public static BigInteger combinations(BigInteger n, BigInteger k) {
if (k.compareTo(n) > 0) {
return BigInteger.ZERO;
} else {
return factorial(n).divide(factorial(k)).divide(factorial(n.subtract(k)));
}
}
protected BigInteger modReduce(BigInteger x) {
if (r != null) {
boolean negative = x.signum() < 0;
if (negative) {
x = x.abs();
}
int qLen = q.bitLength();
boolean rIsOne = r.equals(ECConstants.ONE);
while (x.bitLength() > (qLen + 1)) {
BigInteger u = x.shiftRight(qLen);
BigInteger v = x.subtract(u.shiftLeft(qLen));
if (!rIsOne) {
u = u.multiply(r);
}
x = u.add(v);
}
while (x.compareTo(q) >= 0) {
x = x.subtract(q);
}
if (negative && x.signum() != 0) {
x = q.subtract(x);
}
} else {
x = x.mod(q);
}
return x;
}
/**
* Randomly generates an exponent with a given size.
*
* @param size the size of the exponent
* @return the exponent which is an RSABigInteger
*/
public RSARandomGen(int size) {
this.size = size;
BigInteger p, q, phiN;
BigInteger e;
// Two prime numbers q and p are randomly chosen
p = BigInteger.probablePrime(size / 2, this.random);
q = BigInteger.probablePrime(size / 2, this.random);
// Then we calculate n, such that n = p * q
// this.n = q.multiply(q);
this.modulus = q.multiply(p);
// phiN is calculated such as phiN=(p-1).(q-1)
phiN = p.subtract(BigInteger.ONE);
phiN = phiN.multiply(q.subtract(BigInteger.ONE));
// A random e exponent is calculated such that
do {
e = new BigInteger(size, new Random());
} while (phiN.compareTo(e) != 1 || e.gcd(phiN).compareTo(BigInteger.ONE) != 0);
this.publicKey = e;
this.privateKey = this.publicKey.modInverse(phiN);
}
public void finalTestPreparation() {
BigInteger p = new BigInteger("292634146651759944677438112396289238593");
BigInteger q = new BigInteger("259951719401515993224438940898363904593");
BigInteger n = p.multiply(q);
BigInteger d =
new BigInteger(
"19230821527409863624078497539913356864126656509482952467658625658635184671529");
BigInteger e =
new BigInteger(
"27475944712397552787445445104954180296036650677717137281603953463917489674521");
BigInteger phin = p.subtract(BigInteger.ONE).multiply(q.subtract(BigInteger.ONE));
System.out.println("Check: " + e.multiply(d).mod(phin));
RSAEncryptor rsaenc = new RSAEncryptor(n, e);
RSADecryptor rsadec = new RSADecryptor(p, q, d);
Vector<BigInteger> cipher;
String plain =
"Congratulations!\nYou have successfuly completed the programming exercise!!\nWell done!!!\n";
cipher = rsaenc.encrypt(plain);
String result = rsadec.decrypt(cipher);
System.out.println(result + "\n\n");
System.out.println("Vector<BigInteger> cipher = new Vector<BigInteger>();\n");
for (BigInteger i : cipher) {
System.out.println("cipher.add(new BigInteger(\"" + i + "\"));");
}
}
public void initialize() {
e = BigInteger.valueOf(65537);
SecureRandom sr = new SecureRandom();
BigInteger diff = BigInteger.valueOf(2).pow(256);
/*
generate 2 prime numbers greater than 512 bits and that have difference of 2^256
*/
do {
sr.generateSeed(size);
p = new BigInteger(size, 256, sr);
sr.generateSeed(size);
q = new BigInteger(size, 256, sr);
} while (p.bitLength() < size
|| q.bitLength() < size
|| !p.isProbablePrime(256)
|| !q.isProbablePrime(256)
|| p.subtract(q).abs().compareTo(diff) != 1);
n = p.multiply(q);
