/// <summary>
/// Performs the same as GcdBinary(BigInteger, BigInteger)}, but with numbers of 63 bits,
/// represented in positives values of long type.
/// </summary>
///
/// <param name="X">A positive number</param>
/// <param name="Y">A positive number></param>
///
/// <returns>Returns <c>Gcd(X, Y)</c></returns>
internal static long GcdBinary(long X, long Y)
{
// (op1 > 0) and (op2 > 0)
int lsb1 = IntUtils.NumberOfTrailingZeros(X);
int lsb2 = IntUtils.NumberOfTrailingZeros(Y);
int pow2Count = System.Math.Min(lsb1, lsb2);
if (lsb1 != 0)
{
X = IntUtils.URShift(X, lsb1);
}
if (lsb2 != 0)
{
Y = IntUtils.URShift(Y, lsb2);
}
do
{
if (X >= Y)
{
X -= Y;
X = IntUtils.URShift(X, IntUtils.NumberOfTrailingZeros(X));
}
else
{
Y -= X;
Y = IntUtils.URShift(Y, IntUtils.NumberOfTrailingZeros(Y));
}
} while (X != 0);
return(Y << pow2Count);
}
/// <summary>
/// Create a nxn random lower triangular matrix
/// </summary>
///
/// <param name="N">Number of rows (and columns)</param>
/// <param name="SecRnd">Source of randomness</param>
private void AssignRandomLowerTriangularMatrix(int N, IRandom SecRnd)
{
RowCount = N;
ColumnCount = N;
_length = IntUtils.URShift((N + 31), 5);
_matrix = ArrayUtils.CreateJagged <int[][]>(RowCount, _length);
for (int i = 0; i < RowCount; i++)
{
int q = IntUtils.URShift(i, 5);
int r = i & 0x1f;
int s = 31 - r;
r = 1 << r;
for (int j = 0; j < q; j++)
{
_matrix[i][j] = SecRnd.Next();
}
_matrix[i][q] = (IntUtils.URShift(SecRnd.Next(), s)) | r;
for (int j = q + 1; j < _length; j++)
{
_matrix[i][j] = 0;
}
}
}
/// <summary>
/// Compute exponentiation of a^k
/// </summary>
///
/// <param name="A">The field element A</param>
/// <param name="K">The K degree</param>
///
/// <returns>The sum: <c>a pow k</c></returns>
public int Exp(int A, int K)
{
if (A == 0)
{
return(0);
}
if (A == 1)
{
return(1);
}
int result = 1;
if (K < 0)
{
A = Inverse(A);
K = -K;
}
while (K != 0)
{
if ((K & 1) == 1)
{
result = Multiply(result, A);
}
A = Multiply(A, A);
K = IntUtils.URShift(K, 1);
}
return(result);
}
/// <summary>
/// Compute the product of two polynomials modulo a third polynomial
/// </summary>
///
/// <param name="A">The first polynomial</param>
/// <param name="B">The second polynomial</param>
/// <param name="R">The reduction polynomial</param>
///
/// <returns>Returns <c>a * b mod r</c></returns>
public static int ModMultiply(int A, int B, int R)
{
int result = 0;
int p = Remainder(A, R);
int q = Remainder(B, R);
if (q != 0)
{
int d = 1 << Degree(R);
while (p != 0)
{
byte pMod2 = (byte)(p & 0x01);
if (pMod2 == 1)
{
result ^= q;
}
p = IntUtils.URShift(p, 1);
q <<= 1;
if (q >= d)
{
q ^= R;
}
}
}
return(result);
}
/// <summary>
/// Returns encoded matrix, i.e., this matrix in byte array form
/// </summary>
///
/// <returns>The encoded matrix</returns>
public override byte[] GetEncoded()
{
int n = IntUtils.URShift((ColumnCount + 7), 3);
n *= RowCount;
n += 8;
byte[] enc = new byte[n];
LittleEndian.IntToOctets(RowCount, enc, 0);
LittleEndian.IntToOctets(ColumnCount, enc, 4);
// number of "full" integer
int q = IntUtils.URShift(ColumnCount, 5);
// number of bits in non-full integer
int r = ColumnCount & 0x1f;
int count = 8;
for (int i = 0; i < RowCount; i++)
{
for (int j = 0; j < q; j++, count += 4)
{
LittleEndian.IntToOctets(_matrix[i][j], enc, count);
}
for (int j = 0; j < r; j += 8)
{
enc[count++] = (byte)((IntUtils.URShift(_matrix[i][q], j)) & 0xff);
}
}
return(enc);
}
/// <summary>
/// Returns a byte array encoding of this matrix
/// </summary>
///
/// <returns>The encoded GF2mMatrix</returns>
public override byte[] GetEncoded()
{
int d = 8;
int count = 1;
while (FieldG.Degree > d)
{
count++;
d += 8;
}
byte[] bf = new byte[this.RowCount * this.ColumnCount * count + 4];
bf[0] = (byte)(this.RowCount & 0xff);
