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; }