// complixty of fun add ( O(res.arr.length) + O(total.arr.length) + O(Str1.length ) +O(Str2.length ) + O(1) + O(1)
// in exact case all = N
// total complixty = 4N = O(N)
public static Big_int sub(Big_int fir_num, Big_int sec_num, ref Big_int res)
{
Big_int comp = new Big_int(fir_num.arr.Length); //O(1)
int diff = fir_num.arr.Length - sec_num.arr.Length; //O(1)
for (int i = diff; i < fir_num.arr.Length; i++) //O(fir_num.arr.Length)=O(N)
{
comp.arr[i] = 9 - sec_num.arr[i - diff]; //O(1)
}
for (int i = 0; i < diff; i++) //O(diff) < O(N)
{
comp.arr[i] = 9; //O(1)
}
Big_int one = new Big_int(1); //O(1)
one.arr[0] = 1; //O(1)
ADD(comp, one, ref comp); //O(N)
comp = remove_zeros(comp); //O(N)
ADD(fir_num, comp, ref comp); //O(N)
comp = remove_zeros(comp); //O(N)
res = new Big_int(comp.arr.Length - 1); //O(1)
for (int i = 1; i < comp.arr.Length; i++) //O(N)
{
res.arr[i - 1] = comp.arr[i]; //O(1)
}
res = remove_zeros(res); //O(N)
return(res); //O(1)
}
//complexity = O(N)
public static Big_int pow_mod(Big_int number, Big_int power, Big_int mod, ref Big_int res)
{
if (mod.arr.Length == 1 && mod.arr[0] == 1) //O(1)
{
res = new Big_int(1); //O(1)
res.arr[0] = 0; //O(1)
return(res); //O(1)
}
if (power.arr.Length == 1 && power.arr[0] == 0) //O(1)
{
res = new Big_int(1); //O(1)
res.arr[0] = 1; //O(1)
return(res); //O(1)
}
if (power.arr.Length == 1 && power.arr[0] == 1) //O(N)
{
res = number; //O(1)
res = remove_zeros(res); //O(N)
return(res); //O(1)
}
if (power.arr[power.arr.Length - 1] % 2 == 0) // O(N^1.58)
{
Big_int new_power = new Big_int(1); //O(1)
new_power.arr[0] = 2; //O(1)
Big_int rem = new Big_int(1); //O(1)
div(power, new_power, ref new_power, ref rem); //O(N)
new_power = remove_zeros(new_power); //O(N)
Big_int value = new Big_int(1); //O(1)
pow_mod(number, new_power, mod, ref res); //T(N/2)
res = remove_zeros(res); //O(N)
res = mult(res, res, ref value); //O(1.58)
res = remove_zeros(res); //O(N)
}
else //O(N^1.58)
{
Big_int new_power = new Big_int(1); //O(1)
new_power.arr[0] = 2; //O(1)
Big_int rem = new Big_int(1); //O(1)
div(power, new_power, ref new_power, ref rem); //O(N)
new_power = remove_zeros(new_power); //O(N)
Big_int value = new Big_int(1); //O(1)
pow_mod(number, new_power, mod, ref res); //T(N/2)
res = remove_zeros(res); //O(N)
res = mult(res, res, ref value); //O(N^1.58)
res = remove_zeros(res); //O(N)
mult(res, number, ref res); //O(N^1.58)
res = remove_zeros(res); //O(N)
}
Big_int q = new Big_int(1); //O(1)
div(res, mod, ref q, ref res); //O(N)
res = remove_zeros(res); //O(N)
return(res); //O(1)
}
//complexity : O(N^1.58)
public static Big_int dec(Big_int n, Big_int d, Big_int em)
{
Big_int res = new Big_int(n.arr.Length); //O(1)
Big_int q = new Big_int(n.arr.Length); //O(1)
