protected Address(BigInteger big_int)
{
byte[] buffer = ConvertToAddressBuffer(big_int);
_buffer = MemBlock.Reference(buffer, 0, MemSize);
if (ClassOf(_buffer) != this.Class) {
throw new System.
ArgumentException("Class of address is not my class: ",
this.ToString());
}
}
/**
* Static constructor initializes _half and _full
*/
static Address()
{
//Initialize _half
byte[] tmp = new byte[MemSize];
for (int i = 1; i < MemSize; i++)
{
tmp[i] = 0;
}
//Set the first bit to 1, all else to zero :
tmp[0] = 0x80;
_half = new BigInteger(tmp);
_full = _half * 2;
}
//***********************************************************************
// Computes the Jacobi Symbol for a and b.
// Algorithm adapted from [3] and [4] with some optimizations
//***********************************************************************
public static int Jacobi(BigInteger a, BigInteger b)
{
// Jacobi defined only for odd integers
if ((b.data[0] & 0x1) == 0)
throw(new
ArgumentException
("Jacobi defined only for odd integers."));
if (a >= b)
a %= b;
if (a.dataLength == 1 && a.data[0] == 0)
return 0; // a == 0
if (a.dataLength == 1 && a.data[0] == 1)
return 1; // a == 1
if (a < 0) {
if ((((b - 1).data[0]) & 0x2) == 0) //if( (((b-1) >> 1).data[0] & 0x1) == 0)
return Jacobi(-a, b);
else
return -Jacobi(-a, b);
}
int e = 0;
for (int index = 0; index < a.dataLength; index++) {
uint mask = 0x01;
for (int i = 0; i < 32; i++) {
if ((a.data[index] & mask) != 0) {
index = a.dataLength; // to break the outer loop
break;
}
mask <<= 1;
e++;
}
}
BigInteger a1 = a >> e;
int s = 1;
if ((e & 0x1) != 0
&& ((b.data[0] & 0x7) == 3 || (b.data[0] & 0x7) == 5))
s = -1;
if ((b.data[0] & 0x3) == 3 && (a1.data[0] & 0x3) == 3)
s = -s;
if (a1.dataLength == 1 && a1.data[0] == 1)
return s;
else
return (s * Jacobi(b % a1, a1));
}
public void Test14(ref int op) {
Console.WriteLine("Test 14: Testing 1000 puts and 1 get with 1000 " +
"results with the same key. Then we remove the main owner of the " +
"key.");
RNGCryptoServiceProvider rng = new RNGCryptoServiceProvider();
byte[] key = new byte[10];
byte[] value = new byte[value_size];
rng.GetBytes(key);
ArrayList al_results = new ArrayList();
int count = 60;
BlockingQueue[] results_queue = new BlockingQueue[count];
for(int i = 0; i < count; i++) {
value = new byte[value_size];
rng.GetBytes(value);
al_results.Add(value);
results_queue[i] = new BlockingQueue();
default_dht.AsyncPut(key, value, 3000, results_queue[i]);
}
for (int i = 0; i < count; i++) {
try {
bool res = (bool) results_queue[i].Dequeue();
Console.WriteLine("success in put : " + i);
}
catch {
Console.WriteLine("Failure in put : " + i);
}
}
Console.WriteLine("Insertion done...");
Console.WriteLine("Disconnecting nodes...");
MemBlock[] b = default_dht.MapToRing(key);
BigInteger[] baddrs = new BigInteger[default_dht.DEGREE];
BigInteger[] addrs = new BigInteger[default_dht.DEGREE];
bool first_run = true;
foreach(DictionaryEntry de in nodes) {
Address addr = (Address) de.Key;
for(int j = 0; j < b.Length; j++) {
if(first_run) {
addrs[j] = addr.ToBigInteger();
baddrs[j] = (new AHAddress(b[j])).ToBigInteger();
}
else {
BigInteger caddr = addr.ToBigInteger();
BigInteger new_diff = baddrs[j] - caddr;
if(new_diff < 0) {
new_diff *= -1;
}
BigInteger c_diff = baddrs[j] - addrs[j];
if(c_diff < 0) {
c_diff *= -1;
}
if(c_diff > new_diff) {
addrs[j] = caddr;
}
}
}
first_run = false;
}
for(int i = 0; i < addrs.Length; i++) {
Console.WriteLine(new AHAddress(baddrs[i]) + " " + new AHAddress(addrs[i]));
Address laddr = new AHAddress(addrs[i]);
Node node = (Node) nodes[laddr];
node.Disconnect();
nodes.Remove(laddr);
tables.Remove(laddr);
network_size--;
}
default_dht = new Dht((Node) nodes.GetByIndex(0), degree);
// Checking the ring every 5 seconds..
