! Encrypts an Integer with the RSA Algorithm. Algorithm took from 
! "J. Buchmann - Einfuerung in die Kryptographie"
!
! Input: an integer Smaller than n
!
!
! Author: Clayton Hoss
! Version: very very beta
!

let

	const p ~ 13;		! prime 1
	const q ~ 11;		! prime 2
	const e ~ 23;		! public exponent, gcd((p-1)*(q-1), e) must be 1
	const n ~ p * q;	! public modulo
	
	var d: Integer;		! private exponent: calculated with Xeuclid
	
	! Maxint is 32k!
	! n must be smaller or equal to floor(sqrt(32k)) : 181
	! p times q must be smaller or equal to floor(sqrt(181)) : 13
	! otherwise the fast power function (power()) will not work
	
	proc putInput() ~
	begin
		put('N'); put('u'); put('m'); put('b'); put('e'); put('r'); 
		put(' '); put('t'); put('o'); put(' '); put('e'); put('n'); 
		put('c'); put('r'); put('y'); put('p'); put('t'); put(' '); 
		put('('); put(' '); put('<'); put(' '); putint(n);put(' '); 
		put(')'); put(' '); put(':'); put(' ');
	end;
	
	proc putEncryptMsg() ~
	begin
		put('E'); put('n'); put('c'); put('r'); put('y'); put('p'); 
		put('t'); put('e'); put('d'); put(' '); put('N'); put('u'); 
		put('m'); put('b'); put('e'); put('r'); put(' '); put(':'); 
		put(' ');
	end;
	
	proc putDecrypt1() ~ 
	begin
		put('D'); put('e'); put('c'); put('r'); put('y'); put('p'); 
		put('t'); put('e'); put('d'); put(' '); put('n'); put('o'); 
		put('r'); put('m'); put('a'); put('l'); put('l'); put('y'); 
		put(' '); put(':'); put(' ');
	end;
	
	proc putDecrypt2() ~ 
	begin
		put('D'); put('e'); put('c'); put('r'); put('y'); put('p'); 
		put('t'); put('e'); put('d'); put(' '); put('w'); put('i'); 
		put('t'); put('h'); put(' '); put('C'); put('R'); put('T'); 
		put(' '); put(':'); put(' ');
	end;
	
	! base may not be bigger than 181 since base * base will produce an overflow
	proc power(base: Integer, exponent: Integer, modulo: Integer, var result: Integer) ~ 
	let
		var lbase: Integer;
		var lexponent: Integer;
		var lresult: Integer
	in begin
		lbase := base // modulo;
		lexponent := exponent;
		lresult := 1;
		while lexponent > 0 do
			begin
				if (1 = (lexponent // 2)) then begin 
					lresult := ((lresult * lbase) // modulo);
					lexponent := lexponent - 1;
				end
				else begin
					lbase := ((lbase * lbase) // modulo);
					lexponent := lexponent / 2;
				end
				
			end;				
	result := lresult
	end;
	
	proc power2(base: Integer, exponent: Integer, modulo: Integer, var result: Integer) ~ 
	let 
		var i: Integer
	in begin
		result := 1;
		i := 0;
		while i < exponent do
		begin
			result := (result * base) // modulo;
			i:= i + 1;
		end;
	end;
	
	
	proc Xgcd(pa: Integer, pb: Integer, var gcd: Integer, var x:Integer, var y:Integer) ~
	let
		var a:Integer;
		var b:Integer;
		var q: Integer; 
		var r:Integer; 
		var xx: Integer; 
		var yy: Integer; 
		var sign: Integer;
		var xs: array 2 of Integer;
		var ys: array 2 of Integer
	in begin
		a := pa;
		b := pb;
		
		xs[0] := 1; xs[1] := 0;
		ys[0] := 0; ys[1] := 1;
		sign := 1;
		while b \= 0 do
		begin
			r := a // b;
			q := a / b;
			a := b;
			b := r;
			xx := xs[1];
			yy := ys[1];
			xs[1] := q * xs[1] + xs[0];
			ys[1] := q * ys[1] + ys[0];
			xs[0] := xx;
			ys[0] := yy;
			sign := sign * (0 - 1);
			
		end;
		x := sign * xs[0];
		y := (0 - sign) * ys[0];
		
		gcd := a;
		
	end; 
	
	
	proc encrypt(m: Integer, var c: Integer)  ~
	begin
		power(m, e, n, var c);
	end;
	
	
	proc decrypt(c: Integer, var m: Integer) ~
	begin
		power2(c, d, n, var m);
	end;
	
	
	proc decryptWithCRT(c: Integer, var m: Integer) ~
	let 
		var mp: Integer;
		var mq: Integer;
		var tempd: Integer;
		var gcd: Integer;
		var yp: Integer;
		var yq: Integer
	in begin
		tempd := (d // (p-1));
		power2(c, d, p, var mp);
		tempd := (d // (q-1));	
		power(c, d, q, var mq);
		
		Xgcd(p, q, var gcd, var yp, var yq);

		m := ((mp * yq * q) + (mq * yp * p)) // n;
		
		if m < 0 then begin
			m := n + m;
		end
		else begin end;		  
	end;
	
	
	proc setDecryptionExponentViaXEuclid() ~
	let 
		var gcd:Integer;
		var x: Integer;
		var y: Integer
	in begin
		Xgcd((p-1)*(q-1), e, var gcd, var x, var y);
		if y < 0 then begin
			y := (p-1)*(q-1) + y;
		end 
		else begin end;
		d := y;
		
	end;
		
	var i: Integer; ! Message Text
	var k: Integer  ! Encrypted Text
	
in begin
	setDecryptionExponentViaXEuclid();
	putInput();	
	getint(var i);
	encrypt(i, var k);
	putEncryptMsg();
	putint(k);
	puteol();
	decrypt(k, var i);
	putDecrypt1();
	putint(i);
	puteol();
	decryptWithCRT(k, var i);
	putDecrypt2();
	putint(i);
	puteol();
end