static public bigInt operator %(bigInt x, bigInt n)
{
if (n.equalToZero())
{
throw new ArithmeticException("Cannot module by zero!");
}
else
{
x = standardize(x);
n = standardize(n);
bigInt one = new bigInt("1");
bigInt zero = new bigInt("0");
if (x == n)
{
return(zero);
}
else
{
bigInt a, b, c;
bigInt i = one;
while (x > n || x == n)
{
if (n._length > x._length / 2)
{
x = x - n;
}
else
{
int q = n._length;
String temp = "";
for (int j = 0; j < n._length; j++)
{
temp += ('1' - n._bits[j]);
}
c = new bigInt(temp);
c = c + one;
b = x >> q;
a = new bigInt(x._bits.Substring(x._length - q));
bigInt bvalue = b;
while (i < c)
{
b = b + bvalue;
i = i + one;
}
if (b.equalToZero())
{
x = x - n;
}
else
{
x = a + b;
}
i = one;
}
}
}
return(x);
}
}
static bigInt GCD(bigInt a, bigInt b)
{
if (a.equalToZero() || b.equalToZero())
{
return(a + b);
}
string bits = "1";
bigInt gcd = new bigInt(bits);
while (a._bits[a._length - 1] == '0' && b._bits[b._length - 1] == '0')
{
a = a >> 1;
b = b >> 1;
gcd = gcd << 1;
}
while (!a.equalToZero())
{
while (a._bits[a._length - 1] == '0')
{
a = a >> 1;
}
while (b._bits[b._length - 1] == '0')
{
b = b >> 1;
}
bigInt t;
if (a > b)
{
t = a - b;
}
else
{
t = b - a;
}
t = t >> 1;
if (a > b || a == b)
{
a = t;
}
else
{
b = t;
}
}
if (a._length > b._length)
{
gcd = gcd >> b._length;
}
else
{
gcd = gcd >> a._length;
}
gcd = bigInt.standardize(gcd);
return(gcd);
}
// operator minus two big integer
static public bigInt operator -(bigInt a, bigInt b)
{
a = standardize(a);
b = standardize(b);
if (a == b)
{
return(new bigInt());
}
else if (a < b)
{
throw new ArithmeticException("First parameter must equal or bigger than second parameter");
}
else
{
int mem = 0, flag = 1;
String aRev, bRev;
if (a._bits.Length >= b._bits.Length)
{
flag = 0;
}
if (flag == 0)
{
aRev = Program.reverseString(a._bits);
bRev = Program.reverseString(b._bits);
}
else
{
bRev = Program.reverseString(a._bits);
aRev = Program.reverseString(b._bits);
}
String sum = "";
// Make bRev have the same length as aRev
bRev = bRev.PadRight(aRev.Length, '0');
// OR every bits of aRev, bRev and mem
for (int i = 0; i < aRev.Length; i++)
{
int temp = (aRev[i] - 48) - (bRev[i] - 48) + mem;
if (temp < 0)
{
temp += 2;
mem = -1;
}
else
{
mem = 0;
}
sum += (temp % 2).ToString();
}
bigInt s = new bigInt(Program.reverseString(sum));
return(s);
}
}
static int countTrueBits(bigInt n)
{
int count = 0;
for (int i = 0; i < n._length; i++)
{
if (n._bits[i] == '1')
{
count++;
}
}
return(count);
}
static bigInt subMod(bigInt a, bigInt b, bigInt n)
{
a = a % n;
b = b % n;
// a, b thuoc Zn
if (a < b)
{
return(a - b + n);
}
else
{
return(a - n);
}
}
static bigInt addMod(bigInt a, bigInt b, bigInt n)
{
a = a % n;
b = b % n;
// a, b thuoc Zn
if (a + b < n)
{
return(a + b);
}
else
{
return(a + b - n);
}
}
// Return the Decimal value of the bigInt (use for bigInt <= 32 bits)
static int value(bigInt num)
{
if (num._length > 32)
{
throw new ArithmeticException("The number size is bigger than 32 bits!");
}
int v = 0;
String temp = Program.reverseString(num._bits);
for (int i = 0; i < temp.Length; i++)
{
v += ((temp[i] - 48) * (int)Math.Pow(2, i));
}
return(v);
}
static public bigInt operator >>(bigInt a, int n)
{
bigInt result;
String bits = "";
if (n < a._length)
{
bits = a._bits.Substring(0, a._length - n);
bits = bits.PadLeft(a._length, '0');
result = new bigInt(bits);
}
else
{
result = new bigInt(bits.Length);
}
return(result);
}
static public bigInt operator <<(bigInt a, int n)
{
String bits = "";
if (a._bits.IndexOf('1') < n)
{
bits = a._bits.Substring(a._bits.IndexOf('1'));
bits = bits.PadRight(bits.Length + n - a._bits.IndexOf('1'), '0');
}
else
{
bits = a._bits.Substring(n);
bits = bits.PadRight(bits.Length + n, '0');
}
bigInt result = new bigInt(bits);
return(result);
}
// Behaviors
// operator plus two big integer
static public bigInt operator +(bigInt a, bigInt b)
{
a = standardize(a);
b = standardize(b);
int mem = 0, flag = 1;
String aRev, bRev;
if (a._bits.Length >= b._bits.Length)
{
flag = 0;
}
if (flag == 0)
{
aRev = Program.reverseString(a._bits);