do { Thread.Sleep(5000);}
while(!CheckAllConnections());
Console.WriteLine("Going to sleep now...");
Thread.Sleep(15000);
Console.WriteLine("Timeout done.... now attempting gets");
this.SerialAsyncGet(key, (byte[][]) al_results.ToArray(typeof(byte[])), op++);
Thread.Sleep(5000);
Console.WriteLine("This checks to make sure our follow up Puts succeeded");
this.SerialAsyncGet(key, (byte[][]) al_results.ToArray(typeof(byte[])), op++);
Console.WriteLine("If no error messages successful up to: " + (op - 1));
foreach(TableServer ts in tables.Values) {
Console.WriteLine("Count ... " + ts.Count);
}
}
/**
* Return a byte[] of length MemSize, which holds the integer % Full
* as a buffer which is a binary representation of an Address
*/
static public byte[] ConvertToAddressBuffer(BigInteger num)
{
byte[] bi_buf;
BigInteger val = num % Full;
if( val < 0 ) {
val = val + Full;
}
bi_buf = val.getBytes();
int missing = (MemSize - bi_buf.Length);
if( missing > 0 ) {
//Missing some bytes at the beginning, pad with zero :
byte[] tmp_bi = new byte[Address.MemSize];
for (int i = 0; i < missing; i++) {
tmp_bi[i] = (byte) 0;
}
System.Array.Copy(bi_buf, 0, tmp_bi, missing,
bi_buf.Length);
bi_buf = tmp_bi;
}
else if (missing < 0) {
throw new System.ArgumentException(
"Integer too large to fit in 160 bits: " + num.ToString());
}
return bi_buf;
}
//***********************************************************************
// Overloading of the NOT operator (1's complement)
//***********************************************************************
public static BigInteger operator ~(BigInteger bi1)
{
BigInteger result = new BigInteger(bi1);
for (int i = 0; i < maxLength; i++)
result.data[i] = (uint) (~(bi1.data[i]));
result.dataLength = maxLength;
while (result.dataLength > 1
&& result.data[result.dataLength - 1] == 0)
result.dataLength--;
return result;
}
//***********************************************************************
// Overloading of unary << operators
//***********************************************************************
public static BigInteger operator <<(BigInteger bi1, int shiftVal)
{
BigInteger result = new BigInteger(bi1);
result.dataLength = shiftLeft(result.data, shiftVal);
return result;
}
//***********************************************************************
// Overloading of the unary -- operator
//***********************************************************************
public static BigInteger operator --(BigInteger bi1)
{
BigInteger result = new BigInteger(bi1);
long val;
bool carryIn = true;
int index = 0;
while (carryIn && index < maxLength) {
val = (long) (result.data[index]);
val--;
result.data[index] = (uint) (val & 0xFFFFFFFF);
if (val >= 0)
carryIn = false;
index++;
}
if (index > result.dataLength)
result.dataLength = index;
while (result.dataLength > 1
&& result.data[result.dataLength - 1] == 0)
result.dataLength--;
// overflow check
int lastPos = maxLength - 1;
// overflow if initial value was -ve but -- caused a sign
// change to positive.
if ((bi1.data[lastPos] & 0x80000000) != 0 &&
(result.data[lastPos] & 0x80000000) !=
(bi1.data[lastPos] & 0x80000000)) {
throw(new ArithmeticException("Underflow in --."));
}
return result;
}
//***********************************************************************
// Tests the correct implementation of the /, %, * and + operators
//***********************************************************************
public static void MulDivTest(int rounds)
{
Random rand = new Random();
byte[] val = new byte[64];
byte[] val2 = new byte[64];
for (int count = 0; count < rounds; count++) {
// generate 2 numbers of random length
int t1 = 0;
while (t1 == 0)
t1 = (int) (rand.NextDouble() * 65);
int t2 = 0;
while (t2 == 0)
t2 = (int) (rand.NextDouble() * 65);
bool done = false;
while (!done) {
for (int i = 0; i < 64; i++) {
if (i < t1)
val[i] = (byte) (rand.NextDouble() * 256);
else
val[i] = 0;
if (val[i] != 0)
done = true;
}
}
done = false;
while (!done) {
for (int i = 0; i < 64; i++) {
if (i < t2)
val2[i] = (byte) (rand.NextDouble() * 256);
else
val2[i] = 0;
if (val2[i] != 0)
done = true;
}
}
while (val[0] == 0)
val[0] = (byte) (rand.NextDouble() * 256);
while (val2[0] == 0)
val2[0] = (byte) (rand.NextDouble() * 256);
Console.Error.WriteLine(count);
BigInteger bn1 = new BigInteger(val, t1);
BigInteger bn2 = new BigInteger(val2, t2);
// Determine the quotient and remainder by dividing
// the first number by the second.
BigInteger bn3 = bn1 / bn2;
BigInteger bn4 = bn1 % bn2;
// Recalculate the number
BigInteger bn5 = (bn3 * bn2) + bn4;
// Make sure they're the same
if (bn5 != bn1) {
Console.Error.WriteLine("Error at " + count);
Console.Error.WriteLine(bn1 + "\n");
Console.Error.WriteLine(bn2 + "\n");
Console.Error.WriteLine(bn3 + "\n");
Console.Error.WriteLine(bn4 + "\n");
Console.Error.WriteLine(bn5 + "\n");
return;
}
}
}
//***********************************************************************
// Performs the calculation of the kth term in the Lucas Sequence.
// For details of the algorithm, see reference [9].
//
// k must be odd. i.e LSB == 1
//***********************************************************************
private static BigInteger[] LucasSequenceHelper(BigInteger P,
BigInteger Q,
BigInteger k,
BigInteger n,
BigInteger
constant, int s)
{
BigInteger[] result = new BigInteger[3];
if ((k.data[0] & 0x00000001) == 0)
throw(new ArgumentException("Argument k must be odd."));
int numbits = k.bitCount();
uint mask = (uint) 0x1 << ((numbits & 0x1F) - 1);
// v = v0, v1 = v1, u1 = u1, Q_k = Q^0
BigInteger v = 2 % n, Q_k = 1 % n, v1 = P % n, u1 = Q_k;
bool flag = true;
for (int i = k.dataLength - 1; i >= 0; i--) // iterate on the binary expansion of k
{
//Console.Error.WriteLine("round");
while (mask != 0) {
if (i == 0 && mask == 0x00000001) // last bit
break;
if ((k.data[i] & mask) != 0) // bit is set
{
// index doubling with addition
u1 = (u1 * v1) % n;
v = ((v * v1) - (P * Q_k)) % n;
v1 = n.BarrettReduction(v1 * v1, n, constant);
v1 = (v1 - ((Q_k * Q) << 1)) % n;
if (flag)
flag = false;
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
Q_k = (Q_k * Q) % n;
}
else {
// index doubling
u1 = ((u1 * v) - Q_k) % n;
v1 = ((v * v1) - (P * Q_k)) % n;
v = n.BarrettReduction(v * v, n, constant);
v = (v - (Q_k << 1)) % n;
if (flag) {
Q_k = Q % n;
flag = false;
}
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
}
mask >>= 1;
}
mask = 0x80000000;
}
// at this point u1 = u(n+1) and v = v(n)
// since the last bit always 1, we need to transform u1 to u(2n+1) and v to v(2n+1)
u1 = ((u1 * v) - Q_k) % n;
v = ((v * v1) - (P * Q_k)) % n;
if (flag)
flag = false;
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
Q_k = (Q_k * Q) % n;
for (int i = 0; i < s; i++) {
// index doubling
u1 = (u1 * v) % n;
v = ((v * v) - (Q_k << 1)) % n;
if (flag) {
Q_k = Q % n;
flag = false;
}
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
}
result[0] = u1;
result[1] = v;
result[2] = Q_k;
return result;
}
//***********************************************************************
// Returns the k_th number in the Lucas Sequence reduced modulo n.