phi_n = p.subtract(BigInteger.ONE).multiply(q.subtract(BigInteger.ONE));
d = e.modInverse(phi_n);
}
private static float getProgressForRange(
final ByteSequence start, final ByteSequence end, final ByteSequence position) {
final int maxDepth = Math.min(Math.max(end.length(), start.length()), position.length());
final BigInteger startBI = new BigInteger(AccumuloMRUtils.extractBytes(start, maxDepth));
final BigInteger endBI = new BigInteger(AccumuloMRUtils.extractBytes(end, maxDepth));
final BigInteger positionBI = new BigInteger(AccumuloMRUtils.extractBytes(position, maxDepth));
return (float)
(positionBI.subtract(startBI).doubleValue() / endBI.subtract(startBI).doubleValue());
}
// generate an N-bit (roughly) public and private key
RSA(int N) {
BigInteger p = BigInteger.probablePrime(N / 2, random);
BigInteger q = BigInteger.probablePrime(N / 2, random);
BigInteger phi = (p.subtract(one)).multiply(q.subtract(one));
modulus = p.multiply(q);
publicKey = new BigInteger("65537"); // common value in practice = 2^16 + 1
privateKey = publicKey.modInverse(phi);
}
public static BigInteger fib(BigInteger n) throws Throwable {
if (n.equals(BigInteger.ZERO)) return BigInteger.ZERO;
if (n.equals(BigInteger.ONE)) return BigInteger.ONE;
// return fib(n - 1) + fib(n - 2);
return ((BigInteger) mhDynamic.invokeExact(n.subtract(BigInteger.ONE)))
.add((BigInteger) mhDynamic.invokeExact(n.subtract(BigInteger.valueOf(2))));
}
public RSA(Random random) {
savedRandom = random;
p = getPrime(random); // p and q are arbitrary large primes
q = getPrime(random);
n = p.multiply(q);
phiN = (p.subtract(ONE)).multiply(q.subtract(ONE));
S = getPrime(random); // s is an arbitrary secret; we'll use a prime
V = S.modPow(new BigInteger("2"), n);
}
/**
* Los valores han sido calculados matemáticamente. p --> un número primo; q --> numero primo
* menor que p; e --> numero coPrimo de y menor que n
*/
public EncriptacionRSA() {
p = new BigInteger("37111475501984423786707");
q = new BigInteger("22457587554291135069157");
// n = p * q
n = p.multiply(q);
e = new BigInteger("376816953197990800115868480017153452275607211");
totient = p.subtract(BigInteger.valueOf(1));
totient = totient.multiply(q.subtract(BigInteger.valueOf(1)));
// d = e^1 mod totient
d = e.modInverse(totient);
}
/** Generate a new public and private key set. */
public synchronized void generateKeys() {
SecureRandom r = new SecureRandom();
BigInteger p = new BigInteger(bitlen / 2, 100, r);
BigInteger q = new BigInteger(bitlen / 2, 100, r);
n = p.multiply(q);
BigInteger m = (p.subtract(BigInteger.ONE)).multiply(q.subtract(BigInteger.ONE));
e = new BigInteger("3");
while (m.gcd(e).intValue() > 1) {
e = e.add(new BigInteger("2"));
}
d = e.modInverse(m);
}
/*
See IEEE P1363 A.15.5 (10/05/98 Draft)
*/
public static BigInteger generateRandomPrime(
BigInteger r, BigInteger a, int pmin, int pmax, BigInteger f) {
BigInteger d, w;
// Step 1 - generate prime
BigInteger p = new BigInteger((pmax + pmin) / 2, new Random());
steptwo:
{ // Step 2
w = p.mod(r.multiply(BigInteger.valueOf(2)));
// Step 3
p = p.add(r.multiply(BigInteger.valueOf(2)));
p = p.subtract(w);
p = p.add(a);
// Step 4 - test for even
if (p.mod(BigInteger.valueOf(2)).compareTo(BigInteger.valueOf(0)) == 0) p = p.add(r);
for (; ; ) {
// Step 5