Big_int r = new Big_int(n.arr.Length); //O(1)
Big_int.div(em, n, ref q, ref r); //O(N)
Big_int.pow_mod(r, d, n, ref res); //O(N^1.58)
res = Big_int.remove_zeros(res); //O(N)
return(res); //O(1)
}
//complixty of fun mult = O(subt.arr.Length)+O(bd.arr.Length)+3T(N/2)+O(mid)+O(x_str)+O(Y_str)+O(N)
// in exact case all = N
//T(N) =3T(N/2)+O(N) By Master Case 1
// 𝑁log 3-ε base2=N
// so case 1
// exact O(N^1.6)
public static Big_int remove_zeros(Big_int mul)
{
int zeros = 0; //O(1)
for (int i = 0; i < mul.arr.Length; i++) //O(mul.arr.Length)
{
if (mul.arr[i] == 0)
{
zeros = i; //O(1)
continue; //O(1)
}
else
{
break;//O(1)
}
}
if (zeros == mul.arr.Length)
{
mul = new Big_int(1); //O(1)
mul.arr[0] = 0; //O(1)
return(mul); //O(1)
}
else if (zeros == 0 && mul.arr[0] == 0 && mul.arr.Length > 1)
{
Big_int temp = new Big_int(mul.arr.Length - 1); //O(1)
int count = 0; //O(1)
for (int i = 1; i < mul.arr.Length; i++) //O(1)
{
temp.arr[count] = mul.arr[i]; //O(1)
count++; //O(1)
}
return(temp); //O(1)
}
else
{
Big_int temp = new Big_int(mul.arr.Length - zeros); //O(1)
int count = 0; //O(1)
for (int i = zeros; i < mul.arr.Length; i++) //O(1)
{
temp.arr[count] = mul.arr[i]; //O(1)
count++; //O(1)
}
return(temp); //O(1)
}
}
//complixty of fun remove_zeros = O(mul.arr.Length)
// in exact case all = N
// total complixty O(N)
public static Big_int div(Big_int a, Big_int b, ref Big_int q, ref Big_int r)
{
int great = greater(a, b); //O(1)
if (a.arr.Length < b.arr.Length || great == 2) //O(1)
{
q = new Big_int(1); //O(1)
q.arr[0] = 0; //O(1)
r = a; //O(1)
return(q); //O(1)
}
Big_int twoB = new Big_int(1); //O(1)
ADD(b, b, ref twoB); //O(N)
twoB = remove_zeros(twoB); //O(N)
div(a, twoB, ref q, ref r); //T(2b)
Big_int twoQ = new Big_int(1); //O(1)
ADD(q, q, ref twoQ); //O(N)
q = remove_zeros(twoQ); //O(N)
great = greater(r, b); //O(N)
if (r.arr.Length < b.arr.Length || great == 2) //O(1)
{
return(q); //O(1)
}
else
{
Big_int one = new Big_int(1); //O(1)
one.arr[0] = 1; //O(1)
Big_int Q_one = new Big_int(1); //O(1)
ADD(q, one, ref Q_one); //O(N)
q = remove_zeros(Q_one); //O(N)
Big_int rSb = new Big_int(1); //O(1)
sub(r, b, ref rSb); //O(N)
r = remove_zeros(rSb); //O(N)
return(q); //O(1)
}
}
//T(N)=T(2b)+N ->1 ,T(>a)=a=N
//by iteration :
// T(2b)=T(4b)+2n
//T(N)=T(4b)+2N+N -> 2
//T(4b) = T(8b)+4N
//T(N)=T(2^K b)+ sum from i=0 to i=K-1 N
//Termination : 2^k B = a Log both sides
//k Log B = Log a
//K = log N / Log N = 1
//T(N) = N + (1 - 2 ^ 1+1)/(1-2) N =N+ -3/-1 N = 4 N
//Complexity = O(N)
private static int greater(Big_int a, Big_int b)
{
if (a.arr.Length > b.arr.Length) //O(1)
{
return(1); //O(1)
}
else if (a.arr.Length < b.arr.Length) //O(1)
{
return(2); //O(1)
}
for (int i = 0; i < a.arr.Length; i++)
{
if (a.arr[i] > b.arr[i]) //O(1)
