public void Set(BigNum bigNum)
{
m1MSBLocation = bigNum.m1MSBLocation;
//mBinaryNumber = bigNum.mBinaryNumber;
for (int i = 0; i < GlobalVariables.MAX_NUM; ++i)
{
mBinaryNumber[i] = bigNum.mBinaryNumber[i];
}
}
/// <summary>
/// I.
/// Gets BigNum type and substract between the current value of the binary number with the given one.
/// Let do substraction A = A-B. We know that A-B = A + (-B).
/// Calculating -B: Doing complement and then add 1.
/// </summary>
/// <param name="numberToSubtract"></param>
public void SubNum(BigNum numberToSubtract)
{
// numberToSubstract = B.
BigNum modifiedNumberToSubtract = new BigNum(numberToSubtract);
modifiedNumberToSubtract.Complement(); // numberToSubtract = -B - 1.
modifiedNumberToSubtract.AddNum(GlobalVariables.one); // numberToSubtract = -B.
AddNum(modifiedNumberToSubtract); // Allready updates <mMSB1Location>.
UpdateMSB1Location();
}
public static void PrintNumberInPowersOfTwo(BigNum num)
{
List <int> positionsOf1s = num.WriteNum1sPosition();
for (int i = 0; i < positionsOf1s.Count - 1; ++i)
{
Console.Write($"2^{GlobalVariables.MAX_NUM - positionsOf1s[i] - 1} + ");
}
Console.WriteLine($"2^{GlobalVariables.MAX_NUM - positionsOf1s[positionsOf1s.Count - 1] - 1}");
}
public static void F()
{
Console.WriteLine("(F) Using ShiftLeft method.");
Console.WriteLine("Multiply 25 by 2.");
BigNum bigNumF = new BigNum(25L);
bigNumF.ShiftLeft();
Console.WriteLine(bigNumF.WriteNum());
Console.WriteLine();
}
public BigNum(BigNum bigNum)
{
mBinaryNumber = new int[GlobalVariables.MAX_NUM];
for (int i = 0; i < GlobalVariables.MAX_NUM; ++i)
{
mBinaryNumber[i] = bigNum.mBinaryNumber[i];
}
m1MSBLocation = bigNum.m1MSBLocation;
}
public static void E()
{
Console.WriteLine("(E) Using AddNum method.");
Console.WriteLine("8 + 13 = 21.");
BigNum bigNumE1 = new BigNum(8L);
BigNum bigNumE2 = new BigNum(13L);
bigNumE1.AddNum(bigNumE2);
Console.WriteLine(bigNumE1.WriteNum());
Console.WriteLine();
}
public static void MSB1LocationTest()
{
Console.WriteLine("Creating new BigNum type number.");
BigNum bigNum = new BigNum();
for (int i = 0; i < GlobalVariables.MAX_NUM; ++i)
{
Console.Write(bigNum[i]);
}
Console.WriteLine($"The first 1' digit is in position: {bigNum.MSB1Location}");
Console.WriteLine();
}
public static void C()
{
Console.WriteLine("(C) Using LongToBig method.");
Console.WriteLine("Creating number with long 35.");
BigNum bigNumC1 = new BigNum(35L);
Console.WriteLine(bigNumC1.WriteNum());
Console.WriteLine("Creating number with long 9223372036854775807 (max value of long).");
BigNum bigNumC2 = new BigNum(9223372036854775807L);
Console.WriteLine(bigNumC2.WriteNum());
Console.WriteLine();
}
public static void IIA()
{
Console.WriteLine("I.");
Console.WriteLine("Calculating 1233456897 ^ 8001 mod 1783369431");
BigNum num = new BigNum(1233456897);
BigNum power = new BigNum(8001);
BigNum mod = new BigNum(1783369431);
BigNum result = new BigNum();
result = MathOps.Power(num, power, mod);
Console.WriteLine(result.DecimalValue);
Console.WriteLine();
}
public static void J()
{
Console.WriteLine("(I) Using DivNum method.");
Console.WriteLine("257 / 13 ==> result = 19, reminder 10.");
BigNum divided = new BigNum(257L);
BigNum divider = new BigNum(13L);
BigNum quitient = new BigNum();
BigNum reminder = new BigNum();
MathOps.DivNum(divided, divider, quitient, reminder);
Console.WriteLine($"Quitient is: {quitient.WriteNum()}, Reminder is: {reminder.WriteNum()}.");
Console.WriteLine();
}
/// <summary>
/// L.