if (p.compareTo(BigInteger.valueOf(1).shiftLeft(pmax)) > 0) {
// Step 5.1
p = p.subtract(BigInteger.valueOf(1).shiftLeft(pmax));
p = p.add(BigInteger.valueOf(1).shiftLeft(pmin));
p = p.subtract(BigInteger.valueOf(1));
// Step 5.2 - goto to Step 2
break steptwo;
}
// Step 6
d = p.subtract(BigInteger.valueOf(1));
d = d.gcd(f);
// Step 7 - test d
if (d.compareTo(BigInteger.valueOf(1)) == 0) {
// Step 7.1 - test primality
if (p.isProbablePrime(1) == true) {
// Step 7.2;
return p;
}
}
// Step 8
p = p.add(r.multiply(BigInteger.valueOf(2)));
// Step 9
}
}
// Should never reach here but makes the compiler happy
return BigInteger.valueOf(0);
}
@Override
public Item item(final QueryContext qc, final InputInfo ii) throws QueryException {
final B64 b64 = toB64(exprs[0], qc, true);
long by = toLong(exprs[1], qc);
if (b64 == null) return null;
if (by == 0) return b64;
byte[] bytes = b64.binary(info);
final int bl = bytes.length;
byte[] tmp = new byte[bl];
int r = 0;
if (by > 7) {
tmp = new BigInteger(bytes).shiftLeft((int) by).toByteArray();
if (tmp.length != bl) {
bytes = tmp;
tmp = new byte[bl];
System.arraycopy(bytes, bytes.length - bl, tmp, 0, bl);
}
} else if (by > 0) {
for (int i = bl - 1; i >= 0; i--) {
final byte b = bytes[i];
tmp[i] = (byte) (b << by | r);
r = b >>> 32 - by;
}
} else if (by > -8) {
by = -by;
for (int i = 0; i < bl; i++) {
final int b = bytes[i] & 0xFF;
tmp[i] = (byte) (b >>> by | r);
r = b << 32 - by;
}
} else {
by = -by;
BigInteger bi = new BigInteger(bytes);
if (bi.signum() >= 0) {
bi = bi.shiftRight((int) by);
} else {
final BigInteger o = BigInteger.ONE.shiftLeft(bl * 8 + 1);
final BigInteger m = o.subtract(BigInteger.ONE).shiftRight((int) by + 1);
bi = bi.subtract(o).shiftRight((int) by).and(m);
}
tmp = bi.toByteArray();
final int tl = tmp.length;
if (tl != bl) {
bytes = tmp;
tmp = new byte[bl];
System.arraycopy(bytes, 0, tmp, bl - tl, tl);
}
}
return new B64(tmp);
}
private static BigInteger calculateGenerator_FIPS186_2(
BigInteger p, BigInteger q, SecureRandom r) {
BigInteger e = p.subtract(ONE).divide(q);
BigInteger pSub2 = p.subtract(TWO);
for (; ; ) {
BigInteger h = BigIntegers.createRandomInRange(TWO, pSub2, r);
BigInteger g = h.modPow(e, p);
if (g.bitLength() > 1) {
return g;
}
}
}
/** Create an instance that can both encrypt and decrypt. */
public RSA(int bits) {
bitlen = bits;
SecureRandom r = new SecureRandom();
BigInteger p = new BigInteger(bitlen / 2, 100, r);
BigInteger q = new BigInteger(bitlen / 2, 100, r);
n = p.multiply(q);
BigInteger m = (p.subtract(BigInteger.ONE)).multiply(q.subtract(BigInteger.ONE));
e = new BigInteger("3");
while (m.gcd(e).intValue() > 1) {
e = e.add(new BigInteger("2"));
}
d = e.modInverse(m);
}
/**
* Costruttore della classe: Calcola modulo e chiave privata.
*
* @param key La chiave pubblica.
*/
public RSA(BigInteger key) {
BigInteger p = BigInteger.probablePrime(512, new SecureRandom());
BigInteger q = BigInteger.probablePrime(512, new SecureRandom());
modulus = p.multiply(q);
BigInteger one = BigInteger.ONE;
BigInteger pMin1 = p.subtract(one);
BigInteger qMin1 = q.subtract(one);
BigInteger fi = pMin1.multiply(qMin1);
this.publicKey = key;
privateKey = publicKey.modInverse(fi);
}
/**
* Calcola modulo, chiave pubblica e privata.
