/** <summary>Reassign range info(Start and End) based on recalculated range.</summary> <param name = "rg_size">Current range size(round distance between start address and end address of this Entry).</param> <remarks>new_start = mid - rg_size/2, new_end = mid + rg_size/2 </remarks> */ public Entry ReAssignRange(BigInteger rg_size) { // calculate middle address of range BigInteger start_int = Start.ToBigInteger(); BigInteger end_int = End.ToBigInteger(); BigInteger mid_int = (start_int + end_int) / 2; if (mid_int % 2 == 1) { mid_int = mid_int -1; } AHAddress mid_addr = new AHAddress(mid_int); /* * If we have a case where start -> end includes zero, * this is the wrap around. So, we can imagine that * we have end' = end + Address.Full. So, * mid' = (start + end')/2 = (start + end)/2 + Address.Full/2 = (start + end)/ 2 + Address.Half */ if (!mid_addr.IsBetweenFromLeft(Start, End)) { mid_int += Address.Half; } //addresses for new range BigInteger rg_half = rg_size / 2; if (rg_half % 2 == 1) { rg_half -= 1; } AHAddress n_a = new AHAddress(mid_int - rg_half); AHAddress n_b = new AHAddress(mid_int + rg_half); return new Entry(Content, Alpha, n_a, n_b); }
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; }
/** * When we want to connect to the address closest * to us, we use this address. */ protected Address GetSelfTarget() { /** * try to get at least one neighbor using forwarding through the * leaf . The forwarded address is 2 larger than the address of * the new node that is getting connected. */ BigInteger local_int_add = _node.Address.ToBigInteger(); //must have even addresses so increment twice local_int_add += 2; //Make sure we don't overflow: BigInteger tbi = new BigInteger(local_int_add % Address.Full); return new AHAddress(tbi); }
protected StructuredAddress(BigInteger big_int):base(big_int) { }
/// <summary>Calculates a shortcut using a harmonic distribution as in a /// Symphony-lke shortcut.</summary> protected virtual AHAddress ComputeShortcutTarget(AHAddress addr) { int network_size = _addrs.Count; double logN = (double)(Brunet.Address.MemSize * 8); double logk = Math.Log( (double) network_size, 2.0 ); double p = _rand.NextDouble(); double ex = logN - (1.0 - p)*logk; int ex_i = (int)Math.Floor(ex); double ex_f = ex - Math.Floor(ex); //Make sure 2^(ex_long+1) will fit in a long: int ex_long = ex_i % 63; int ex_big = ex_i - ex_long; ulong dist_long = (ulong)Math.Pow(2.0, ex_long + ex_f); //This is 2^(ex_big): BigInteger big_one = 1; BigInteger dist_big = big_one << ex_big; BigInteger rand_dist = dist_big * dist_long; // Add or subtract random distance to the current address BigInteger t_add = addr.ToBigInteger(); // Random number that is 0 or 1 if( _rand.Next(2) == 0 ) { t_add += rand_dist; } else { t_add -= rand_dist; } BigInteger target_int = new BigInteger(t_add % Address.Full); if((target_int & 1) == 1) { target_int -= 1; } byte[]buf = Address.ConvertToAddressBuffer(target_int); Address.SetClass(buf, AHAddress.ClassValue); return new AHAddress(buf); }
//*********************************************************************** // 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; }
//*********************************************************************** // 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; }
//*********************************************************************** // 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; }
//*********************************************************************** // 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)); }
//*********************************************************************** // 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 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; }
//*********************************************************************** // 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; } } }
//*********************************************************************** // 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; }
//*********************************************************************** // 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 unary << operators //*********************************************************************** public static BigInteger operator <<(BigInteger bi1, int shiftVal) { BigInteger result = new BigInteger(bi1); result.dataLength = shiftLeft(result.data, shiftVal); 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 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; }
