Affine cipher decryption, output differs for upper case and lower case - c++

Question

I have the problem when decrypting a plaintext using Affine cipher.
Encryption works fine, but applying the same logic for decryption of lower case/upper case characters returns different output.
Here is the output:
Encrypted Message is : ulctkbsjarizqhypgxofwnevmd ULCTKBSJARIZQHYPGXOFWNEVMD
Decrypted Message is: opqrstuvwxyzabcdefghijklmn ABCDEFGHIJKLMNOPQRSTUVWXYZ
I suspect it has something to do with retrieving of ASCII values, can someone correct me?
Here is my code:
#include<bits/stdc++.h>
using namespace std;
//Key values of a and b
const int a = 17;
const int b = 20;
string encryptMessage(string plainText)
{
string cipher = "";
for (int i = 0; i < plainText.length(); i++)
{
if(plainText[i]!=' ')
{
if ((plainText[i] >= 'a' && plainText[i] <= 'z') || (plainText[i] >= 'A' && plainText[i] <= 'Z'))
{
if (plainText[i] >= 'a' && plainText[i] <= 'z')
{
cipher = cipher + (char) ((((a * (plainText[i]-'a') ) + b) % 26) + 'a');
}
else if (plainText[i] >= 'A' && plainText[i] <= 'Z')
{
cipher = cipher + (char) ((((a * (plainText[i]-'A') ) + b) % 26) + 'A');
}
}
else
{
cipher += plainText[i];
}
}
else
{
cipher += plainText[i];
}
}
return cipher;
}
string decryptCipher(string cipher)
{
string plainText = "";
int aInverse = 0;
int flag = 0;
for (int i = 0; i < 26; i++)
{
flag = (a * i) % 26;
if (flag == 1)
{
aInverse = i;
}
}
for (int i = 0; i < cipher.length(); i++)
{
if(cipher[i] != ' ')
{
if ((cipher[i] >= 'a' && cipher[i] <= 'z') || (cipher[i] >= 'A' && cipher[i] <= 'Z'))
{
if (cipher[i] >= 'a' && cipher[i] <= 'z')
{
plainText = plainText + (char) ((((aInverse * (cipher[i]+ 'a') ) - b) % 26) + 'a');
}
else if (cipher[i] >= 'A' && cipher[i] <= 'Z')
{
plainText = plainText + (char) (((aInverse * ((cipher[i]+'A' - b)) % 26)) + 'A');
}
}
else
{
plainText += cipher[i];
}
}
else
plainText += cipher[i];
}
return plainText;
}
//Driver Program
int main(void)
{
string msg = "abcdefghijklmnopqrstuvwxyz ABCDEFGHIJKLMNOPQRSTUVWXYZ";
//Calling encryption function
string cipherText = encryptMessage(msg);
cout << "Encrypted Message is : " << cipherText<<endl;
//Calling Decryption function
cout << "Decrypted Message is: " << decryptCipher(cipherText);
return 0;
}

Answer 1

I have been thinking about this for some time and, although I can't provide a complete explanation, I have a couple of 'observations' that may be useful, plus a 'cheat' workaround.
First, although you say you use "the same logic for decryption of lower case/upper case," a character-wise alignment of the code from each of your decryption blocks shows that this isn't quite true:
plainText = plainText + (char) ((((aInverse * (cipher[i]+ 'a') ) - b) % 26) + 'a'); // Lower case
plainText = plainText + (char) (((aInverse * ((cipher[i]+'A' - b)) % 26)) + 'A'); // Upper case
So, 'fixing' the lower case code to be exactly analogous to the (working) code for upper case (and removing redundant parentheses) gives this:
if (cipher[i] >= 'a' && cipher[i] <= 'z')
{
plainText = plainText + (char)( ( (aInverse * (cipher[i] + 'a' - b) ) % 26 ) + 'a' );
}
else if (cipher[i] >= 'A' && cipher[i] <= 'Z')
{
plainText = plainText + (char)( ( (aInverse * (cipher[i] + 'A' - b) ) % 26 ) + 'A' );
}
However, this doesn't actually resolve the issue (it just changes it slightly), as the output then is as follows:
Encrypted Message is : ulctkbsjarizqhypgxofwnevmd ULCTKBSJARIZQHYPGXOFWNEVMD
Decrypted Message is : qrstuvwxyzabcdefghijklmnop ABCDEFGHIJKLMNOPQRSTUVWXYZ
The problem here is that the lowercase values are all 'rotated' by the value 16 - which looks suspiciously close to the value for a. Also, note that, although a is used in the encryption formula, it is not used in your decryption.
So, I have come up with the following workaround, assuming that (for reasons yet to be deduced) when decoding upper case values, this 16 is somehow lost in the bit-representation of the ASCII values:
if ((cipher[i] >= 'a' && cipher[i] <= 'z') || (cipher[i] >= 'A' && cipher[i] <= 'Z'))
{
int offset = ((cipher[i] - 'A') / 26) ? a - 1 : 0;
if (cipher[i] >= 'a' && cipher[i] <= 'z') {
plainText = plainText + (char)( ( (aInverse * (cipher[i] + 'a' - b) - offset ) % 26 ) + 'a' );
}
else if (cipher[i] >= 'A' && cipher[i] <= 'Z') {
plainText = plainText + (char)( ( (aInverse * (cipher[i] + 'A' - b) - offset ) % 26 ) + 'A' );
}
}
Note that your code can be further simplified/clarified using functions provided by the standard library and removing some 'redundant' checks:
for (int i = 0; i < cipher.length(); i++) {
if (isalpha(cipher[i])) {
int offset = islower(cipher[i]) ? a - 1 : 0;
int letter = islower(cipher[i]) ? 'a' : 'A';
plainText = plainText + (char)(((aInverse * (cipher[i] + letter - b) - offset) % 26) + letter);
}
else {
plainText += cipher[i];
}
}