public RSA(int b, BigInteger e)
{
this.e = e;
int qs = b >> 1;
while (true)
{
while (true)
{
p = BigInteger.genPseudoPrime(b - qs, 1, new Random());
if ((p - 1).gcd(this.e) == 1 && p.isProbablePrime(10))
{
break;
}
}
while (true)
{
q = BigInteger.genPseudoPrime(qs, 1, new Random());
if ((q - 1).gcd(this.e) == 1 && p.isProbablePrime(10))
{
break;
}
}
if (p < q)
{
BigInteger t = p;
p = q;
q = t;
}
BigInteger phi = (p - 1) * (q - 1);
if (phi.gcd(this.e) == 1)
{
n = p * q;
d = this.e.modInverse(phi);
dmp1 = d % (p - 1);
dmq1 = d % (q - 1);
coeff = q.modInverse(p);
break;
}
}
canEncrypt = n != 0 && this.e != 0;
canDecrypt = canEncrypt && d != 0;
}
public RSA(BigInteger n, BigInteger e, BigInteger d, BigInteger p, BigInteger q, BigInteger dmp1,
BigInteger dmq1, BigInteger coeff)
{
this.n = n;
this.e = e;
this.d = d;
this.p = p;
this.q = q;
this.dmp1 = dmp1;
this.dmq1 = dmq1;
this.coeff = coeff;
canEncrypt = this.n != 0 && this.e != 0;
canDecrypt = canEncrypt && this.d != 0;
}
public DiffieHellman(BigInteger prime, BigInteger generator)
{
this.Prime = prime;
this.Generator = generator;
this.PrivateKey = new BigInteger(GenerateRandomHexString(BITLENGTH), 16);
if (this.Generator > this.Prime)
{
BigInteger temp = this.Prime;
this.Prime = this.Generator;
this.Generator = temp;
}
this.PublicKey = this.Generator.modPow(this.PrivateKey, this.Prime);
}
public RSA(BigInteger e, BigInteger p, BigInteger q)
{
this.e = e;
this.p = p;
this.q = q;
BigInteger phi = (this.p - 1) * (this.q - 1);
if (phi.gcd(this.e) == 1)
{
n = this.p * this.q;
d = this.e.modInverse(phi);
dmp1 = d % (this.p - 1);
dmq1 = d % (this.q - 1);
coeff = this.q.modInverse(this.p);
}
canEncrypt = n != 0 && this.e != 0;
canDecrypt = canEncrypt && d != 0;
}
//***********************************************************************
// 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;
}
//***********************************************************************
// 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;
}
//***********************************************************************
// 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;
}
public string Encrypt(string text)
{
if (text.Length > GetBlockSize() - 11)
{
Console.WriteLine("RSA Encrypt: Message is to big!");
}
var m = new BigInteger(pkcs1pad2(Encoding.GetEncoding("iso-8859-1").GetBytes(text), GetBlockSize()));
if (m == 0)
{
return null;
}
BigInteger c = DoPublic(m);
if (c == 0)
{
return null;
}
string result = c.ToString(16);
if ((result.Length & 1) == 0)
{
return result;
}
return "0" + 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;
}
//***********************************************************************
// 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.WriteLine(result.ToString(16));
// gcd test
BigInteger g = result.gcd(this);
if (g.dataLength == 1 && g.data[0] == 1)
done = true;
}
return result;
}
public BigInteger DoPrivate(BigInteger x)
{
if (canDecrypt)
{
return x.modPow(d, n);
}
return 0;
}
//***********************************************************************
// 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.WriteLine("\ne =\n" + bi_e.ToString(10));
Console.WriteLine("\nd =\n" + bi_d.ToString(10));
Console.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.WriteLine("\nError at round " + count);
Console.WriteLine(bi_data + "\n");
return;
}
Console.WriteLine(" <PASSED>.");
}
}
//***********************************************************************
// 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.WriteLine("\nError at round " + count);
Console.WriteLine(a + "\n");
return;
}
Console.WriteLine(" <PASSED>.");
}
}
//***********************************************************************
// 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.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.WriteLine("Error at " + count);
Console.WriteLine(bn1 + "\n");
Console.WriteLine(bn2 + "\n");
Console.WriteLine(bn3 + "\n");
Console.WriteLine(bn4 + "\n");
Console.WriteLine(bn5 + "\n");
return;
}
}
}
//***********************************************************************
// 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.WriteLine("e =\n" + bi_e.ToString(10));
Console.WriteLine("\nd =\n" + bi_d.ToString(10));
Console.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.WriteLine("\nError at round " + count);
Console.WriteLine(bi_data + "\n");
return;
}
Console.WriteLine(" <PASSED>.");
}
}
//***********************************************************************
// 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;
}
//***********************************************************************
// 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.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.WriteLine("s = " + s + " t = " + t);
return LucasSequenceHelper(P, Q, t, n, constant, s);
}
//***********************************************************************
// 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 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;
}
//***********************************************************************
// Overloading of the NEGATE operator (2's complement)
//***********************************************************************
public static BigInteger operator -(BigInteger bi1)
{
// handle neg of zero separately since it'll cause an overflow
// if we proceed.
if (bi1.dataLength == 1 && bi1.data[0] == 0)
return (new BigInteger());
BigInteger result = new BigInteger(bi1);
// 1's complement
for (int i = 0; i < maxLength; i++)
result.data[i] = (uint)(~(bi1.data[i]));
// add one to result of 1's complement
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 ((bi1.data[maxLength - 1] & 0x80000000) == (result.data[maxLength - 1] & 0x80000000))
throw (new ArithmeticException("Overflow in negation.\n"));
result.dataLength = maxLength;
while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
result.dataLength--;
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;
}
public string Decrypt(string ctext)
{
var c = new BigInteger(ctext, 16);
BigInteger m = DoPrivate(c);
if (m == 0)
{
return null;
}
byte[] bytes = pkcs1unpad2(m, GetBlockSize());
if (bytes == null)
{
return null;
}
return Encoding.GetEncoding("iso-8859-1").GetString(bytes);
}
//***********************************************************************
// 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];
}
public BigInteger DoPublic(BigInteger x)
{
if (canEncrypt)
{
return x.modPow(e, n);
}
return 0;
}
//***********************************************************************
// 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;
}
private byte[] pkcs1unpad2(BigInteger m, int b)
{
byte[] bytes = m.getBytes();
int i = 0;
while (i < bytes.Length && bytes[i] == 0) ++i;
if (bytes.Length - i != (b - 1) || bytes[i] != 0x2)
{
return null;
}
while (bytes[i] != 0)
{
if (++i >= bytes.Length)
{
return null;
}
}
var result = new byte[bytes.Length - i + 1];
int p = 0;
while (++i < bytes.Length)
{
result[p++] = bytes[i];
}
return result;
}
//***********************************************************************
// 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;
}
//***********************************************************************
// 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;
}
//***********************************************************************
// 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.WriteLine(quotient.dataLength);
Console.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;
}