/// Gets two BigNums, calculates the opposite number of a in mod m. ([a^-1][mod m]).
/// Returns null if the a does not have an inverse mode m. (i.e: gcd(a, m) != 1).
/// </summary>
/// <param name="a"></param>
/// <param name="m"></param>
public static BigNum Inverse(BigNum a, BigNum m)
{
BigNum inverse = null;
BigNum x = new BigNum();
BigNum y = new BigNum();
BigNum d = new BigNum(); // d will be gcd(a, m).
ExtendedGCD(a, m, x, y, d);
if (d.CompNumWithoutPrint(GlobalVariables.one))
{
inverse = y;
}
return(inverse);
}
private bool IsBigNumFitsIntoLongType(BigNum num)
{
bool isBigNumFitsIntoLongType;
if (m1MSBLocation.HasValue)
{
isBigNumFitsIntoLongType =
(GlobalVariables.MAX_NUM - num.m1MSBLocation.Value <= GlobalVariables.MaxNumberOfDigitsInLongType);
}
else // It means that num is zero.
{
isBigNumFitsIntoLongType = true;
}
return(isBigNumFitsIntoLongType);
}
/// <summary>
/// G.
/// Every number can be represented as 2N or 2N+1, when N is even and natural number.
/// Converts <numberToMult> into long and into representation of 2N or 2N+1.
/// Then doing N times ShiftLeft() method, If the number is 2N+1, adding one time the initial value
/// of this instance.
/// Or
/// Let the current value of this intance be <value>.
/// If <numberToMult[i]> == 0 then mult by 2 (ShiftLeft() method).
/// If <numberToMult[i]> == 1 then mult by 2 (ShiftLeft() method) and adds <value>.
/// </summary>
/// <param name="numberToMult"></param>
public void MultNum(BigNum numberToMult)
{
BigNum valueToAdd = new BigNum(this);
InitializeToZero();
for (int i = GlobalVariables.MAX_NUM - 1; i >= numberToMult.m1MSBLocation; --i)
{
if (numberToMult[i] == 1)
{
AddNum(valueToAdd);
}
valueToAdd.ShiftLeft();
}
UpdateMSB1Location();
}
/// <summary>
/// Gets a number m.
/// Finds p >= 0 and k (k is odd), where m = 2^p * k.
/// Return p and k by ref.
///
/// p = 0;
/// if (!IsEven(m))
/// {
/// k = m;
/// }
/// else // m is even.
/// {
/// while(IsEven(m))
/// {
/// m /= 2;
/// p++;
/// }
/// k = m;
/// }
/// </summary>
/// <param name=""></param>
/// <param name=""></param>
public static void FindExpressionOfGivenNumberByPowerOfTwoTimesOddNumber(BigNum m, BigNum p, BigNum k)
{
if (!m.IsEven())
{
k.Set(m);
}
else
{
while (m.IsEven())
{
DivNum(m, GlobalVariables.two, m, new BigNum());
p.AddNum(GlobalVariables.one);
}
k.Set(m);
}
}
public static void N()
{
Console.WriteLine("(N) Using IsPrime method.");
Console.WriteLine("Checking if 7, 513, 9973, 2147483647. We should get: true, false, true, true.");
BigNum n1 = new BigNum(7);
BigNum n2 = new BigNum(513);
BigNum n3 = new BigNum(9973);
BigNum eightMarsenNumber = new BigNum(2147483647);
int k = 20;
Console.WriteLine(MathOps.IsPrime(n1, k).ToString());
Console.WriteLine(MathOps.IsPrime(n2, k).ToString());
Console.WriteLine(MathOps.IsPrime(n3, k).ToString());
Console.WriteLine(MathOps.IsPrime(eightMarsenNumber, k).ToString());
Console.WriteLine();
}
/// <summary>
/// K.
