/**
* 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);
}
// 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);
}
/**
* 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);
}
/**
* 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);
}
public static int matches(byte[] input, byte[] pattern) {
if (pattern.length > input.length) {
return 0;
}
long p = BigInteger.probablePrime(63, r).longValue();
long b = r.nextInt(1 << 16);
long bpow = 1;
long patternHash = 0;
long inputHash = 0;
int count = 0;
for (int i = 1; i < pattern.length; i++) {
bpow = (bpow * b) % p;
}
for (int i = 0; i < pattern.length; i++) {
patternHash = (patternHash * b + pattern[i]) % p;
inputHash = (inputHash * b + input[i]) % p;
}
if (inputHash == patternHash && isSubarray(input, pattern, 0)) {
count++;
}
for (int i = pattern.length; i < input.length; i++) {
byte oldChar = input[i - pattern.length];
byte newChar = input[i];
inputHash = ((inputHash - oldChar * bpow) * b + newChar) % p;
if (inputHash == patternHash && isSubarray(input, pattern, i - pattern.length + 1)) {
count++;
}
}
return count;
}
private static void generateTestVectors(
Random rng, ArrayList<TestVector> list, int bitLength, int wordLength, int max) {
for (int i = 0; i < max; i++) {
final long seed = rng.nextLong();
rng.setSeed(seed);
BigInteger m = BigInteger.probablePrime(bitLength, rng);
BigInteger x = BigInteger.probablePrime(bitLength, rng);
BigInteger e = BigInteger.probablePrime(bitLength, rng);
BigInteger z = x.modPow(e, m);
TestVector tv =
Util.generateTestVector(
"BASIC_" + bitLength, Long.toString(seed), wordLength, m, x, e, z);
list.add(tv);
System.out.printf(
"%s Generated test: bits: %d seed: %d\n",
TestGeneratorBasic.class.getName(), bitLength, seed);
}
}
public KeyPair<RSAPublicKey, RSAPrivateKey> buildRSAKeyPair(int keysize) {
RSAPublicKey pubk;
RSAPrivateKey privk;
SecureRandom sr = new SecureRandom();
BigInteger p = BigInteger.probablePrime(keysize / 2, sr);
BigInteger q = BigInteger.probablePrime(keysize / 2, sr);
BigInteger n = p.multiply(q);
BigInteger tot = p.subtract(BigInteger.ONE).multiply(q.subtract(BigInteger.ONE));
BigInteger e = BigInteger.valueOf(0x10001);
BigInteger d = e.modInverse(tot);
pubk = new RSAPublicKey(n, e);
privk = new RSAPrivateKey(n, e, d);
return new KeyPair<RSAPublicKey, RSAPrivateKey>(pubk, privk);
}
private long burnTime(int burn_ms) {
long prime = 2;
long begin = System.currentTimeMillis();
long endTime = begin + burn_ms;
long last = 0;
do {
prime = BigInteger.probablePrime(64, new Random()).longValue();
last = System.currentTimeMillis();
} while (last < endTime);
if (prime == 2) {
throw new IllegalStateException("Not a prime!");
}
return last - begin;
}
/** @tests java.math.BigInteger#probablePrime(int, java.util.Random) */
@TestTargetNew(
level = TestLevel.COMPLETE,
notes = "",
method = "probablePrime",
args = {int.class, java.util.Random.class})
public void test_probablePrime() {
for (int bitLength = 50; bitLength <= 1050; bitLength += 100) {
BigInteger a = BigInteger.probablePrime(bitLength, rand);
assertTrue("isProbablePrime(probablePrime()) failed for: " + bi, a.isProbablePrime(80));
// System.out.println(a);
// BigInteger prime = a.nextProbablePrime();
// System.out.print("Next Probable Prime is ");
// System.out.println(prime);
}
}
public static void nextProbablePrime() throws Exception {
int failCount = 0;
BigInteger p1, p2, p3;
p1 = p2 = p3 = ZERO;
// First test nextProbablePrime on the low range starting at zero