bf[1] = (byte)((this.RowCount >> 8) & 0xff);
bf[2] = (byte)((this.RowCount >> 16) & 0xff);
bf[3] = (byte)((this.RowCount >> 24) & 0xff);
count = 4;
for (int i = 0; i < this.RowCount; i++)
{
for (int j = 0; j < this.ColumnCount; j++)
{
for (int jj = 0; jj < d; jj += 8)
{
bf[count++] = (byte)(IntUtils.URShift(MatrixN[i][j], jj));
}
}
}
return(bf);
}
/// <summary>
/// A random number is generated until a probable prime number is found
/// </summary>
internal static BigInteger ConsBigInteger(int BitLength, int Certainty, SecureRandom Rnd)
{
// PRE: bitLength >= 2;
// For small numbers get a random prime from the prime table
if (BitLength <= 10)
{
int[] rp = m_offsetPrimes[BitLength];
return(m_biPrimes[rp[0] + Rnd.NextInt32(rp[1])]);
}
int shiftCount = (-BitLength) & 31;
int last = (BitLength + 31) >> 5;
BigInteger n = new BigInteger(1, last, new int[last]);
last--;
do
{// To fill the array with random integers
for (int i = 0; i < n.m_numberLength; i++)
{
n.m_digits[i] = Rnd.Next();
}
// To fix to the correct bitLength
// n.digits[last] |= 0x80000000;
n.m_digits[last] |= int.MinValue;
n.m_digits[last] = IntUtils.URShift(n.m_digits[last], shiftCount);
// To create an odd number
n.m_digits[0] |= 1;
} while (!IsProbablePrime(n, Certainty));
return(n);
}
/// <summary>
/// Compute the square root of this element
/// </summary>
public override void SquareRootThis()
{
long[] pol = GetElement();
int f = m_Length - 1;
int b = m_Bit - 1;
// Shift the coefficients one bit to the right.
long TWOTOMAXLONGM1 = _mBitmask[MAXLONG - 1];
bool old, now;
old = (pol[0] & 1) != 0;
for (int i = f; i >= 0; i--)
{
now = (pol[i] & 1) != 0;
pol[i] = IntUtils.URShift(pol[i], 1);
if (old)
{
if (i == f)
{
pol[i] ^= _mBitmask[b];
}
else
{
pol[i] ^= TWOTOMAXLONGM1;
}
}
old = now;
}
Assign(pol);
}
/// <summary>
/// Returns a new BigInteger whose value is <c>this >> N</c>
/// <para>For negative arguments, the result is also negative.
/// The shift distance may be negative which means that this is shifted left.
/// </para>
/// </summary>
///
/// <param name="Result">The result</param>
/// <param name="ResultLen">The result length</param>
/// <param name="Value">The source BigIntger</param>
/// <param name="IntCount">The number integers</param>
/// <param name="N">Shift distance</param>
///
/// <returns>this >> N, if N >= 0; this << (-n) otherwise</returns>
internal static bool ShiftRight(int[] Result, int ResultLen, int[] Value, int IntCount, int N)
{
int i;
bool allZero = true;
for (i = 0; i < IntCount; i++)
{
allZero &= Value[i] == 0;
}
if (N == 0)
{
Array.Copy(Value, IntCount, Result, 0, ResultLen);
i = ResultLen;
}
else
{
int leftShiftCount = 32 - N;
allZero &= (Value[i] << leftShiftCount) == 0;
for (i = 0; i < ResultLen - 1; i++)
{
Result[i] = IntUtils.URShift(Value[i + IntCount], N) |
(Value[i + IntCount + 1] << leftShiftCount);
}
Result[i] = IntUtils.URShift(Value[i + IntCount], N);
i++;
}
return(allZero);
}
private static int[] Square(int[] X, int XLen, int[] Result)
{
long carry;
for (int i = 0; i < XLen; i++)
{
carry = 0;
for (int j = i + 1; j < XLen; j++)
{
carry = UnsignedMultAddAdd(X[i], X[j], Result[i + j], (int)carry);
Result[i + j] = (int)carry;
carry = IntUtils.URShift(carry, 32);
}
Result[i + XLen] = (int)carry;
}
BitLevel.ShiftLeftOneBit(Result, Result, XLen << 1);
carry = 0;
for (int i = 0, index = 0; i < XLen; i++, index++)
{
carry = UnsignedMultAddAdd(X[i], X[i], Result[index], (int)carry);
Result[index] = (int)carry;
carry = IntUtils.URShift(carry, 32);
index++;
carry += Result[index] & 0xFFFFFFFFL;
Result[index] = (int)carry;
carry = IntUtils.URShift(carry, 32);
}
return(Result);
}
/// <summary>
/// Decodes a <c>byte</c> array encoded with EncodeModQ(int[], int)} back to an <c>int</c> array.