//
// Uses index doubling to speed up the process. For example, to calculate V(k),
// we maintain two numbers in the sequence V(n) and V(n+1).
//
// To obtain V(2n), we use the identity
// V(2n) = (V(n) * V(n)) - (2 * Q^n)
// To obtain V(2n+1), we first write it as
// V(2n+1) = V((n+1) + n)
// and use the identity
// V(m+n) = V(m) * V(n) - Q * V(m-n)
// Hence,
// V((n+1) + n) = V(n+1) * V(n) - Q^n * V((n+1) - n)
// = V(n+1) * V(n) - Q^n * V(1)
// = V(n+1) * V(n) - Q^n * P
//
// We use k in its binary expansion and perform index doubling for each
// bit position. For each bit position that is set, we perform an
// index doubling followed by an index addition. This means that for V(n),
// we need to update it to V(2n+1). For V(n+1), we need to update it to
// V((2n+1)+1) = V(2*(n+1))
//
// This function returns
// [0] = U(k)
// [1] = V(k)
// [2] = Q^n
//
// Where U(0) = 0 % n, U(1) = 1 % n
// V(0) = 2 % n, V(1) = P % n
//***********************************************************************
public static BigInteger[] LucasSequence(BigInteger P,
BigInteger Q,
BigInteger k,
BigInteger n)
{
if (k.dataLength == 1 && k.data[0] == 0) {
BigInteger[] result = new BigInteger[3];
result[0] = 0;
result[1] = 2 % n;
result[2] = 1 % n;
return result;
}
// calculate constant = b^(2k) / m
// for Barrett Reduction
BigInteger constant = new BigInteger();
int nLen = n.dataLength << 1;
constant.data[nLen] = 0x00000001;
constant.dataLength = nLen + 1;
constant = constant / n;
// calculate values of s and t
int s = 0;
for (int index = 0; index < k.dataLength; index++) {
uint mask = 0x01;
for (int i = 0; i < 32; i++) {
if ((k.data[index] & mask) != 0) {
index = k.dataLength; // to break the outer loop
break;
}
mask <<= 1;
s++;
}
}
BigInteger t = k >> s;
//Console.Error.WriteLine("s = " + s + " t = " + t);
return LucasSequenceHelper(P, Q, t, n, constant, s);
}
//***********************************************************************
// Returns a value that is equivalent to the integer square root
// of the BigInteger.
//
// The integer square root of "this" is defined as the largest integer n
// such that (n * n) <= this
//
//***********************************************************************
public BigInteger sqrt()
{
uint numBits = (uint) this.bitCount();
if ((numBits & 0x1) != 0) // odd number of bits
numBits = (numBits >> 1) + 1;
else
numBits = (numBits >> 1);
uint bytePos = numBits >> 5;
byte bitPos = (byte) (numBits & 0x1F);
uint mask;
BigInteger result = new BigInteger();
if (bitPos == 0)
mask = 0x80000000;
else {
mask = (uint) 1 << bitPos;
bytePos++;
}
result.dataLength = (int) bytePos;
for (int i = (int)bytePos - 1; i >= 0; i--) {
while (mask != 0) {
// guess
result.data[i] ^= mask;
// undo the guess if its square is larger than this
if ((result * result) > this)
result.data[i] ^= mask;
mask >>= 1;
}
mask = 0x80000000;
}
return result;
}
//***********************************************************************
// Returns the modulo inverse of this. Throws ArithmeticException if
// the inverse does not exist. (i.e. gcd(this, modulus) != 1)
//***********************************************************************
public BigInteger modInverse(BigInteger modulus)
{
BigInteger[] p = {
0, 1};
BigInteger[] q = new BigInteger[2]; // quotients
BigInteger[] r = {
0, 0}; // remainders
int step = 0;
BigInteger a = modulus;
BigInteger b = this;
while (b.dataLength > 1
|| (b.dataLength == 1 && b.data[0] != 0)) {
BigInteger quotient = new BigInteger();
BigInteger remainder = new BigInteger();
if (step > 1) {
BigInteger pval = (p[0] - (p[1] * q[0])) % modulus;
p[0] = p[1];
p[1] = pval;
}
if (b.dataLength == 1)
singleByteDivide(a, b, quotient, remainder);
else
multiByteDivide(a, b, quotient, remainder);
/*
* Console.Error.WriteLine(quotient.dataLength);
* Console.Error.WriteLine("{0} = {1}({2}) + {3} p = {4}", a.ToString(10),
* b.ToString(10), quotient.ToString(10), remainder.ToString(10),
* p[1].ToString(10));
*/
q[0] = q[1];
r[0] = r[1];
q[1] = quotient;
r[1] = remainder;
a = b;
b = remainder;
step++;
}
if (r[0].dataLength > 1
|| (r[0].dataLength == 1 && r[0].data[0] != 1))
throw(new ArithmeticException("No inverse!"));
BigInteger result = ((p[0] - (p[1] * q[0])) % modulus);
if ((result.data[maxLength - 1] & 0x80000000) != 0)
result += modulus; // get the least positive modulus
return result;
}
//***********************************************************************
// Generates a random number with the specified number of bits such
// that gcd(number, this) = 1
//***********************************************************************
public BigInteger genCoPrime(int bits, Random rand)
{
bool done = false;
BigInteger result = new BigInteger();
while (!done) {
result.genRandomBits(bits, rand);
//Console.Error.WriteLine(result.ToString(16));
// gcd test
BigInteger g = result.gcd(this);
if (g.dataLength == 1 && g.data[0] == 1)
done = true;
}
return result;
}
//***********************************************************************
// Generates a positive BigInteger that is probably prime.