/// Gets two BigNum type numbers a and m and returns by reference (d, x, y), also BigNum type numbers.
/// d represents GCD(m,a). (Greatest common divider).
/// Note: If d = 1, it means that x is the opposite number of m(mod a) and
/// y is the opposite number of a(mod m).
/// Proofe for Note: 1 = [m*x + a*y](mod m) ==> 1 = a*y.
/// </summary>
/// <param name="a"></param>
/// <param name="m"></param>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="d"></param>
public static void ExtendedGCD(BigNum a, BigNum m, BigNum x, BigNum y, BigNum d)
{
BigNum r0 = new BigNum(m);
BigNum x0 = new BigNum(GlobalVariables.one);
BigNum y0 = new BigNum(GlobalVariables.zero);
BigNum r1 = new BigNum(a);
BigNum x1 = new BigNum(GlobalVariables.zero);
BigNum y1 = new BigNum(GlobalVariables.one);
BigNum r = new BigNum(GlobalVariables.one); // Just to be able to enter the while loop.
BigNum q = new BigNum();
DivNum(r0, r1, q, r);
while (!r.CompNumWithoutPrint(GlobalVariables.zero))
{
// x = x0 - qx1.
BigNum qx1 = new BigNum(q);
qx1.MultNum(x1);
x.Set(x0);
x.SubNum(qx1);
// y = y0 - qy1.
BigNum qy1 = new BigNum(q);
qy1.MultNum(y1);
y.Set(y0);
y.SubNum(qy1);
r0.Set(r1);
x0.Set(x1);
y0.Set(y1);
r1.Set(r);
x1.Set(x);
y1.Set(y);
DivNum(r0, r1, q, r);
}
d.Set(r1);
x.Set(x1);
y.Set(y1);
}
/// <summary>
/// E.
/// Gets BigNum type and adds it into this instance.
/// Uses <carry> of type BigNum to implement the binary adding.
/// Let do summing B = A + B when a[i] is the i'th digit of A. C is the carry.
/// If a[i] + c[i] == 0, b[i] does not changes.
/// If a[i] + c[i] == 1, b[i] changes it's value and c[i-1] gets 1.
/// If a[i] + c[i] == 2, b[i] does not changes and c[i-1] gets 1.
/// </summary>
/// <param name="numberToAdd"></param>
public void AddNum(BigNum numberToAdd)
{
BigNum carry = new BigNum(); // <carry> = 00..0.
for (int i = GlobalVariables.MAX_NUM - 1; i > 0; --i)
{
if (numberToAdd[i] + carry[i] == 1)
{
if (mBinaryNumber[i] == 0)
{
mBinaryNumber[i] = 1;
}
else
{
mBinaryNumber[i] = 0;
carry[i - 1] = 1;
}
}
else if (numberToAdd[i] + carry[i] == 2)
{
carry[i - 1] = 1;
}
}
// Handles i == 0.