for (int i = 0; i < primesTo100.length; i++) {
p1 = p1.nextProbablePrime();
if (p1.longValue() != primesTo100[i]) {
System.err.println("low range primes failed");
System.err.println("p1 is " + p1);
System.err.println("expected " + primesTo100[i]);
failCount++;
}
}
// Test nextProbablePrime on a relatively small, known prime sequence
p1 = BigInteger.valueOf(aPrimeSequence[0]);
for (int i = 1; i < aPrimeSequence.length; i++) {
p1 = p1.nextProbablePrime();
if (p1.longValue() != aPrimeSequence[i]) {
System.err.println("prime sequence failed");
failCount++;
}
}
// Next, pick some large primes, use nextProbablePrime to find the
// next one, and make sure there are no primes in between
for (int i = 0; i < 100; i += 10) {
p1 = BigInteger.probablePrime(50 + i, rnd);
p2 = p1.add(ONE);
p3 = p1.nextProbablePrime();
while (p2.compareTo(p3) < 0) {
if (p2.isProbablePrime(100)) {
System.err.println("nextProbablePrime failed");
System.err.println("along range " + p1.toString(16));
System.err.println("to " + p3.toString(16));
failCount++;
break;
}
p2 = p2.add(ONE);
}
}
report("nextProbablePrime", failCount);
}
/** Find an acceptable prime (equal to 3 mod 4) * */
BigInteger makeBlumInt(int size) {
for (; ; ) {
BigInteger p = BigInteger.probablePrime(size, rand);
if (p.mod(four).equals(three)) return p;
}
}
public static void prime() {
BigInteger p1, p2, c1;
int failCount = 0;
// Test consistency
for (int i = 0; i < 10; i++) {
p1 = BigInteger.probablePrime(100, rnd);
if (!p1.isProbablePrime(100)) {
System.err.println("Consistency " + p1.toString(16));
failCount++;
}
}
// Test some known Mersenne primes (2^n)-1
// The array holds the exponents, not the numbers being tested
for (int i = 0; i < NUM_MERSENNES_TO_TEST; i++) {
p1 = new BigInteger("2");
p1 = p1.pow(mersenne_powers[i]);
p1 = p1.subtract(BigInteger.ONE);
if (!p1.isProbablePrime(100)) {
System.err.println("Mersenne prime " + i + " failed.");
failCount++;
}
}
// Test some primes reported by customers as failing in the past
for (int i = 0; i < customer_primes.length; i++) {
p1 = new BigInteger(customer_primes[i]);
if (!p1.isProbablePrime(100)) {
System.err.println("Customer prime " + i + " failed.");
failCount++;
}
}
// Test some known Carmichael numbers.
for (int i = 0; i < carmichaels.length; i++) {
c1 = BigInteger.valueOf(carmichaels[i]);
if (c1.isProbablePrime(100)) {
System.err.println("Carmichael " + i + " reported as prime.");
failCount++;
}
}
// Test some computed Carmichael numbers.
// Numbers of the form (6k+1)(12k+1)(18k+1) are Carmichael numbers if
// each of the factors is prime
int found = 0;
BigInteger f1 = new BigInteger(40, 100, rnd);
while (found < NUM_CARMICHAELS_TO_TEST) {
BigInteger k = null;
BigInteger f2, f3;
f1 = f1.nextProbablePrime();
BigInteger[] result = f1.subtract(ONE).divideAndRemainder(SIX);
if (result[1].equals(ZERO)) {
k = result[0];
f2 = k.multiply(TWELVE).add(ONE);
if (f2.isProbablePrime(100)) {
f3 = k.multiply(EIGHTEEN).add(ONE);
if (f3.isProbablePrime(100)) {
c1 = f1.multiply(f2).multiply(f3);
if (c1.isProbablePrime(100)) {
System.err.println("Computed Carmichael " + c1.toString(16));
failCount++;
}
found++;
}
}
}
f1 = f1.add(TWO);
}
// Test some composites that are products of 2 primes
for (int i = 0; i < 50; i++) {
p1 = BigInteger.probablePrime(100, rnd);
p2 = BigInteger.probablePrime(100, rnd);
c1 = p1.multiply(p2);
if (c1.isProbablePrime(100)) {
System.err.println("Composite failed " + c1.toString(16));
failCount++;
}
}