*
* @deprecated
*/
public void prepare() {
BigInteger p = BigInteger.probablePrime(512, new SecureRandom());
BigInteger q = BigInteger.probablePrime(512, new SecureRandom());
modulus = p.multiply(q);
BigInteger one = BigInteger.ONE;
BigInteger pMin1 = p.subtract(one);
BigInteger qMin1 = q.subtract(one);
BigInteger fi = pMin1.multiply(qMin1);
publicKey = new BigInteger("65537");
privateKey = publicKey.modInverse(fi);
}
public boolean isPrime(BigInteger n, int iteration) {
if (n.equals(BigInteger.ZERO) || n.equals(BigInteger.ONE)) return false;
BigInteger two = BigInteger.valueOf(2);
if (n.equals(two)) return true;
if (n.mod(two).equals(BigInteger.ZERO)) return false;
// long s = n - 1;
BigInteger s = n.subtract(BigInteger.ONE);
// while (s % 2 == 0)
while (s.mod(two).equals(BigInteger.ZERO)) s = s.divide(two);
// s /= 2;
Random rand = new Random();
for (int i = 0; i < iteration; i++) {
/* long r = Math.abs(rand.nextLong());
long a = r % (n - 1) + 1, temp = s;
long mod = modPow(a, temp, n);*/
BigInteger r, a, temp, mod;
r = BigInteger.valueOf(Math.abs(rand.nextLong()));
a = r.mod(n.subtract(BigInteger.ONE)).add(BigInteger.ONE);
temp = new BigInteger(s.toString());
mod = modPow(a, temp, n);
while (!temp.equals(n.subtract(BigInteger.ONE))
&& !mod.equals(BigInteger.ONE)
&& !mod.equals(n.subtract(BigInteger.ONE))) {
mod = mulMod(mod, mod, n);
temp = temp.multiply(two);
}
/* while (temp != n - 1 && mod != 1 && mod != n - 1)
{
mod = mulMod(mod, mod, n);
temp *= 2;
}*/
/* if (mod != n - 1 && temp % 2 == 0)
return false;*/
if (!mod.equals(n.subtract(BigInteger.ONE)) && temp.mod(two).equals(BigInteger.ZERO))
return false;
}
return true;
}
public static Set fill(Set n) {
BigInteger a = new BigInteger("100");
BigInteger b = new BigInteger("100");
while (b.compareTo(BigInteger.ONE) > 0) {
while (a.compareTo(BigInteger.ONE) > 0) {
int exp = (int) b.longValue();
n.add(a.pow(exp));
a = a.subtract(BigInteger.ONE);
}
a = BigInteger.valueOf(100);
b = b.subtract(BigInteger.ONE);
}
return n;
}
public static ArrayList<BigInteger> generatePublicKeyOfBitLength(int bitLength) {
ArrayList<BigInteger> pAndQ = findPAndQ(bitLength);
BigInteger p = pAndQ.get(0);
BigInteger q = pAndQ.get(1);
// Find PQ and phiPQ
BigInteger pq = p.multiply(q);
BigInteger phiPQ = (p.subtract(BigInteger.ONE)).multiply(q.subtract(BigInteger.ONE));
BigInteger e = findE(phiPQ);
ArrayList<BigInteger> publicKey = new ArrayList<BigInteger>();
publicKey.add(pq);
publicKey.add(e);
return publicKey;
}
/**
* Create public and private keys. Doesn't check if parameters are suitable. It is done by
* testInputEligibility() method.
*
* @param p Prime p.
* @param q Prime q.
* @param e Public exponent.
*/
public void createKeys(BigInteger p, BigInteger q, BigInteger e) {
// Calculate the Euler's function.
BigInteger phi = p.subtract(BigInteger.ONE).multiply(q.subtract(BigInteger.ONE));
// Compute private exponent
BigInteger d = e.modInverse(phi);
// Calculate modulo
BigInteger n = p.multiply(q);
// Create keys
publicKey = new RsaPublicKey(n, e);
privateKey = new RsaPrivateKey(p, q, e, d);
}
public BigPoint multiply(BigInteger Factor) {
// Punkt mit sich selbst addieren
if (Factor.compareTo(BigInteger.ONE) == 0) return this;
if (Configuration._ellipticCurvePointY.compareTo(BigInteger.ZERO) == 0)
throw new IllegalArgumentException(
"Der Y-Wert des Generatorpunktes darf für eine Punktverdopplung nicht 0 sein!");
BigInteger s, xR, yR;
// ((3x^2 + a) * 2y_p^-1 mod p
s =
X.pow(2)
.multiply(new BigInteger("3"))
.add(Configuration._ellipticCurveParamA)
.multiply(
ECCField.GetInverseValue(
Y.multiply(new BigInteger("2")), Configuration._ellipticCurveParamP))
.mod(Configuration._ellipticCurveParamP);
// Normalisieren
if (s.compareTo(BigInteger.ZERO) < 0) s = s.add(Configuration._ellipticCurveParamP);