if (numberToAdd[0] + carry[0] == 1)
{
if (mBinaryNumber[0] == 0)
{
mBinaryNumber[0] = 1;
}
else
{
mBinaryNumber[0] = 0;
// Console.WriteLine("There is an overflow. Carry 1 is dropped.");
}
}
else if (numberToAdd[0] + carry[0] == 2)
{
// Console.WriteLine("There is an overflow. Carry 1 is dropped.");
}
UpdateMSB1Location();
}
public static void G()
{
Console.WriteLine("(G) Using MultNum method.");
Console.WriteLine("Multiply 7 by 3. Equals 21 (10101 in base 2)");
BigNum bigNumG1 = new BigNum(7L);
BigNum bigNumG2 = new BigNum(3L);
bigNumG1.MultNum(bigNumG2);
Console.WriteLine(bigNumG1.WriteNum());
Console.WriteLine("Multiply 113 by 73. Equals 8249 (10000000111001 in base 2)");
BigNum bigNumG3 = new BigNum(113L);
BigNum bigNumG4 = new BigNum(73L);
bigNumG3.MultNum(bigNumG4);
Console.WriteLine(bigNumG3.WriteNum());
Console.WriteLine();
}
/// <summary>
/// Gets BigNum type number and an index.
/// Returns the sub number if the number by the index.
/// Example: number = 0..001101101 (length of 400 bits), index = 398.
/// The returned number will be 0..000110110.
/// </summary>
/// <param name="divided"></param>
/// <param name="indexPos"></param>
/// <returns></returns>
public static BigNum GetSubBigNumFromLeftToIndex(BigNum divided, int indexPos)
{
BigNum bigNumFromLeftToIndex = new BigNum();
List <int> positionsOf1s = new List <int>();
int initialIndexPos = indexPos;
while (indexPos >= divided.MSB1Location)
{
if (divided[indexPos] == 1)
{
positionsOf1s.Add(GlobalVariables.MAX_NUM - (initialIndexPos - indexPos) - 1);
}
indexPos--;
}
bigNumFromLeftToIndex.ReadNum(positionsOf1s);
return(bigNumFromLeftToIndex);
}
public static void I()
{
Console.WriteLine("(I) Using SubNum method.");
Console.WriteLine("18 - 5 = 13");
BigNum bigNumI1 = new BigNum(18L);
BigNum bigNumI2 = new BigNum(5L);
bigNumI1.SubNum(bigNumI2);
Console.WriteLine(bigNumI1.WriteNum());
Console.WriteLine("375683 - 12345 = 363338 (1011000101101001010 in binary.)");
BigNum bigNumI3 = new BigNum(375683L);
BigNum bigNumI4 = new BigNum(12345L);
bigNumI3.SubNum(bigNumI4);
Console.WriteLine(bigNumI3.WriteNum());
Console.WriteLine();
}
public static void M()
{
Console.WriteLine("(M) Using Power method.");
Console.WriteLine("Calculating 30^14 mod 7 = 4.");
BigNum x = new BigNum(30);
BigNum power = new BigNum(14);
BigNum mod = new BigNum(7);
Console.WriteLine(MathOps.Power(x, power, mod).DecimalValue);
Console.WriteLine("Calculating 130^27 mod 41 = 24.");
BigNum x2 = new BigNum(130);
BigNum power2 = new BigNum(27);
BigNum mod2 = new BigNum(41);
Console.WriteLine(MathOps.Power(x2, power2, mod2).DecimalValue);
Console.WriteLine();
}
/// <summary>
/// H.
/// Gets another BigNum type number and compare between the two.
/// </summary>
/// <returns></returns>
public bool CompNum(BigNum numberToCompare)
{
bool isEqual = true;
bool isFinishCompare = false;
if ((!m1MSBLocation.HasValue) && (!numberToCompare.m1MSBLocation.HasValue))
{
// That means that they both equal to zero.
isFinishCompare = true;
}
else if (((m1MSBLocation.HasValue) && (!numberToCompare.m1MSBLocation.HasValue)) ||
((!m1MSBLocation.HasValue) && (numberToCompare.m1MSBLocation.HasValue)))
{
// That means that one is zero and other is not.
isEqual = false;
isFinishCompare = true;
}
if (!isFinishCompare)
{
for (int i = m1MSBLocation.Value; i < GlobalVariables.MAX_NUM; ++i)
{
if (mBinaryNumber[i] != numberToCompare.mBinaryNumber[i])
{
isEqual = false;
break;
}
}
}
if (isEqual)
{
Console.WriteLine("The numbers are equal.");
}
else
{
Console.WriteLine("The numbers are NOT equal.");
}
return(isEqual);
}
/// <summary>
/// N.