/// <para><c>N</c> is the number of coefficients. <c>Q</c> must be a power of <c>2</c>.
/// Ignores any excess bytes.</para>
/// </summary>
///
/// <param name="Data">Data an encoded ternary polynomial</param>
/// <param name="N">The number of coefficients</param>
/// <param name="Q">The modulus</param>
///
/// <returns>Returns an array containing <c>N</c> coefficients between <c>0</c> and <c>q-1</c></returns>
public static int[] DecodeModQ(byte[] Data, int N, int Q)
{
int[] coeffs = new int[N];
int bitsPerCoeff = 31 - IntUtils.NumberOfLeadingZeros(Q);
int mask = IntUtils.URShift(-1, (32 - bitsPerCoeff)); // for truncating values to bitsPerCoeff bits
int byteIndex = 0;
int bitIndex = 0; // next bit in data[byteIndex]
int coeffBuf = 0; // contains (bitIndex) bits
int coeffBits = 0; // length of coeffBuf
int coeffIndex = 0; // index into coeffs
while (coeffIndex < N)
{
// copy bitsPerCoeff or more into coeffBuf
while (coeffBits < bitsPerCoeff)
{
coeffBuf += (Data[byteIndex] & 0xFF) << coeffBits;
coeffBits += 8 - bitIndex;
byteIndex++;
bitIndex = 0;
}
// low bitsPerCoeff bits = next coefficient
coeffs[coeffIndex] = coeffBuf & mask;
coeffIndex++;
coeffBuf = IntUtils.URShift(coeffBuf, bitsPerCoeff);
coeffBits -= bitsPerCoeff;
}
return(coeffs);
}
private static BigInteger MultiplyPAP(BigInteger X, BigInteger Y)
{
// Multiplies two BigIntegers. Implements traditional scholar algorithm described by Knuth.
// PRE: a >= b
int aLen = X.m_numberLength;
int bLen = Y.m_numberLength;
int resLength = aLen + bLen;
int resSign = (X.m_sign != Y.m_sign) ? -1 : 1;
// A special case when both numbers don't exceed int
if (resLength == 2)
{
long val = UnsignedMultAddAdd(X.m_digits[0], Y.m_digits[0], 0, 0);
int valueLo = (int)val;
int valueHi = (int)IntUtils.URShift(val, 32);
return((valueHi == 0) ?
new BigInteger(resSign, valueLo) :
new BigInteger(resSign, 2, new int[] { valueLo, valueHi }));
}
int[] aDigits = X.m_digits;
int[] bDigits = Y.m_digits;
int[] resDigits = new int[resLength];
// Common case
MultiplyArraysPAP(aDigits, aLen, bDigits, bLen, resDigits);
BigInteger result = new BigInteger(resSign, resLength, resDigits);
result.CutOffLeadingZeroes();
return(result);
}
/// <summary>
/// Multiplies a number by a positive integer
/// </summary>
///
/// <param name="X">An arbitrary BigInteger</param>
/// <param name="Factor">A positive int number</param>
///
/// <returns>X * Factor</returns>
internal static BigInteger MultiplyByPositiveInt(BigInteger X, int Factor)
{
int resSign = X.m_sign;
if (resSign == 0)
{
return(BigInteger.Zero);
}
int aNumberLength = X.m_numberLength;
int[] aDigits = X.m_digits;
if (aNumberLength == 1)
{
long res = UnsignedMultAddAdd(aDigits[0], Factor, 0, 0);
int resLo = (int)res;
int resHi = (int)IntUtils.URShift(res, 32);
return((resHi == 0) ?
