Trouble with operation - c

Question

So I am making a Caesar cipher program I have the encryption working just fine it is the decryption I am having trouble with.
Here is the code that works for encryption on uppercase letters:
if (isupper(p[i])){
char c = ((p[i] - 'A') + k % 26) + 'A';
}
Now I would think that decryption would be:
if (isupper(pp[i])){
char c = (abs((p[i] - 'A') - k) % 26) + 'A';
}
The issue that I'm having is that if k=1 and p[i]='A' it will just output the letter 'B' and not 'Z' it does not wrap around like it should so if k=2 and p[i]='A' it should output the letter 'Y'. It works if k=1 and p[i]='B' it will output 'A' thanks for any help.

Answer 1

This should do it:
if (isupper(p[i])){
char c = (p[i] - 'A' + 26 - k) % 26) + 'A';
}
The + 26 gives you your wrapping
Think of it this way (the three digit number format is just to make things line up nicely):
| 000 | 001 | 002 | ... | 024 | 025 | plain
| A | B | C | ... | Y | Z |
| 003 | 004 | 005 | ... | 001 | 002 | crypto
Now, recognize that
(n + 26) % 26 === (n % 26)
So:
| 000 | 001 | 002 | ... | 024 | 025 | plain
| A | B | C | ... | Y | Z |
| 029 | 030 | 031 | ... | 053 | 054 | crypto
is equivalent to the above when you consider modulo 26
This makes life a lot easier. The plaintext symbol set is made up of a contiguous set of integers from 'A' to 'A' + 25. The problem is that the ciphertext symbol set is not contiguous... there's a discontinuity at 025. By adding 26, you can convert the cipher text to a contiguous range from 'A' + k + 26 to 'A' + k + 49.
It's much easier then to map your contiguous ciphertext symbol set to your plaintext symbol set.
Since the Caesar code could be a shift in either direction and the decrypt is just the opposite shift, you could combine this to
boolean decrypt;
int k;
...
k = k % 26; // Ensure that the shift doesn't include any wrapping
if(decrypt) {
k *= -1;
}
if (isupper(p[i])){
char c = (p[i] - 'A' + 26 + k) % 26) + 'A';
}

Answer 2

In the encryption,
((p[i] - 'A') + k % 26) + 'A'
consider that it is evaluated as
t1 = p[i] - 'A'
t2 = k % 26
result = t1 + t2 + 'A'
That probably is not what you intended. The decryption would not reverse that arithmetic, mostly because the extra grouping changes the order of operations.

Answer 3

You are not considering the fact that they wrap around, try it like this:
if ((p[i] - 'A' - k) < 0 )
c = 'Z' - (abs(p[i] - 'A' - k) % 26) + 1;
else
c = (abs(p[i] - 'A' - k) % 26) + 'A';
And I think you don't need the moudulo "%" either.