{
return(1); //O(1)
}
else if (a.arr[i] < b.arr[i]) //O(N)
{
return(2); //O(1)
}
}
return(0);//O(1)
}
static void Main(string[] args)
{
FileStream file = new FileStream("C:\\Users\\Dell\\Desktop\\RSA_Project\\RSA_Project\\bin\\Debug\\SampleRSA.txt", FileMode.Open, FileAccess.Read);
StreamReader sr = new StreamReader(file);
FileStream file2 = new FileStream("C:\\Users\\Dell\\Desktop\\RSA_Project\\RSA_Project\\bin\\Debug\\SampleRSAOutput.txt", FileMode.OpenOrCreate, FileAccess.Write);
StreamWriter sw = new StreamWriter(file2);
Big_int n, e, msg;
int fun;
string line1 = "";
string line2 = "";
string line3 = "";
string line4 = "";
int filelen = int.Parse(sr.ReadLine());
for (int j = 0; j < filelen; j++)
{
int caseNo = j + 1;
line1 = sr.ReadLine();
line2 = sr.ReadLine();
line3 = sr.ReadLine();
line4 = sr.ReadLine();
n = new Big_int(line1);
e = new Big_int(line2);
msg = new Big_int(line3);
fun = int.Parse(line4);
if (fun == 0)
{
float start_time = System.Environment.TickCount;
Big_int res = Big_int.encr(n, e, msg);
float end_time = System.Environment.TickCount;
float sec = (end_time - start_time) / 1000;
Console.WriteLine("Case " + caseNo + " : ");
Console.WriteLine("Seconds : " + sec + "sec");
float ms = (end_time - start_time);
Console.WriteLine("Milliseconds : " + ms + " ms");
foreach (int i in res.arr)
{
sw.Write(i);
}
sw.WriteLine();
}
else
{
float start_time = System.Environment.TickCount;
Big_int res = Big_int.dec(n, e, msg);
float end_time = System.Environment.TickCount;
float sec = (end_time - start_time) / 1000;
Console.WriteLine("Case " + caseNo + " : ");
Console.WriteLine("Seconds : " + sec + "sec");
float ms = (end_time - start_time);
Console.WriteLine("Milliseconds : " + ms + " ms");
foreach (int i in res.arr)
{
sw.Write(i);
}
sw.WriteLine();
}
}
sw.Close();
sr.Close();
Console.WriteLine("########################### COMPLETE TEST CASES ############################");
file = new FileStream("C:\\Users\\Dell\\Desktop\\RSA_Project\\RSA_Project\\bin\\Debug\\TestRSA.txt", FileMode.Open, FileAccess.Read);
sr = new StreamReader(file);
file2 = new FileStream("C:\\Users\\Dell\\Desktop\\RSA_Project\\RSA_Project\\bin\\Debug\\TestRSAOutput.txt", FileMode.OpenOrCreate, FileAccess.Write);
sw = new StreamWriter(file2);
filelen = int.Parse(sr.ReadLine());
for (int j = 0; j < filelen; j++)
{
int caseNo = j + 1;
line1 = sr.ReadLine();
line2 = sr.ReadLine();
line3 = sr.ReadLine();
line4 = sr.ReadLine();
n = new Big_int(line1);
e = new Big_int(line2);
msg = new Big_int(line3);
fun = int.Parse(line4);
if (fun == 0)
{
float start_time = System.Environment.TickCount;
Big_int res = Big_int.encr(n, e, msg);
float end_time = System.Environment.TickCount;
float sec = (end_time - start_time) / 1000;