//***********************************************************************
public static BigInteger genPseudoPrime(int bits, int confidence,
Random rand)
{
BigInteger result = new BigInteger();
bool done = false;
while (!done) {
result.genRandomBits(bits, rand);
result.data[0] |= 0x01; // make it odd
// prime test
done = result.isProbablePrime(confidence);
}
return result;
}
//***********************************************************************
// Overloading of the unary ++ operator
//***********************************************************************
public static BigInteger operator ++(BigInteger bi1)
{
BigInteger result = new BigInteger(bi1);
long val, carry = 1;
int index = 0;
while (carry != 0 && index < maxLength) {
val = (long) (result.data[index]);
val++;
result.data[index] = (uint) (val & 0xFFFFFFFF);
carry = val >> 32;
index++;
}
if (index > result.dataLength)
result.dataLength = index;
else {
while (result.dataLength > 1
&& result.data[result.dataLength - 1] == 0)
result.dataLength--;
}
// overflow check
int lastPos = maxLength - 1;
// overflow if initial value was +ve but ++ caused a sign
// change to negative.
if ((bi1.data[lastPos] & 0x80000000) == 0 &&
(result.data[lastPos] & 0x80000000) !=
(bi1.data[lastPos] & 0x80000000)) {
throw(new ArithmeticException("Overflow in ++."));
}
return result;
}
//***********************************************************************
// Overloading of subtraction operator
//***********************************************************************
public static BigInteger operator -(BigInteger bi1,
BigInteger bi2)
{
BigInteger result = new BigInteger();
result.dataLength =
(bi1.dataLength >
bi2.dataLength) ? bi1.dataLength : bi2.dataLength;
long carryIn = 0;
for (int i = 0; i < result.dataLength; i++) {
long diff;
diff = (long) bi1.data[i] - (long) bi2.data[i] - carryIn;
result.data[i] = (uint) (diff & 0xFFFFFFFF);
if (diff < 0)
carryIn = 1;
else
carryIn = 0;
}
// roll over to negative
if (carryIn != 0) {
for (int i = result.dataLength; i < maxLength; i++)
result.data[i] = 0xFFFFFFFF;
result.dataLength = maxLength;
}
// fixed in v1.03 to give correct datalength for a - (-b)
while (result.dataLength > 1
&& result.data[result.dataLength - 1] == 0)
result.dataLength--;
// overflow check
int lastPos = maxLength - 1;
if ((bi1.data[lastPos] & 0x80000000) !=
(bi2.data[lastPos] & 0x80000000)
&& (result.data[lastPos] & 0x80000000) !=
(bi1.data[lastPos] & 0x80000000)) {
throw(new ArithmeticException());
}
return result;
}
//***********************************************************************
// Constructor (Default value provided by BigInteger)
//***********************************************************************
public BigInteger(BigInteger bi)
{
data = new uint[maxLength];
dataLength = bi.dataLength;
for (int i = 0; i < dataLength; i++)
data[i] = bi.data[i];
}
//***********************************************************************
// Overloading of multiplication operator
//***********************************************************************
public static BigInteger operator *(BigInteger bi1,
BigInteger bi2)
{
int lastPos = maxLength - 1;
bool bi1Neg = false, bi2Neg = false;
// take the absolute value of the inputs
try {
if ((bi1.data[lastPos] & 0x80000000) != 0) // bi1 negative
{
bi1Neg = true;
bi1 = -bi1;
}
if ((bi2.data[lastPos] & 0x80000000) != 0) // bi2 negative
{
bi2Neg = true;
bi2 = -bi2;
}
}
catch(Exception) {
}
BigInteger result = new BigInteger();
// multiply the absolute values
try {
for (int i = 0; i < bi1.dataLength; i++) {
if (bi1.data[i] == 0)
continue;
ulong mcarry = 0;
for (int j = 0, k = i; j < bi2.dataLength; j++, k++) {
// k = i + j
ulong val = ((ulong) bi1.data[i] * (ulong) bi2.data[j]) +
(ulong) result.data[k] + mcarry;
result.data[k] = (uint) (val & 0xFFFFFFFF);
mcarry = (val >> 32);
}
if (mcarry != 0)
result.data[i + bi2.dataLength] = (uint) mcarry;
}
}
catch(Exception) {
throw(new ArithmeticException("Multiplication overflow."));
}
result.dataLength = bi1.dataLength + bi2.dataLength;
if (result.dataLength > maxLength)
result.dataLength = maxLength;
while (result.dataLength > 1
&& result.data[result.dataLength - 1] == 0)
result.dataLength--;
// overflow check (result is -ve)
if ((result.data[lastPos] & 0x80000000) != 0) {
if (bi1Neg != bi2Neg && result.data[lastPos] == 0x80000000) // different sign
{
// handle the special case where multiplication produces
// a max negative number in 2's complement.
if (result.dataLength == 1)
return result;
else {
bool isMaxNeg = true;
for (int i = 0; i < result.dataLength - 1 && isMaxNeg;
i++) {
if (result.data[i] != 0)
isMaxNeg = false;
}
if (isMaxNeg)
return result;
}
}
throw(new ArithmeticException("Multiplication overflow."));
}
// if input has different signs, then result is -ve
if (bi1Neg != bi2Neg)
return -result;
return result;
}
//***********************************************************************
// Tests the correct implementation of the modulo exponential function
// using RSA encryption and decryption (using pre-computed encryption and
// decryption keys).
