();
if (x.signum() == 0) {
if (k != -1) failCount3++;
} else {
BigInteger z = x.and(x.negate());
int j;
for (j = 0; j < z.bitLength() && !z.testBit(j); j++) ;
if (k != j) failCount3++;
}
}
report("getLowestSetBit", failCount3);
}
/** Returns {@code true} if {@code x} represents a power of two. */
public static boolean isPowerOfTwo(BigInteger x) {
checkNotNull(x);
return x.signum() > 0 && x.getLowestSetBit() == x.bitLength() - 1;
}
/** Constructs a BigFraction from a floating-point number. */
private static BigFraction valueOfHelper(final double d) {
if (Double.isInfinite(d)) {
throw new IllegalArgumentException("double val is infinite");
}
if (Double.isNaN(d)) {
throw new IllegalArgumentException("double val is NaN");
}
// special case - math below won't work right for 0.0 or -0.0
if (d == 0) {
return BigFraction.ZERO;
}
// Per IEEE spec...
final long bits = Double.doubleToLongBits(d);
final int sign = (int) (bits >> 63) & 0x1;
final int exponent = ((int) (bits >> 52) & 0x7ff) - 0x3ff;
final long mantissa = bits & 0xfffffffffffffL;
// Number is: (-1)^sign * 2^(exponent) * 1.mantissa
// Neglecting sign bit, this gives:
// 2^(exponent) * 1.mantissa
// = 2^(exponent) * (1 + mantissa/2^52)
// = 2^(exponent) * (2^52 + mantissa)/2^52
// For exponent > 52:
// = 2^(exponent - 52) * (2^52 + mantissa)
// For exponent = 52:
// = 2^52 + mantissa
// For exponent < 52:
// = (2^52 + mantissa) / 2^(52 - exponent)
BigInteger tmpNumerator = BigInteger.valueOf(0x10000000000000L + mantissa);
BigInteger tmpDenominator = BigInteger.ONE;
if (exponent > 52) {
// numerator * 2^(exponent - 52) === numerator << (exponent - 52)
tmpNumerator = tmpNumerator.shiftLeft(exponent - 52);
} else if (exponent < 52) {
// The gcd of (2^52 + mantissa) / 2^(52 - exponent) must be of the
// form 2^y,
// since the only prime factors of the denominator are 2. In base-2,
// it is
// easy to determine how many factors of 2 a number has--it is the
// number of
// trailing "0" bits at the end of the number. (This is the same as
// the number
// of trailing 0's of a base-10 number indicating the number of
// factors of 10
// the number has).
final int y = Math.min(tmpNumerator.getLowestSetBit(), 52 - exponent);
// Now 2^y = gcd( 2^52 + mantissa, 2^(52 - exponent) ), giving:
// (2^52 + mantissa) / 2^(52 - exponent)
// = ((2^52 + mantissa) / 2^y) / (2^(52 - exponent) / 2^y)
// = ((2^52 + mantissa) / 2^y) / (2^(52 - exponent - y))
// = ((2^52 + mantissa) >> y) / (1 << (52 - exponent - y))
tmpNumerator = tmpNumerator.shiftRight(y);
tmpDenominator = tmpDenominator.shiftLeft(52 - exponent - y);
}
// else: exponent == 52: do nothing
// Set sign bit if needed
if (sign != 0) {
tmpNumerator = tmpNumerator.negate();
}
// Guaranteed there is no gcd, so fraction is in lowest terms
return new BigFraction(tmpNumerator, tmpDenominator, Reduced.YES);
}