Console.WriteLine("Case " + caseNo + " : ");
Console.WriteLine("Seconds : " + sec + "sec");
float ms = (end_time - start_time);
Console.WriteLine("Milliseconds : " + ms + " ms");
foreach (int i in res.arr)
{
sw.Write(i);
}
sw.WriteLine();
}
else
{
float start_time = System.Environment.TickCount;
Big_int res = Big_int.dec(n, e, msg);
float end_time = System.Environment.TickCount;
float sec = (end_time - start_time) / 1000;
Console.WriteLine("Case " + caseNo + " : ");
Console.WriteLine("Seconds : " + sec + "sec");
float ms = (end_time - start_time);
Console.WriteLine("Milliseconds : " + ms + " ms");
foreach (int i in res.arr)
{
sw.Write(i);
}
sw.WriteLine();
}
}
sw.Close();
sr.Close();
}
public static Big_int ADD(Big_int str1, Big_int str2, ref Big_int res)
{
int numofzero; //O(1)
int carry = 0; //O(1)
Big_int total; //O(1)
if (str1.arr.Length > str2.arr.Length) //O(1)
{
numofzero = str1.arr.Length - str2.arr.Length; //O(1)
total = new Big_int(str1.arr.Length + 1); //O(1)
for (int i = str2.arr.Length - 1; i >= 0; i--) //O(Str2.length ) -> O(N)
{
int num = 0; //O(1)
num = str1.arr[i + numofzero] + str2.arr[i] + carry; //O(1)
if (num >= 10) //O(1)
{
total.arr[i + numofzero + 1] = num % 10; //O(1)
carry = 1; //O(1)
}
else
{
total.arr[i + numofzero + 1] = num; //O(1)
carry = 0; //O(1)
}
}
for (int i = numofzero; i > 0; i--) //O(numofzero)
{
total.arr[i] = str1.arr[i - 1] + carry; //O(1)
if (total.arr[i] >= 10) //O(1)
{
total.arr[i] = total.arr[i] % 10; //O(1)
carry = 1; //O(1)
}
else
{
carry = 0; //O(1)
}
}
total.arr[0] = carry; //O(1)
}
else
{
numofzero = str2.arr.Length - str1.arr.Length; //O(1)
total = new Big_int(str2.arr.Length + 1); //O(1)
for (int i = str1.arr.Length - 1; i >= 0; i--) //O(Str1.length ) -> O(N)
{
int num = 0; //O(1)
num = str1.arr[i] + str2.arr[i + numofzero] + carry; //O(1)
if (num >= 10) //O(1)
{
total.arr[i + numofzero + 1] = num % 10; //O(1)
carry = 1; //O(1)
}
else
{
total.arr[i + numofzero + 1] = num; //O(1)
carry = 0; //O(1)
}
}
for (int i = numofzero; i > 0; i--) //O(numofzero)
{
total.arr[i] = str2.arr[i - 1] + carry; //O(1)
if (total.arr[i] >= 10) //O(1)
{
total.arr[i] = total.arr[i] % 10; //O(1)
carry = 1; //O(1)
}
else
{
carry = 0; //O(1)
}
}
total.arr[0] = carry; //O(1)
}
int non_zero = 0; //O(1)
for (int i = 0; i < total.arr.Length; i++) //O(total.arr.length)
{
if (total.arr[i] == 0)
{
continue; //O(1)
}
non_zero = i; //O(1)
break; //O(1)
}
res = new Big_int(total.arr.Length - non_zero); //O(1)
for (int i = 0; i < res.arr.Length; i++) //O(res.arr.length)
{
res.arr[i] = total.arr[i + non_zero]; //O(1)
}
return(res); //O(1)
}
// in exact case all = N
// total complixty = 7N = O(N)
public static Big_int mult(Big_int x, Big_int y, ref Big_int res)
{