xR =
s.modPow(new BigInteger("2"), Configuration._ellipticCurveParamP)
.subtract(X.multiply(new BigInteger("2")))
.mod(Configuration._ellipticCurveParamP);
// Normalisieren
if (xR.compareTo(BigInteger.ZERO) < 0) xR = xR.add(Configuration._ellipticCurveParamP);
yR = Y.negate().add(s.multiply(X.subtract(xR))).mod(Configuration._ellipticCurveParamP);
// Normalisieren
if (yR.compareTo(BigInteger.ZERO) < 0) yR = yR.add(Configuration._ellipticCurveParamP);
Factor = Factor.subtract(BigInteger.ONE);
BigPoint res = new BigPoint(xR, yR);
// 3P = 2P + P
// x * P = 2P + P + P + ... + P
while (Factor.compareTo(BigInteger.ONE) > 0) {
res = addPoint(this, res);
Factor = Factor.subtract(BigInteger.ONE);
}
return res;
}
protected BigInteger modSubtract(BigInteger x1, BigInteger x2) {
BigInteger x3 = x1.subtract(x2);
if (x3.signum() < 0) {
x3 = x3.add(q);
}
return x3;
}
private static void checkNormaliseBaseTenResult(ExpandedDouble orig, NormalisedDecimal result) {
String sigDigs = result.getSignificantDecimalDigits();
BigInteger frac = orig.getSignificand();
while (frac.bitLength() + orig.getBinaryExponent() < 200) {
frac = frac.multiply(BIG_POW_10);
}
int binaryExp = orig.getBinaryExponent() - orig.getSignificand().bitLength();
String origDigs = frac.shiftLeft(binaryExp + 1).toString(10);
if (!origDigs.startsWith(sigDigs)) {
throw new AssertionFailedError("Expected '" + origDigs + "' but got '" + sigDigs + "'.");
}
double dO = Double.parseDouble("0." + origDigs.substring(sigDigs.length()));
double d1 = Double.parseDouble(result.getFractionalPart().toPlainString());
BigInteger subDigsO = BigInteger.valueOf((int) (dO * 32768 + 0.5));
BigInteger subDigsB = BigInteger.valueOf((int) (d1 * 32768 + 0.5));
if (subDigsO.equals(subDigsB)) {
return;
}
BigInteger diff = subDigsB.subtract(subDigsO).abs();
if (diff.intValue() > 100) {
// 100/32768 ~= 0.003
throw new AssertionFailedError("minor mistake");
}
}
private BigInteger previousTransactionId(BigInteger id) {
if (id.equals(INIT_TXID)) {
return null;
} else {
return id.subtract(BigInteger.ONE);
}
}
/** Create an instance that can both encrypt and decrypt. */
public RSA(int bits) {
bitlen = bits;
// Standartowe obliczenie n
/*
BigInteger p = new BigInteger(MillerRabin.ZnajdzPierwsza(bitlen/2));
BigInteger q = new BigInteger(MillerRabin.ZnajdzPierwsza(bitlen/2));
n = p.multiply(q);
*/
// N dla k liczb
n = new BigInteger("1");
for (BigInteger e : Lista.liczbyp) {
n = n.multiply(e);
}
// obliczanie funkcji Eulera m=f(n)=(p-1)*(q-1)
/*
BigInteger m = (p.subtract(BigInteger.ONE)).multiply(q
.subtract(BigInteger.ONE));
*/
m = new BigInteger("1");
for (BigInteger e : Lista.liczbyp) {
m = m.multiply(e.subtract(new BigInteger("1")));
}
// int zakresE = 2^(bits-2);
e =
new BigInteger(2 ^ (bitlen * Lista.liczbyp.size() - 2), rnd)
.shiftLeft(1)
.add(new BigInteger("1"));
while (m.gcd(e).intValue() > 1) {
e = e.add(new BigInteger("2"));
}
d = e.modInverse(m);
}
public ECFieldElement multiplyMinusProduct(
ECFieldElement b, ECFieldElement x, ECFieldElement y) {
BigInteger ax = this.x, bx = b.toBigInteger(), xx = x.toBigInteger(), yx = y.toBigInteger();
BigInteger ab = ax.multiply(bx);
BigInteger xy = xx.multiply(yx);
return new Fp(q, r, modReduce(ab.subtract(xy)));
}
public void calculate_S() {
S =
B.subtract(k.multiply(g.modPow(x, N)))
.modPow(a.add(u.multiply(x)), N); // S = (B - (k*g^x))^(a+ux)
System.out.println("S in Client: " + S.toString());
}
protected BigInteger modAdd(BigInteger x1, BigInteger x2) {
BigInteger x3 = x1.add(x2);
if (x3.compareTo(q) >= 0) {
x3 = x3.subtract(q);
}
return x3;
}
protected BigInteger modDouble(BigInteger x) {
BigInteger _2x = x.shiftLeft(1);
if (_2x.compareTo(q) >= 0) {
_2x = _2x.subtract(q);
}
return _2x;
}
