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; }