new BigInteger(resSign, resLo) :
new BigInteger(resSign, 2, new int[] { resLo, resHi }));
}
// Common case
int resLength = aNumberLength + 1;
int[] resDigits = new int[resLength];
resDigits[aNumberLength] = MultiplyByInt(resDigits, aDigits, aNumberLength, Factor);
BigInteger result = new BigInteger(resSign, resLength, resDigits);
result.CutOffLeadingZeroes();
return(result);
}
private static void MonReduction(int[] Result, BigInteger Modulus, int N2)
{
// res + m*modulus_digits
int[] modulus_digits = Modulus.m_digits;
int modulusLen = Modulus.m_numberLength;
long outerCarry = 0;
for (int i = 0; i < modulusLen; i++)
{
long innnerCarry = 0;
int m = (int)Multiplication.UnsignedMultAddAdd(Result[i], N2, 0, 0);
for (int j = 0; j < modulusLen; j++)
{
innnerCarry = Multiplication.UnsignedMultAddAdd(m, modulus_digits[j], Result[i + j], (int)innnerCarry);
Result[i + j] = (int)innnerCarry;
innnerCarry = IntUtils.URShift(innnerCarry, 32);
}
outerCarry += (Result[i + modulusLen] & 0xFFFFFFFFL) + innnerCarry;
Result[i + modulusLen] = (int)outerCarry;
outerCarry = IntUtils.URShift(outerCarry, 32);
}
Result[modulusLen << 1] = (int)outerCarry;
// res / r
for (int j = 0; j < modulusLen + 1; j++)
{
Result[j] = Result[j + modulusLen];
}
}
/// <summary>
/// Adds two numbers, <c>A</c> and <c>B</c>, after shifting <c>B</c> by <c>numElements</c> elements.
/// </summary>
///
/// <param name="A">A number in base 2^32 starting with the lowest digit</param>
/// <param name="B">A number in base 2^32 starting with the lowest digit</param>
/// <param name="NumElements">The shift amount in bits</param>
///
/// <remarks>
/// Both numbers are given as <c>int</c> arrays and must be positive numbers (meaning they are interpreted as unsigned).
/// The result is returned in the first argument. If any elements of B are shifted outside the valid range for <c>A</c>, they are dropped.
/// </remarks>
public static void AddShifted(int[] A, int[] B, int NumElements)
{
bool carry = false;
int i = 0;
while (i < Math.Min(B.Length, A.Length - NumElements))
{
int ai = A[i + NumElements];
int sum = ai + B[i];
if (carry)
{
sum++;
}
carry = (IntUtils.URShift(sum, 31) < IntUtils.URShift(ai, 31) + IntUtils.URShift(B[i], 31)); // carry if signBit(sum) < signBit(a)+signBit(b)
A[i + NumElements] = sum;
i++;
}
while (carry)
{
A[i + NumElements]++;
carry = A[i + NumElements] == 0;
i++;
}
}
private void AddShifted(int[] A, int[] B, int NumElements)
{
// drops elements of b that are shifted outside the valid range
bool carry = false;
int i = 0;
while (i < Math.Min(B.Length, A.Length - NumElements))
{
int ai = A[i + NumElements];
int sum = ai + B[i];
if (carry)
{
sum++;
}
carry = (IntUtils.URShift(sum, 31) < IntUtils.URShift(ai, 31) + IntUtils.URShift(B[i], 31)); // carry if signBit(sum) < signBit(a)+signBit(b)
A[i + NumElements] = sum;
i++;
}
i += NumElements;
while (carry)
{
A[i]++;
carry = A[i] == 0;
i++;
}
}
/// <remarks>
/// Subtracts two positive numbers (meaning they are interpreted as unsigned) that are given as
/// int arrays and returns the result in a new array.