for (int i = 0; i < 4; i++) {
p1 = BigInteger.probablePrime(600, rnd);
p2 = BigInteger.probablePrime(600, rnd);
c1 = p1.multiply(p2);
if (c1.isProbablePrime(100)) {
System.err.println("Composite failed " + c1.toString(16));
failCount++;
}
}
report("Prime", failCount);
}
/** @tests java.math.BigInteger#isProbablePrime(int) */
@TestTargets({
@TestTargetNew(
level = TestLevel.COMPLETE,
notes = "",
method = "isProbablePrime",
args = {int.class}),
@TestTargetNew(
level = TestLevel.COMPLETE,
notes = "",
method = "probablePrime",
args = {int.class, java.util.Random.class})
})
public void test_isProbablePrimeI() {
int fails = 0;
bi = new BigInteger(20, 20, rand);
if (!bi.isProbablePrime(17)) {
fails++;
}
bi = new BigInteger("4", 10);
if (bi.isProbablePrime(17)) {
fail("isProbablePrime failed for: " + bi);
}
bi = BigInteger.valueOf(17L * 13L);
if (bi.isProbablePrime(17)) {
fail("isProbablePrime failed for: " + bi);
}
for (long a = 2; a < 1000; a++) {
if (isPrime(a)) {
assertTrue(
"false negative on prime number <1000", BigInteger.valueOf(a).isProbablePrime(5));
} else if (BigInteger.valueOf(a).isProbablePrime(17)) {
System.out.println("isProbablePrime failed for: " + a);
fails++;
}
}
for (int a = 0; a < 1000; a++) {
bi =
BigInteger.valueOf(rand.nextInt(1000000))
.multiply(BigInteger.valueOf(rand.nextInt(1000000)));
if (bi.isProbablePrime(17)) {
System.out.println("isProbablePrime failed for: " + bi);
fails++;
}
}
for (int a = 0; a < 200; a++) {
bi = new BigInteger(70, rand).multiply(new BigInteger(70, rand));
if (bi.isProbablePrime(17)) {
System.out.println("isProbablePrime failed for: " + bi);
fails++;
}
}
assertTrue("Too many false positives - may indicate a problem", fails <= 1);
//
// And now some tests on real big integers:
//
bi =
new BigInteger(
"153890972191202256150310830154922163807316525358455215516067727076235016932726922093888770552128767458882963869421440585369743",
10);
if (!bi.isProbablePrime(80)) {
fail("isProbablePrime failed for: " + bi);
}
bi =
new BigInteger(
"2090575416269141767246491983797422123741252476560371649798066134123893524014911825188890458270426076468664046568752890122415061377308817346303546688282957897504000216241497550243010257911214329646877810655164658470278901030511157372440751259674247310396158238588463284702737181653",
10);
if (!bi.isProbablePrime(80)) {
fail("isProbablePrime failed for: " + bi);
}
//
for (int bitLength = 100; bitLength <= 600; bitLength += 100) {
BigInteger a = BigInteger.probablePrime(bitLength, rand);
BigInteger b = BigInteger.probablePrime(bitLength, rand);
BigInteger c = a.multiply(b);
assertFalse(
"isProbablePrime failed for product of two large primes"
+ a
+ " * "
+ b
+ " = "
+ c
+ " (bitLength = "
+ bitLength
+ ")",
c.isProbablePrime(80));
}
}
private BigInteger getPrime(Random random) {
return BigInteger.probablePrime(numberOfBits, random);
}
/**
* Returns a probably prime BigInteger having bitLength
*
* @param bitLength
* @return prime number
*/
public static BigInteger getProbablePrime(int bitLength) {
return BigInteger.probablePrime(bitLength, new Random(System.nanoTime()));
}
// some private methods
private BigInteger generateRandomNumber() {
return BigInteger.probablePrime(getPublicInfo().getNumBits() - 1, random);
// return new BigInteger(getPublicInfo().getNumBits()-1,random);
}
/** generate a random 31 bit prime * */
private static long longRandomPrime() {
BigInteger prime = BigInteger.probablePrime(31, new Random());
return prime.longValue();
}