//***********************************************************************
public static void RSATest(int rounds)
{
Random rand = new Random(1);
byte[] val = new byte[64];
// private and public key
BigInteger bi_e =
new
BigInteger
("a932b948feed4fb2b692609bd22164fc9edb59fae7880cc1eaff7b3c9626b7e5b241c27a974833b2622ebe09beb451917663d47232488f23a117fc97720f1e7",
16);
BigInteger bi_d =
new
BigInteger
("4adf2f7a89da93248509347d2ae506d683dd3a16357e859a980c4f77a4e2f7a01fae289f13a851df6e9db5adaa60bfd2b162bbbe31f7c8f828261a6839311929d2cef4f864dde65e556ce43c89bbbf9f1ac5511315847ce9cc8dc92470a747b8792d6a83b0092d2e5ebaf852c85cacf34278efa99160f2f8aa7ee7214de07b7",
16);
BigInteger bi_n =
new
BigInteger
("e8e77781f36a7b3188d711c2190b560f205a52391b3479cdb99fa010745cbeba5f2adc08e1de6bf38398a0487c4a73610d94ec36f17f3f46ad75e17bc1adfec99839589f45f95ccc94cb2a5c500b477eb3323d8cfab0c8458c96f0147a45d27e45a4d11d54d77684f65d48f15fafcc1ba208e71e921b9bd9017c16a5231af7f",
16);
Console.Error.WriteLine("e =\n" + bi_e.ToString(10));
Console.Error.WriteLine("\nd =\n" + bi_d.ToString(10));
Console.Error.WriteLine("\nn =\n" + bi_n.ToString(10) + "\n");
for (int count = 0; count < rounds; count++) {
// generate data of random length
int t1 = 0;
while (t1 == 0)
t1 = (int) (rand.NextDouble() * 65);
bool done = false;
while (!done) {
for (int i = 0; i < 64; i++) {
if (i < t1)
val[i] = (byte) (rand.NextDouble() * 256);
else
val[i] = 0;
if (val[i] != 0)
done = true;
}
}
while (val[0] == 0)
val[0] = (byte) (rand.NextDouble() * 256);
Console.Write("Round = " + count);
// encrypt and decrypt data
BigInteger bi_data = new BigInteger(val, t1);
BigInteger bi_encrypted = bi_data.modPow(bi_e, bi_n);
BigInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n);
// compare
if (bi_decrypted != bi_data) {
Console.Error.WriteLine("\nError at round " + count);
Console.Error.WriteLine(bi_data + "\n");
return;
}
Console.Error.WriteLine(" <PASSED>.");
}
}
//***********************************************************************
// Overloading of unary >> operators
//***********************************************************************
public static BigInteger operator >>(BigInteger bi1, int shiftVal)
{
BigInteger result = new BigInteger(bi1);
result.dataLength = shiftRight(result.data, shiftVal);
if ((bi1.data[maxLength - 1] & 0x80000000) != 0) // negative
{
for (int i = maxLength - 1; i >= result.dataLength; i--)
result.data[i] = 0xFFFFFFFF;
uint mask = 0x80000000;
for (int i = 0; i < 32; i++) {
if ((result.data[result.dataLength - 1] & mask) != 0)
break;
result.data[result.dataLength - 1] |= mask;
mask >>= 1;
}
result.dataLength = maxLength;
}
return result;
}
//***********************************************************************
// Tests the correct implementation of the modulo exponential and
// inverse modulo functions using RSA encryption and decryption. The two
// pseudoprimes p and q are fixed, but the two RSA keys are generated
// for each round of testing.
//***********************************************************************
public static void RSATest2(int rounds)
{
Random rand = new Random();
byte[] val = new byte[64];
byte[] pseudoPrime1 = {
(byte) 0x85, (byte) 0x84, (byte) 0x64, (byte) 0xFD,
(byte) 0x70, (byte) 0x6A, (byte) 0x9F, (byte) 0xF0,
(byte) 0x94, (byte) 0x0C, (byte) 0x3E, (byte) 0x2C,
(byte) 0x74, (byte) 0x34, (byte) 0x05, (byte) 0xC9,
(byte) 0x55, (byte) 0xB3, (byte) 0x85, (byte) 0x32,
(byte) 0x98, (byte) 0x71, (byte) 0xF9, (byte) 0x41,
(byte) 0x21, (byte) 0x5F, (byte) 0x02, (byte) 0x9E,
(byte) 0xEA, (byte) 0x56, (byte) 0x8D, (byte) 0x8C,
(byte) 0x44, (byte) 0xCC, (byte) 0xEE, (byte) 0xEE,
(byte) 0x3D, (byte) 0x2C, (byte) 0x9D, (byte) 0x2C,
(byte) 0x12, (byte) 0x41, (byte) 0x1E, (byte) 0xF1,
(byte) 0xC5, (byte) 0x32, (byte) 0xC3, (byte) 0xAA,
(byte) 0x31, (byte) 0x4A, (byte) 0x52, (byte) 0xD8,
(byte) 0xE8, (byte) 0xAF, (byte) 0x42, (byte) 0xF4,
(byte) 0x72, (byte) 0xA1, (byte) 0x2A, (byte) 0x0D,
(byte) 0x97, (byte) 0xB1, (byte) 0x31, (byte) 0xB3,};
byte[] pseudoPrime2 = {
(byte) 0x99, (byte) 0x98, (byte) 0xCA, (byte) 0xB8,
(byte) 0x5E, (byte) 0xD7, (byte) 0xE5, (byte) 0xDC,
(byte) 0x28, (byte) 0x5C, (byte) 0x6F, (byte) 0x0E,
(byte) 0x15, (byte) 0x09, (byte) 0x59, (byte) 0x6E,