/// </remarks>
private static int[] SubExpand(int[] A, int[] B)
{
int[] c = A.CopyOf(Math.Max(A.Length, B.Length));
bool carry = false;
int i = 0;
while (i < Math.Min(B.Length, A.Length))
{
int diff = A[i] - B[i];
if (carry)
{
diff--;
}
// carry if signBit(diff) > signBit(a)-signBit(b)
carry = (IntUtils.URShift(diff, 31) > IntUtils.URShift(A[i], 31) - IntUtils.URShift(B[i], 31));
c[i] = diff;
i++;
}
while (carry)
{
c[i]--;
carry = c[i] == -1;
i++;
}
return(c);
}
private void SubShifted(int[] A, int[] B, int NumElements)
{
bool carry = false;
int i = 0;
// drops elements of b that are shifted outside the valid range
while (i < Math.Min(B.Length, A.Length - NumElements))
{
int ai = A[i + NumElements];
int diff = ai - B[i];
if (carry)
{
diff--;
}
carry = (IntUtils.URShift(diff, 31) > IntUtils.URShift(A[i], 31) - IntUtils.URShift(B[i], 31)); // carry if signBit(diff) > signBit(a)-signBit(b)
A[i + NumElements] = diff;
i++;
}
i += NumElements;
while (carry)
{
A[i]--;
carry = A[i] == -1;
i++;
}
}
private static long DivideLongByBillion(long N)
{
long quot;
long rem;
if (N >= 0)
{
long bLong = 1000000000L;
quot = (N / bLong);
rem = (N % bLong);
}
else
{
/*
* Make the dividend positive shifting it right by 1 bit then get
* the quotient an remainder and correct them properly
*/
long aPos = IntUtils.URShift(N, 1);
long bPos = IntUtils.URShift(1000000000L, 1);
quot = aPos / bPos;
rem = aPos % bPos;
// double the remainder and add 1 if 'a' is odd
rem = (rem << 1) + (N & 1);
}
return((rem << 32) | (quot & 0xFFFFFFFFL));
}
/// <summary>
/// Reads BitLenB bits from <c>B</c>, starting at array index
/// <c>StartB</c>, and copies them into <c>A</c>, starting at bit
/// <c>BitLenA</c>. The result is returned in <c>A</c>.
/// </summary>
///
/// <param name="A">Array A</param>
/// <param name="BitLenA">Array A bit length</param>
/// <param name="B">Array B</param>
/// <param name="StartB">B starting position</param>
/// <param name="BitLenB">Array B bit length</param>
public static void AppendBits(int[] A, int BitLenA, int[] B, int StartB, int BitLenB)
{
int aIdx = BitLenA / 32;
int bit32 = BitLenA % 32;
for (int i = StartB; i < (StartB + BitLenB) / 32; i++)
{
if (bit32 > 0)
{
A[aIdx] |= B[i] << bit32;
aIdx++;
A[aIdx] = IntUtils.URShift(B[i], (32 - bit32));
}
else
{
A[aIdx] = B[i];
aIdx++;
}
}
if (BitLenB % 32 > 0)
{
int bIdx = BitLenB / 32;
int bi = B[StartB + bIdx];
bi &= IntUtils.URShift(-1, (32 - BitLenB));
A[aIdx] |= bi << bit32;
if (bit32 + (BitLenB % 32) > 32)
{
A[aIdx + 1] = IntUtils.URShift(bi, (32 - bit32));
}
}
}
/// <summary>
/// Rewrite this vector as a vector over <c>GF(2^m)</c> with <c>t</c> elements
/// </summary>
///
/// <param name="Field">The finite field <c>GF(2<sup>m</sup>)</c></param>
///
/// <returns>Returns the converted vector over <c>GF(2<sup>m</sup>)</c></returns>
public GF2mVector ToExtensionFieldVector(GF2mField Field)
{
int m = Field.Degree;
if ((Length % m) != 0)
{
throw new ArithmeticException("GF2Vector: Conversion is impossible!");
}
int t = Length / m;
int[] result = new int[t];
int count = 0;
for (int i = t - 1; i >= 0; i--)
{
for (int j = Field.Degree - 1; j >= 0; j--)
{
int q = IntUtils.URShift(count, 5);
int r = count & 0x1f;
int e = (IntUtils.URShift(m_elements[q], r)) & 1;
if (e == 1)
{
result[i] ^= 1 << j;
}
count++;
}
}
return(new GF2mVector(Field, result));
}
/// <summary>
/// Adds two positive numbers (meaning they are interpreted as unsigned) modulo 2^2^N+1,
/// where N is <c>A.Length*32/2</c>; in other words, n is half the number of bits in <c>A</c>.