int max = Math.Max(x.arr.Length, y.arr.Length); //O(1)
int mid = max / 2; //O(1)
if (x.arr.Length == 1 && y.arr.Length == 1)
{
res.arr[res.arr.Length - 1] = x.arr[mid] * y.arr[mid]; //O(1)
int num = res.arr[res.arr.Length - 1] % 10; //O(1)
int num2 = res.arr[res.arr.Length - 1] / 10; //O(1)
if (res.arr[res.arr.Length - 1] / 10 != 0)
{
res = new Big_int(2); //O(1)
res.arr[res.arr.Length - 1] = num; //O(1)
res.arr[res.arr.Length - 2] = num2; //O(1)
}
return(res); //O(1)
}
if ((max == x.arr.Length && max % 2 != 0) || (max == y.arr.Length && max % 2 != 0))
{
max += 1; //O(1)
string x_str = String.Join("", x.arr); //O(N)
string y_str = String.Join("", y.arr); //O(N)
x_str = x_str.PadLeft(max, '0'); //O(N)
y_str = y_str.PadLeft(max, '0'); //O(N)
x = new Big_int(x_str); //O(x_str)
y = new Big_int(y_str); //O(y_str)
}
else if (x.arr.Length != y.arr.Length)
{
if (x.arr.Length < y.arr.Length)
{
string x_str = String.Join("", x.arr); //O(N)
x_str = x_str.PadLeft(max, '0'); //O(N)
x = new Big_int(x_str); //O(x_str)
}
else
{
string y_str = String.Join("", y.arr); //O(N)
y_str = y_str.PadLeft(max, '0'); //O(N)
y = new Big_int(y_str); //O(y_str)
}
}
mid = max / 2; //O(1)
Big_int a = new Big_int(mid); //O(1)
Big_int b = new Big_int(mid); //O(1)
Big_int c = new Big_int(mid); //O(1)
Big_int d = new Big_int(mid); //O(1)
for (int i = 0; i < mid; i++) //O(mid)
{
b.arr[i] = x.arr[i]; //O(1)
d.arr[i] = y.arr[i]; //O(1)
}
for (int i = mid; i < max; i++) //O(mid)
{
a.arr[i - mid] = x.arr[i]; //O(1)
c.arr[i - mid] = y.arr[i]; //O(1)
}
Big_int ac = new Big_int(mid); //O(1)
mult(a, c, ref ac); //T(N/2)
ac = remove_zeros(ac); //O(N)
Big_int bd = new Big_int(mid); //O(1)
mult(b, d, ref bd); //T(N/2)
bd = remove_zeros(bd); //O(N)
Big_int acPbd = new Big_int(0); //O(1)
ADD(ac, bd, ref acPbd); //O(N)
acPbd = remove_zeros(acPbd); //O(N)
Big_int aPb = new Big_int(0); //O(1)
Big_int.ADD(a, b, ref aPb); //O(N)
aPb = remove_zeros(aPb); //O(N)
Big_int cPd = new Big_int(0); //O(1)
Big_int.ADD(c, d, ref cPd); //O(N)
cPd = remove_zeros(cPd); //O(N)
Big_int aPbcPd = new Big_int(mid); //O(1)
mult(aPb, cPd, ref aPbcPd); //T(N/2)
aPbcPd = remove_zeros(aPbcPd); //O(N)
Big_int subt = new Big_int(0); //O(1)
sub(aPbcPd, acPbd, ref subt); //O(N)
Big_int bdz = new Big_int(x.arr.Length + bd.arr.Length); //O(1)
for (int i = 0; i < bd.arr.Length; i++) //O(bd.arr.Length)
{
bdz.arr[i] = bd.arr[i]; //O(1)
}
Big_int subz = new Big_int((mid) + subt.arr.Length); //O(1)
for (int i = 0; i < subt.arr.Length; i++) //O(subt.arr.Length)
{
subz.arr[i] = subt.arr[i]; //O(1)
}
Big_int sum = new Big_int(0); //O(1)
ADD(bdz, subz, ref sum); //O(N)
sum = remove_zeros(sum); //O(N)
res = new Big_int(0); //O(1)
ADD(sum, ac, ref res); //O(N)
res = remove_zeros(res); //O(N)
return(res); //O(1)
}