/// Runs Miller-Rabin algorithm k times.
/// </summary>
/// <param name="n"></param>
/// <param name="k"></param>
/// <returns></returns>
public static bool IsPrime(BigNum n, int k)
{
bool isPrimeNumber = true;
BigNum t = new BigNum();
BigNum u = new BigNum();
BigNum nMinusOne = new BigNum(n);
nMinusOne.SubNum(GlobalVariables.one);
FindExpressionOfGivenNumberByPowerOfTwoTimesOddNumber(nMinusOne, t, u);
for (int i = 0; i < k; ++i)
{
if (!MillerRabinAlgorithm(n, new BigNum(t), u))
{
isPrimeNumber = false;
break;
}
}
return(isPrimeNumber);
}
public static void A()
{
Console.WriteLine("(A) Using ReadNum methods.");
Console.WriteLine("1. reading 0101");
BigNum bigNum1a = new BigNum();
bigNum1a.ReadNum("0101");
Console.WriteLine(bigNum1a.WriteNum());
Console.WriteLine($"The first 1' digit is in position: {bigNum1a.MSB1Location}");
Console.WriteLine("2. reading positions of 1s. Getting a the list {399, 385}.");
BigNum bigNum2a = new BigNum();
bigNum2a.ReadNum(new List <int> {
399, 385
});
Console.WriteLine(bigNum2a.WriteNum());
Console.WriteLine($"The first 1' digit is in position: {bigNum2a.MSB1Location}");
Console.WriteLine();
}
public static void L()
{
Console.WriteLine("(L) Using Inverse method.");
BigNum bigNum1 = new BigNum(26);
BigNum bigNum2 = new BigNum(21);
Console.WriteLine("Calculates the opposite number of 26 mod 21:");
Console.WriteLine(MathOps.Inverse(bigNum1, bigNum2).DecimalValue);
Console.WriteLine("Calculates the opposite number of 21 mod 26:");
Console.WriteLine(MathOps.Inverse(bigNum2, bigNum1).DecimalValue);
BigNum bigNum3 = new BigNum(15);
BigNum bigNum4 = new BigNum(10);
Console.WriteLine("Calculates the opposite number of 15 mod 10:");
if (MathOps.Inverse(bigNum3, bigNum4) == null)
{
Console.WriteLine("There is no opposite for 15");
}
Console.WriteLine();
}
/// <summary>
/// Gets BigNum number.
/// Finds the index of the MSB 1 digit, run from it to the LSB.
/// It has boolean variable <isSmaller> that set to true when the first 1's digits is cleared
/// (set to 0).
/// Unless <isSmaller> = true, this method cannot set any bit.
/// Use random (IsGeneratedToSet() method) to set or clear that bit.
/// </summary>
/// <param name="top"></param>
/// <returns></returns>
private static BigNum GenerateNumberFromOneToGivenTop(BigNum top)
{
BigNum generatedNumber = new BigNum();
if (top.MSB1Location.HasValue)
{
do
{
bool isSmaller = false;
List <int> PositionsOf1sList = new List <int>();
for (int i = top.MSB1Location.Value; i < GlobalVariables.MAX_NUM; ++i)
{
if (top[i] == 1)
{
if (GenerateOneOrZero() == 0)
{
isSmaller = true;
}
else
{
PositionsOf1sList.Add(i);
}
}
else
{
if ((GenerateOneOrZero() == 1) && (isSmaller))
{
PositionsOf1sList.Add(i);
}
}
}
generatedNumber.ReadNum(PositionsOf1sList);
} while ((generatedNumber.CompNumWithoutPrint(GlobalVariables.zero)) ||
(generatedNumber.CompNumWithoutPrint(top)));
}
return(generatedNumber);
}
public static void D()
{
Console.WriteLine("(D) Using BigToLong method.");
BigNum bigNumC1 = new BigNum(35L);
long? num1 = bigNumC1.BigToLong();
Console.WriteLine(num1);
BigNum bigNumC2 = new BigNum(9223372036854775807L);
long? num2 = bigNumC2.BigToLong();
Console.WriteLine(num2);
BigNum bigNumD = new BigNum();
bigNumD.Complement();
long?num3 = bigNumD.BigToLong();
Console.WriteLine(num3);
Console.WriteLine();
}
/// <summary>
/// O.