/// <para>Both input values are given as <c>int</c> arrays; they must be the same length.
/// The result is returned in the first argument.</para>
/// </summary>
///
/// <param name="A">A number in base 2^32 starting with the lowest digit; the length must be a power of 2</param>
/// <param name="B">A number in base 2^32 starting with the lowest digit; the length must be a power of 2</param>
public static void AddModFn(int[] A, int[] B)
{
bool carry = false;
for (int i = 0; i < A.Length; i++)
{
int sum = A[i] + B[i];
if (carry)
{
sum++;
}
carry = (IntUtils.URShift(sum, 31) < IntUtils.URShift(A[i], 31) + IntUtils.URShift(B[i], 31)); // carry if signBit(sum) < signBit(a)+signBit(b)
A[i] = sum;
}
// take a mod Fn by adding any remaining carry bit to the lowest bit;
// since Fn ≡ 1 (mod 2^n), it suffices to add 1
int j = 0;
while (carry)
{
int sum = A[j] + 1;
A[j] = sum;
carry = sum == 0;
j++;
if (j >= A.Length)
{
j = 0;
}
}
}
/// <summary>
/// Return the resultant of division two polynomials
/// </summary>
///
/// <param name="P">The P polynomial</param>
/// <param name="Q">The Q polynomial</param>
///
/// <returns>The rest value</returns>
public static int Rest(long P, int Q)
{
long p1 = P;
if (Q == 0)
{
return(0);
}
long q1 = Q & 0x00000000ffffffffL;
while ((IntUtils.URShift(p1, 32)) != 0)
{
p1 ^= q1 << (Degree(p1) - Degree(q1));
}
int result = (int)(p1 & 0xffffffff);
while (Degree(result) >= Degree(Q))
{
result ^= Q << (Degree(result) - Degree(Q));
}
return(result);
}
/// <summary>
/// Subtracts two positive numbers (meaning they are interpreted as unsigned) modulo 2^numBits.
/// <para>Both input values are given as <c>int</c> arrays.
/// The result is returned in the first argument.</para>
/// </summary>
///
/// <param name="A">A number in base 2^32 starting with the lowest digit</param>
/// <param name="B">A number in base 2^32 starting with the lowest digit</param>
/// <param name="NumBits">The number of bits to shift</param>
public static void SubModPow2(int[] A, int[] B, int NumBits)
{
int numElements = (NumBits + 31) / 32;
bool carry = false;
int i;
for (i = 0; i < numElements; i++)
{
int diff = A[i] - B[i];
if (carry)
{
diff--;
}
carry = (IntUtils.URShift(diff, 31) > IntUtils.URShift(A[i], 31) - IntUtils.URShift(B[i], 31)); // carry if signBit(diff) > signBit(a)-signBit(b)
A[i] = diff;
}
A[i - 1] &= IntUtils.URShift(-1, 32 - (NumBits % 32));
for (; i < A.Length; i++)
{
A[i] = 0;
}
}
/// <summary>
/// Compute the product of this matrix and a permutation matrix which is generated from an n-permutation
/// </summary>
///
/// <param name="P">The permutation</param>
///
/// <returns>Returns GF2Matrix <c>this*P</c></returns>
public override Matrix RightMultiply(Permutation P)//3
{
int[] pVec = P.GetVector();
if (pVec.Length != ColumnCount)
{
throw new ArithmeticException("GF2Matrix: Length mismatch!");
}
GF2Matrix result = new GF2Matrix(RowCount, ColumnCount);
for (int i = ColumnCount - 1; i >= 0; i--)
{
int q = IntUtils.URShift(i, 5);
int r = i & 0x1f;
int pq = IntUtils.URShift(pVec[i], 5);
int pr = pVec[i] & 0x1f;
for (int j = RowCount - 1; j >= 0; j--)
{
result._matrix[j][q] |= ((IntUtils.URShift(_matrix[j][pq], pr)) & 1) << r;
}
}
return(result);
}
/// <summary>
/// Adds two positive numbers (meaning they are interpreted as unsigned) that are given as
/// int arrays and returns the result in a new array. The result may be one longer
/// than the input due to a carry.