(byte) 0x84, (byte) 0xF3, (byte) 0x81, (byte) 0xCD,
(byte) 0xDE, (byte) 0x42, (byte) 0xDC, (byte) 0x93,
(byte) 0xC2, (byte) 0x7A, (byte) 0x62, (byte) 0xAC,
(byte) 0x6C, (byte) 0xAF, (byte) 0xDE, (byte) 0x74,
(byte) 0xE3, (byte) 0xCB, (byte) 0x60, (byte) 0x20,
(byte) 0x38, (byte) 0x9C, (byte) 0x21, (byte) 0xC3,
(byte) 0xDC, (byte) 0xC8, (byte) 0xA2, (byte) 0x4D,
(byte) 0xC6, (byte) 0x2A, (byte) 0x35, (byte) 0x7F,
(byte) 0xF3, (byte) 0xA9, (byte) 0xE8, (byte) 0x1D,
(byte) 0x7B, (byte) 0x2C, (byte) 0x78, (byte) 0xFA,
(byte) 0xB8, (byte) 0x02, (byte) 0x55, (byte) 0x80,
(byte) 0x9B, (byte) 0xC2, (byte) 0xA5, (byte) 0xCB,};
BigInteger bi_p = new BigInteger(pseudoPrime1);
BigInteger bi_q = new BigInteger(pseudoPrime2);
BigInteger bi_pq = (bi_p - 1) * (bi_q - 1);
BigInteger bi_n = bi_p * bi_q;
for (int count = 0; count < rounds; count++) {
// generate private and public key
BigInteger bi_e = bi_pq.genCoPrime(512, rand);
BigInteger bi_d = bi_e.modInverse(bi_pq);
Console.Error.WriteLine("\ne =\n" + bi_e.ToString(10));
Console.Error.WriteLine("\nd =\n" + bi_d.ToString(10));
Console.Error.WriteLine("\nn =\n" + bi_n.ToString(10) + "\n");
// generate data of random length
int t1 = 0;
while (t1 == 0)
t1 = (int) (rand.NextDouble() * 65);
bool done = false;
while (!done) {
for (int i = 0; i < 64; i++) {
if (i < t1)
val[i] = (byte) (rand.NextDouble() * 256);
else
val[i] = 0;
if (val[i] != 0)
done = true;
}
}
while (val[0] == 0)
val[0] = (byte) (rand.NextDouble() * 256);
Console.Write("Round = " + count);
// encrypt and decrypt data
BigInteger bi_data = new BigInteger(val, t1);
BigInteger bi_encrypted = bi_data.modPow(bi_e, bi_n);
BigInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n);
// compare
if (bi_decrypted != bi_data) {
Console.Error.WriteLine("\nError at round " + count);
Console.Error.WriteLine(bi_data + "\n");
return;
}
Console.Error.WriteLine(" <PASSED>.");
}
}
public virtual BigInteger ToBigInteger()
{
if( null == _big_int ) {
_big_int = new BigInteger(_buffer);
}
return _big_int;
}
//***********************************************************************
// Tests the correct implementation of sqrt() method.
//***********************************************************************
public static void SqrtTest(int rounds)
{
Random rand = new Random();
for (int count = 0; count < rounds; count++) {
// generate data of random length
int t1 = 0;
while (t1 == 0)
t1 = (int) (rand.NextDouble() * 1024);
Console.Write("Round = " + count);
BigInteger a = new BigInteger();
a.genRandomBits(t1, rand);
BigInteger b = a.sqrt();
BigInteger c = (b + 1) * (b + 1);
// check that b is the largest integer such that b*b <= a
if (c <= a) {
Console.Error.WriteLine("\nError at round " + count);
Console.Error.WriteLine(a + "\n");
return;
}
Console.Error.WriteLine(" <PASSED>.");
}
}
public void Test() {
System.Random r = new System.Random();
for(int i = 0; i < 1024; i++) {
//Test ClassOf and SetClass:
int c = r.Next(160);
byte[] buf0 = new byte[Address.MemSize];
//Fill it with junk
r.NextBytes(buf0);
Address.SetClass(buf0, c);
int c2 = Address.ClassOf(MemBlock.Reference(buf0, 0, Address.MemSize));
Assert.AreEqual(c,c2, "Class Round Trip");
//Test BigInteger stuff:
int size = r.Next(1, MemSize + 1);
byte[] buf1 = new byte[size];
r.NextBytes(buf1);
BigInteger b1 = new BigInteger(buf1);
byte[] buf2 = Address.ConvertToAddressBuffer(b1);
//Check to see if the bytes are equivalent:
int min_len = System.Math.Min(buf1.Length, buf2.Length);
bool all_eq = true;
for(int j = 0; j < min_len; j++) {
all_eq = all_eq
&& (buf2[buf2.Length - j - 1] == buf1[buf1.Length - j - 1]);
}
if( !all_eq ) {
System.Console.Error.WriteLine("Buf1: ");
foreach(byte b in buf1) {
System.Console.Write("{0} ",b);
}
System.Console.Error.WriteLine();
System.Console.Error.WriteLine("Buf2: ");
foreach(byte b in buf2) {
System.Console.Write("{0} ",b);
}
System.Console.Error.WriteLine();
}
Assert.IsTrue(all_eq, "bytes are equivalent");
BigInteger b2 = new BigInteger(buf2);
Assert.AreEqual(b1, b2, "BigInteger round trip");
}
}
public static void Main(string[] args)
{
// Known problem -> these two pseudoprimes passes my implementation of
// primality test but failed in JDK's isProbablePrime test.