/// Generates random prime number in the length of MAX_NUN/4.
/// </summary>
public static BigNum GenPrime()
{
BigNum randomPrimeNumber = new BigNum();
BigNum top = new BigNum();
int k = 20;
int tryNumber = 1;
List <int> positionsOf1s = new List <int>();
for (int i = 392; i < GlobalVariables.MAX_NUM; ++i) // TODO change back.
{
positionsOf1s.Add(i);
}
top.ReadNum(positionsOf1s);
Console.WriteLine("Generating random prime number...");
do
{
Console.WriteLine($"try number: {tryNumber++}");
randomPrimeNumber = GenerateNumberFromOneToGivenTop(top);
} while (!IsPrime(randomPrimeNumber, k));
return(randomPrimeNumber);
}
/// <summary>
/// J.
/// Gets two BigNum type numbers, divided and divider.
/// Returns by reference the result - quotient and reminder.
/// </summary>
/// <param name="divider"></param>
public static void DivNum(BigNum divided, BigNum divider, BigNum quotientRetrunByRef, BigNum reminderReturnByRef)
{
List <int> positionsOf1s = new List <int>();
if (divided.MSB1Location.HasValue)
{
int indexPos = divided.MSB1Location.Value + divider.Length - 1;
BigNum subResult = new BigNum(divided);
while (indexPos < GlobalVariables.MAX_NUM)
{
BigNum numberFromLeftToIndex = GetSubBigNumFromLeftToIndex(subResult, indexPos);
if (numberFromLeftToIndex >= divider)
{
// Saving quotient's info.
positionsOf1s.Add(indexPos);
// Subtract.
int numberOfShifts = GlobalVariables.MAX_NUM - indexPos - 1;
BigNum numberToSubtract = new BigNum(divider);
numberToSubtract.ShiftLeft(numberOfShifts);
subResult.SubNum(numberToSubtract);
}
indexPos++;
}
quotientRetrunByRef.ReadNum(positionsOf1s);
reminderReturnByRef.Set(subResult);
}
else
{
Console.WriteLine("Cannot divide by zero");
}
}
public static void K()
{
Console.WriteLine("(K) Using ExtendedGCD method.");
Console.WriteLine("Calculates GCD(26, 21). Should be = 1");
BigNum bigNum3 = new BigNum(26);
BigNum bigNum4 = new BigNum(21);
BigNum x = new BigNum();
BigNum y = new BigNum();
BigNum gcd = new BigNum();
MathOps.ExtendedGCD(bigNum4, bigNum3, x, y, gcd);
Console.WriteLine($"GCD = {gcd.WriteNum()} = {bigNum3.DecimalValue}*{x.DecimalValue}" +
$" + {bigNum4.DecimalValue}*{y.DecimalValue}");
Console.WriteLine("Calculates GCD(15, 10). Should be = 5");
BigNum bigNum1 = new BigNum(15);
BigNum bigNum2 = new BigNum(10);
MathOps.ExtendedGCD(bigNum2, bigNum1, x, y, gcd);
Console.WriteLine($"GCD = {gcd.DecimalValue} = {bigNum1.DecimalValue}*{x.DecimalValue}" +
$" + {bigNum2.DecimalValue}*{y.DecimalValue}");
Console.WriteLine();
}