/// </summary>
///
/// <param name="A">A number in base 2^32 starting with the lowest digit</param>
/// <param name="B">A number in base 2^32 starting with the lowest digit</param>
///
/// <returns>The sum</returns>
private static int[] AddExpand(int[] A, int[] B)
{
int[] c = A.CopyOf(Math.Max(A.Length, B.Length));
bool carry = false;
int i = 0;
while (i < Math.Min(B.Length, A.Length))
{
int sum = A[i] + B[i];
if (carry)
{
sum++;
}
carry = (IntUtils.URShift(sum, 31) < IntUtils.URShift(A[i], 31) + IntUtils.URShift(B[i], 31)); // carry if signBit(sum) < signBit(a)+signBit(b)
c[i] = sum;
i++;
}
while (carry)
{
if (i == c.Length)
{
c = c.CopyOf(c.Length + 1);
}
c[i]++;
carry = c[i] == 0;
i++;
}
return(c);
}
/// <summary>
/// Returns the last <c>NumBits</c> bits from the end of the bit string
/// </summary>
///
/// <param name="NumBits">Number of bits to return</param>
///
/// <returns>A new <c>BitString</c> of length <c>numBits</c></returns>
public BitString GetTrailing(int NumBits)
{
BitString newStr = new BitString();
newStr._numBytes = (NumBits + 7) / 8;
newStr.Bytes = new byte[newStr._numBytes];
for (int i = 0; i < newStr._numBytes; i++)
{
newStr.Bytes[i] = Bytes[i];
}
newStr._lastByteBits = NumBits % 8;
if (newStr._lastByteBits == 0)
{
newStr._lastByteBits = 8;
}
else
{
int s = 32 - newStr._lastByteBits;
newStr.Bytes[newStr._numBytes - 1] = (byte)(IntUtils.URShift((newStr.Bytes[newStr._numBytes - 1] << s), s));
}
return(newStr);
}
/// <summary>
/// Adds two positive numbers (meaning they are interpreted as unsigned) modulo 2^numBits.
/// Both input values are given as int arrays. The result is returned in the first argument.
/// </summary>
/// <param name="A">A number in base 2^32 starting with the lowest digit</param>
/// <param name="B">A number in base 2^32 starting with the lowest digit</param>
/// <param name="NumBits">The modulo bit size</param>
private static void AddModPow2(int[] A, int[] B, int NumBits)
{
int numElements = (NumBits + 31) / 32;
bool carry = false;
int i;
for (i = 0; i < numElements; i++)
{
int sum = A[i] + B[i];
if (carry)
{
sum++;
}
// carry if signBit(sum) < signBit(a)+signBit(b)
carry = (IntUtils.URShift(sum, 31) < IntUtils.URShift(A[i], 31) + IntUtils.URShift(B[i], 31));
A[i] = sum;
}
A[i - 1] &= IntUtils.URShift(-1, 32 - (NumBits % 32));
for (; i < A.Length; i++)
{
A[i] = 0;
}
}
private static String PolyToString(int P)
{
String str = "";
if (P == 0)
{
str = "0";
}
else
{
byte b = (byte)(P & 0x01);
if (b == 1)
{
str = "1";
}
P = IntUtils.URShift(P, 1);
int i = 1;
while (P != 0)
{
b = (byte)(P & 0x01);
if (b == 1)
{
str = str + "+x^" + i;
}
P = IntUtils.URShift(P, 1);
i++;
}
}
return(str);
}
void rearrange(int[] a_0, int[] a_1)
{
int i;
int bit1, bit2, bit3, bit4, bit5, bit6, bit7;
int swp_index;
int u1, u2;
for (i = 0; i < Globals.M / 2; i++)
{
bit1 = i % 2;
bit2 = IntUtils.URShift(i, 1) % 2;
bit3 = IntUtils.URShift(i, 2) % 2;
bit4 = IntUtils.URShift(i, 3) % 2;
bit5 = IntUtils.URShift(i, 4) % 2;
bit6 = IntUtils.URShift(i, 5) % 2;
bit7 = IntUtils.URShift(i, 6) % 2;
swp_index = bit1 * 64 + bit2 * 32 + bit3 * 16 + bit4 * 8 + bit5 * 4 + bit6 * 2 + bit7;
if (swp_index > i)
{
u1 = a_0[i];
u2 = a_1[i];
a_0[i] = a_0[swp_index];
a_1[i] = a_1[swp_index];
a_0[swp_index] = u1;
a_1[swp_index] = u2;
}
}
}