byte[] pseudoPrime1 = {
(byte) 0x00,
(byte) 0x85, (byte) 0x84, (byte) 0x64, (byte) 0xFD,
(byte) 0x70, (byte) 0x6A, (byte) 0x9F, (byte) 0xF0,
(byte) 0x94, (byte) 0x0C, (byte) 0x3E, (byte) 0x2C,
(byte) 0x74, (byte) 0x34, (byte) 0x05, (byte) 0xC9,
(byte) 0x55, (byte) 0xB3, (byte) 0x85, (byte) 0x32,
(byte) 0x98, (byte) 0x71, (byte) 0xF9, (byte) 0x41,
(byte) 0x21, (byte) 0x5F, (byte) 0x02, (byte) 0x9E,
(byte) 0xEA, (byte) 0x56, (byte) 0x8D, (byte) 0x8C,
(byte) 0x44, (byte) 0xCC, (byte) 0xEE, (byte) 0xEE,
(byte) 0x3D, (byte) 0x2C, (byte) 0x9D, (byte) 0x2C,
(byte) 0x12, (byte) 0x41, (byte) 0x1E, (byte) 0xF1,
(byte) 0xC5, (byte) 0x32, (byte) 0xC3, (byte) 0xAA,
(byte) 0x31, (byte) 0x4A, (byte) 0x52, (byte) 0xD8,
(byte) 0xE8, (byte) 0xAF, (byte) 0x42, (byte) 0xF4,
(byte) 0x72, (byte) 0xA1, (byte) 0x2A, (byte) 0x0D,
(byte) 0x97, (byte) 0xB1, (byte) 0x31, (byte) 0xB3,};
byte[] pseudoPrime2 = {
(byte) 0x00,
(byte) 0x99, (byte) 0x98, (byte) 0xCA, (byte) 0xB8,
(byte) 0x5E, (byte) 0xD7, (byte) 0xE5, (byte) 0xDC,
(byte) 0x28, (byte) 0x5C, (byte) 0x6F, (byte) 0x0E,
(byte) 0x15, (byte) 0x09, (byte) 0x59, (byte) 0x6E,
(byte) 0x84, (byte) 0xF3, (byte) 0x81, (byte) 0xCD,
(byte) 0xDE, (byte) 0x42, (byte) 0xDC, (byte) 0x93,
(byte) 0xC2, (byte) 0x7A, (byte) 0x62, (byte) 0xAC,
(byte) 0x6C, (byte) 0xAF, (byte) 0xDE, (byte) 0x74,
(byte) 0xE3, (byte) 0xCB, (byte) 0x60, (byte) 0x20,
(byte) 0x38, (byte) 0x9C, (byte) 0x21, (byte) 0xC3,
(byte) 0xDC, (byte) 0xC8, (byte) 0xA2, (byte) 0x4D,
(byte) 0xC6, (byte) 0x2A, (byte) 0x35, (byte) 0x7F,
(byte) 0xF3, (byte) 0xA9, (byte) 0xE8, (byte) 0x1D,
(byte) 0x7B, (byte) 0x2C, (byte) 0x78, (byte) 0xFA,
(byte) 0xB8, (byte) 0x02, (byte) 0x55, (byte) 0x80,
(byte) 0x9B, (byte) 0xC2, (byte) 0xA5, (byte) 0xCB,};
Console.
WriteLine("List of primes < 2000\n---------------------");
int limit = 100, count = 0;
for (int i = 0; i < 2000; i++) {
if (i >= limit) {
Console.Error.WriteLine();
limit += 100;
}
BigInteger p = new BigInteger(-i);
if (p.isProbablePrime()) {
Console.Write(i + ", ");
count++;
}
}
Console.Error.WriteLine("\nCount = " + count);
BigInteger bi1 = new BigInteger(pseudoPrime1);
Console.Error.WriteLine("\n\nPrimality testing for\n" +
bi1.ToString() + "\n");
Console.Error.WriteLine("SolovayStrassenTest(5) = " +
bi1.SolovayStrassenTest(5));
Console.Error.WriteLine("RabinMillerTest(5) = " +
bi1.RabinMillerTest(5));
Console.Error.WriteLine("FermatLittleTest(5) = " +
bi1.FermatLittleTest(5));
Console.Error.WriteLine("isProbablePrime() = " +
bi1.isProbablePrime());
/* POB: added the above also for pseudoPrime2 to clear compiler warning */
bi1 = new BigInteger(pseudoPrime2);
Console.Error.WriteLine("\n\nPrimality testing for\n" +
bi1.ToString() + "\n");
Console.Error.WriteLine("SolovayStrassenTest(5) = " +
bi1.SolovayStrassenTest(5));
Console.Error.WriteLine("RabinMillerTest(5) = " +
bi1.RabinMillerTest(5));
Console.Error.WriteLine("FermatLittleTest(5) = " +
bi1.FermatLittleTest(5));
Console.Error.WriteLine("isProbablePrime() = " +
bi1.isProbablePrime());
Console.Write("\nGenerating 512-bits random pseudoprime. . .");
Random rand = new Random();
BigInteger prime = BigInteger.genPseudoPrime(512, 5, rand);
Console.Error.WriteLine("\n" + prime);
//int dwStart = System.Environment.TickCount;
//BigInteger.MulDivTest(100000);
//BigInteger.RSATest(10);
//BigInteger.RSATest2(10);
//Console.Error.WriteLine(System.Environment.TickCount - dwStart);
}
//***********************************************************************
// Constructor (Default value provided by a string of digits of the
// specified base)
//
// Example (base 10)
// -----------------
// To initialize "a" with the default value of 1234 in base 10
// BigInteger a = new BigInteger("1234", 10)
//
// To initialize "a" with the default value of -1234
// BigInteger a = new BigInteger("-1234", 10)
//
// Example (base 16)
// -----------------
// To initialize "a" with the default value of 0x1D4F in base 16
// BigInteger a = new BigInteger("1D4F", 16)
//
// To initialize "a" with the default value of -0x1D4F
// BigInteger a = new BigInteger("-1D4F", 16)
//
// Note that string values are specified in the <sign><magnitude>
// format.