bRev = Program.reverseString(b._bits);
}
else
{
bRev = Program.reverseString(a._bits);
aRev = Program.reverseString(b._bits);
}
String sum = "";
// Make bRev have the same length as aRev
bRev = bRev.PadRight(aRev.Length, '0');
// OR every bits of aRev, bRev and mem
for (int i = 0; i < aRev.Length; i++)
{
sum += ((aRev[i] - 48 + bRev[i] - 48 + mem) % 2).ToString();
if (aRev[i] - 48 + bRev[i] - 48 + mem < 2)
{
mem = 0;
}
else
{
mem = 1;
}
}
sum += mem.ToString();
bigInt s = new bigInt(Program.reverseString(sum));
return(s);
}
static bigInt mulMod(bigInt a, bigInt b, bigInt n)
{
bigInt result = new bigInt("0");
a = a % n;
b = b % n;
// a, b thuoc Zn
if (b._bits[b._length - 1] == '1')
{
result = a;
}
for (int i = 1; i < b._length; i++)
{
a = addMod(a, a, n);
if (b._bits[b._length - 1 - i] == '1')
{
result = addMod(result, a, n);
}
}
return(result);
}
static public bigInt standardize(bigInt a)
{
bigInt zero = new bigInt("0");
if (a._bits.IndexOf('1') != 0)
{
if (a._bits.IndexOf('1') != -1)
{
String bits = a._bits.Substring(a._bits.IndexOf('1'));
bigInt result = new bigInt(bits);
return(result);
}
else
{
return(zero);
}
}
else
{
return(a);
}
}
static bigInt powerMod(bigInt x, bigInt p, bigInt n)
{
//Return: result = (x ^ p) % n
x = x % n;
String bits = "1";
bigInt result = new bigInt(bits);
// if (p == 0) return 1;
if (p.equalToZero())
{
return(result);
}
else
{
//Cach 1:
//bigInt a = new bigInt(x._bits);
//if (p._bits[p._length - 1] == '1') result = x;
//for (int i = 1; i < p._length; i++)
//{
// a = mulMod(a, a, n);
// if (p._bits[p._length - 1 - i] == '1') result = mulMod(result, a, n);
//}
//Cach 2
for (int i = 0; i < p._length; i++)
{
result = mulMod(result, result, n);
if (p._bits[i] == '1')
{
result = mulMod(result, x, n);
}
}
}
result = bigInt.standardize(result);
return(result);
}
static void Main(string[] args)
{
Console.WriteLine("Du lieu lan luot cho x, y, p, n phai thoa dieu kien gia tri x, y < n va p tuy y!");
Console.WriteLine("Neu khong thoa dieu kien tren qua trinh tinh toan se xay ra kha lau khi gap so lon!");
Console.WriteLine("Lua chon cac cach tao du lieu:");
Console.WriteLine("1. Lay du lieu tu file data.txt (moi dong tuong ung voi chuoi bit cua lan luot cac so: x, y, p, n).");
Console.WriteLine("2. Tao du lieu ngau nhien cho tung so.");
Console.Write("Nhap lua chon (1 hoac 2): ");
int select = -1;
select = Console.ReadKey().KeyChar;
while (select != '1' && select != '2')
{
Console.Write("\nLua chon khong hop le! Vui long nhap lai: ");
select = Console.ReadKey().KeyChar;
}
String str1 = "";
String str2 = "";
String str3 = "";
String str4 = "";
Console.WriteLine();
if (select == '1')
{
//đọc dữ liệu từ file data.txt, các số x, y, p, n lần lượt là các dòng trong file data.txt
string filePath = @"data.txt";
string[] lines = ReadAllLines(filePath);
if (lines == null)
{
Console.ReadKey();
return;
}
int lineNum = 0;
str1 = lines[lineNum];
str2 = lines[lineNum + 1];
str3 = lines[lineNum + 2];
str4 = lines[lineNum + 3];
}
if (select == '2')
{
// bigIntGen(int n) là hàm tạo ra số nguyên ngẫu nhiên n bit
Console.WriteLine("Nhap do dai chuoi nhi phan cua tung so: ");
Console.Write("x.Length = ");
int len = ReadInt();
if (len != -1)
{
str1 = new String(bigIntGen(len));
}
Console.Write("y.Length = ");
len = ReadInt();
if (len != -1)
{
str2 = new String(bigIntGen(len));
}
Console.Write("p.Length = ");
len = ReadInt();
if (len != -1)
{
str3 = new String(bigIntGen(len));
}
Console.Write("n.Length = ");
len = ReadInt();
if (len != -1)
{
str4 = new String(bigIntGen(len));
}
}
bigInt x = new bigInt(str1);
bigInt y = new bigInt(str2);
bigInt p = new bigInt(str3);
bigInt n = new bigInt(str4);
Console.WriteLine($"x = {x._bits}"); // x thuoc Zn
Console.WriteLine($"y = {y._bits}"); // y thuoc Zn
Console.WriteLine($"p = {p._bits}");
Console.WriteLine($"n = {n._bits}");
Console.WriteLine($"gcd (x, y) = {GCD(x, y)._bits}");
Console.WriteLine($"x * y (mod n) = {mulMod(x, y, n)._bits}");
Console.WriteLine($"x ^ p (mod n) = {powerMod(x, p, n)._bits}");
Console.WriteLine("Done!");
Console.ReadKey(true);
}