//*********************************************************************** // 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>."); } }
protected MemBlock[] MapToRing(byte[] key) { MemBlock[] targets = new MemBlock[DHT_DEGREE]; // Setup the first key HashAlgorithm algo = new SHA1CryptoServiceProvider(); byte[] target = algo.ComputeHash(key); Address.SetClass(target, AHAddress._class); targets[0] = MemBlock.Reference(target, 0, Address.MemSize); // Setup the rest of the keys BigInteger inc_addr = Address.Full/DHT_DEGREE; BigInteger curr_addr = new BigInteger(targets[0]); for (int k = 1; k < targets.Length; k++) { curr_addr = curr_addr + inc_addr; target = Address.ConvertToAddressBuffer(curr_addr); Address.SetClass(target, AHAddress._class); targets[k] = target; } return targets; }
//*********************************************************************** // 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 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; }
/// Determine if there are any unuseful STRUC_NEAR that we can trim protected void TrimConnections() { ConnectionTable tab = _node.ConnectionTable; ConnectionList cons = tab.GetConnections(ConnectionType.Structured); ArrayList trim_candidates = new ArrayList(); foreach(Connection c in cons) { if(!c.ConType.Equals(STRUC_NEAR)) { continue; } int left_pos = cons.LeftInclusiveCount(_node.Address, c.Address); int right_pos = cons.RightInclusiveCount(_node.Address, c.Address); if( right_pos >= 2 * DESIRED_NEIGHBORS && left_pos >= 2 * DESIRED_NEIGHBORS ) { //These are near neighbors that are not so near trim_candidates.Add(c); } } if(trim_candidates.Count == 0) { return; } //Delete a farthest trim candidate: BigInteger biggest_distance = new BigInteger(0); BigInteger tmp_distance = new BigInteger(0); Connection to_trim = null; foreach(Connection tc in trim_candidates ) { AHAddress t_ah_add = (AHAddress)tc.Address; tmp_distance = t_ah_add.DistanceTo( (AHAddress)_node.Address).abs(); if (tmp_distance > biggest_distance) { biggest_distance = tmp_distance; //Console.Error.WriteLine("...finding far distance for trim: {0}",biggest_distance.ToString() ); to_trim = tc; } } #if POB_DEBUG Console.Error.WriteLine("Attempt to trim Near: {0}", to_trim); #endif _node.GracefullyClose( to_trim.Edge, "SCO, near connection trim" ); }
//*********************************************************************** // Probabilistic prime test based on Solovay-Strassen (Euler Criterion) // // p is probably prime if for any a < p (a is not multiple of p), // a^((p-1)/2) mod p = J(a, p) // // where J is the Jacobi symbol. // // Otherwise, p is composite. // // Returns // ------- // True if "this" is a Euler pseudoprime to randomly chosen // bases. The number of chosen bases is given by the "confidence" // parameter. // // False if "this" is definitely NOT prime. // //*********************************************************************** public bool SolovayStrassenTest(int confidence) { BigInteger thisVal; if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative thisVal = -this; else thisVal = this; if (thisVal.dataLength == 1) { // test small numbers if (thisVal.data[0] == 0 || thisVal.data[0] == 1) return false; else if (thisVal.data[0] == 2 || thisVal.data[0] == 3) return true; } if ((thisVal.data[0] & 0x1) == 0) // even numbers return false; int bits = thisVal.bitCount(); BigInteger a = new BigInteger(); BigInteger p_sub1 = thisVal - 1; BigInteger p_sub1_shift = p_sub1 >> 1; Random rand = new Random(); for (int round = 0; round < confidence; round++) { bool done = false; while (!done) // generate a < n { int testBits = 0; // make sure "a" has at least 2 bits while (testBits < 2) testBits = (int) (rand.NextDouble() * bits); a.genRandomBits(testBits, rand); int byteLen = a.dataLength; // make sure "a" is not 0 if (byteLen > 1 || (byteLen == 1 && a.data[0] != 1)) done = true; } // check whether a factor exists (fix for version 1.03) BigInteger gcdTest = a.gcd(thisVal); if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1) return false; // calculate a^((p-1)/2) mod p BigInteger expResult = a.modPow(p_sub1_shift, thisVal); if (expResult == p_sub1) expResult = -1; // calculate Jacobi symbol BigInteger jacob = Jacobi(a, thisVal); //Console.Error.WriteLine("a = " + a.ToString(10) + " b = " + thisVal.ToString(10)); //Console.Error.WriteLine("expResult = " + expResult.ToString(10) + " Jacob = " + jacob.ToString(10)); // if they are different then it is not prime if (expResult != jacob) return false; } return true; }