//
//***********************************************************************
public BigInteger(string value, int radix)
{
BigInteger multiplier = new BigInteger(1);
BigInteger result = new BigInteger();
value = (value.ToUpper()).Trim();
int limit = 0;
if (value[0] == '-')
limit = 1;
for (int i = value.Length - 1; i >= limit; i--) {
int posVal = (int) value[i];
if (posVal >= '0' && posVal <= '9')
posVal -= '0';
else if (posVal >= 'A' && posVal <= 'Z')
posVal = (posVal - 'A') + 10;
else
posVal = 9999999; // arbitrary large
if (posVal >= radix)
throw(new
ArithmeticException
("Invalid string in constructor."));
else {
if (value[0] == '-')
posVal = -posVal;
result = result + (multiplier * posVal);
if ((i - 1) >= limit)
multiplier = multiplier * radix;
}
}
if (value[0] == '-') // negative values
{
if ((result.data[maxLength - 1] & 0x80000000) == 0)
throw(new
ArithmeticException
("Negative underflow in constructor."));
}
else // positive values
{
if ((result.data[maxLength - 1] & 0x80000000) != 0)
throw(new
ArithmeticException
("Positive overflow in constructor."));
}
data = new uint[maxLength];
for (int i = 0; i < result.dataLength; i++)
data[i] = result.data[i];
dataLength = result.dataLength;
}
//***********************************************************************
// Overloading of addition operator
//***********************************************************************
public static BigInteger operator +(BigInteger bi1,
BigInteger bi2)
{
BigInteger result = new BigInteger();
result.dataLength =
(bi1.dataLength >
bi2.dataLength) ? bi1.dataLength : bi2.dataLength;
long carry = 0;
for (int i = 0; i < result.dataLength; i++) {
long sum = (long) bi1.data[i] + (long) bi2.data[i] + carry;
carry = sum >> 32;
result.data[i] = (uint) (sum & 0xFFFFFFFF);
}
if (carry != 0 && result.dataLength < maxLength) {
result.data[result.dataLength] = (uint) (carry);
result.dataLength++;
}
while (result.dataLength > 1
&& result.data[result.dataLength - 1] == 0)
result.dataLength--;
// overflow check
int lastPos = maxLength - 1;
if ((bi1.data[lastPos] & 0x80000000) ==
(bi2.data[lastPos] & 0x80000000)
&& (result.data[lastPos] & 0x80000000) !=
(bi1.data[lastPos] & 0x80000000)) {
throw(new ArithmeticException());
}
return result;
}
public AHAddress(BigInteger big_int):base(big_int)
{
if (ClassOf(_buffer) != this.Class) {
throw new System.
ArgumentException("Class of address is not my class: ",
this.ToString());
}
}
private bool LucasStrongTestHelper(BigInteger thisVal)
{
// Do the test (selects D based on Selfridge)
// Let D be the first element of the sequence
// 5, -7, 9, -11, 13, ... for which J(D,n) = -1
// Let P = 1, Q = (1-D) / 4
long D = 5, sign = -1, dCount = 0;
bool done = false;
while (!done) {
int Jresult = BigInteger.Jacobi(D, thisVal);
if (Jresult == -1)
done = true; // J(D, this) = 1
else {
if (Jresult == 0 && Math.Abs(D) < thisVal) // divisor found
return false;
if (dCount == 20) {
// check for square
BigInteger root = thisVal.sqrt();
if (root * root == thisVal)
return false;
}
//Console.Error.WriteLine(D);
D = (Math.Abs(D) + 2) * sign;
sign = -sign;
}
dCount++;
}
long Q = (1 - D) >> 2;
/*
* Console.Error.WriteLine("D = " + D);
* Console.Error.WriteLine("Q = " + Q);
* Console.Error.WriteLine("(n,D) = " + thisVal.gcd(D));
* Console.Error.WriteLine("(n,Q) = " + thisVal.gcd(Q));
* Console.Error.WriteLine("J(D|n) = " + BigInteger.Jacobi(D, thisVal));
*/
BigInteger p_add1 = thisVal + 1;
int s = 0;
for (int index = 0; index < p_add1.dataLength; index++) {
uint mask = 0x01;
for (int i = 0; i < 32; i++) {
if ((p_add1.data[index] & mask) != 0) {
index = p_add1.dataLength; // to break the outer loop
break;
}
mask <<= 1;
s++;
}
}
BigInteger t = p_add1 >> s;
// calculate constant = b^(2k) / m
// for Barrett Reduction
BigInteger constant = new BigInteger();
int nLen = thisVal.dataLength << 1;
constant.data[nLen] = 0x00000001;
constant.dataLength = nLen + 1;
constant = constant / thisVal;
BigInteger[] lucas =
LucasSequenceHelper(1, Q, t, thisVal, constant, 0);
bool isPrime = false;
if ((lucas[0].dataLength == 1 && lucas[0].data[0] == 0) ||
(lucas[1].dataLength == 1 && lucas[1].data[0] == 0)) {
// u(t) = 0 or V(t) = 0
isPrime = true;
}
for (int i = 1; i < s; i++) {
if (!isPrime) {
// doubling of index
lucas[1] =
thisVal.BarrettReduction(lucas[1] * lucas[1], thisVal,
constant);
lucas[1] = (lucas[1] - (lucas[2] << 1)) % thisVal;
//lucas[1] = ((lucas[1] * lucas[1]) - (lucas[2] << 1)) % thisVal;
if ((lucas[1].dataLength == 1 && lucas[1].data[0] == 0))
isPrime = true;
}
lucas[2] = thisVal.BarrettReduction(lucas[2] * lucas[2], thisVal, constant); //Q^k
}
if (isPrime) // additional checks for composite numbers
{
// If n is prime and gcd(n, Q) == 1, then
// Q^((n+1)/2) = Q * Q^((n-1)/2) is congruent to (Q * J(Q, n)) mod n
BigInteger g = thisVal.gcd(Q);
if (g.dataLength == 1 && g.data[0] == 1) // gcd(this, Q) == 1
{
if ((lucas[2].data[maxLength - 1] & 0x80000000) != 0)
lucas[2] += thisVal;
BigInteger temp =
(Q * BigInteger.Jacobi(Q, thisVal)) % thisVal;
if ((temp.data[maxLength - 1] & 0x80000000) != 0)
temp += thisVal;
if (lucas[2] != temp)
isPrime = false;
}
}
return isPrime;
}
