Caesar

tl;dr

Implement a program that encrypts messages using Caesar’s cipher, per the below.

$ ./caesar 13
plaintext:  HELLO
ciphertext: URYYB

Supposedly, Caesar (yes, that Caesar) used to "encrypt" (i.e., conceal in a reversible way) confidential messages by shifting each letter therein by some number of places. For instance, he might write A as B, B as C, C as D, …, and, wrapping around alphabetically, Z as A. And so, to say HELLO to someone, Caesar might write IFMMP. Upon receiving such messages from Caesar, recipients would have to "decrypt" them by shifting letters in the opposite direction by the same number of places.

The secrecy of this "cryptosystem" relied on only Caesar and the recipients knowing a secret, the number of places by which Caesar had shifted his letters (e.g., 1). Not particularly secure by modern standards, but, hey, if you’re perhaps the first in the world to do it, pretty secure!

Unencrypted text is generally called plaintext. Encrypted text is generally called ciphertext. And the secret used is called a key.

Table 1. Encrypting HELLO with a key of 1 yields IFMMP.
plaintext	H	E	L	L	O
+ key	1	1	1	1	1
= ciphertext	I	F	M	M	P

More generally, Caesar’s algorithm (i.e., cipher) encrypts messages by "rotating" each letter by k positions. More formally, if p is some plaintext (i.e., an unencrypted message), p_i is the i^th character in p, and k is a secret key (i.e., a non-negative integer), then each letter, c_i, in the ciphertext, c, is computed as

\[c_i = (p_i + k) \bmod 26\]

wherein \(\bmod 26\) here means "remainder when dividing by 26." This formula perhaps makes the cipher seem more complicated than it is, but it’s really just a concise way of expressing the algorithm precisely.

Specification

Design and implement a program, caesar, that encrypts messages using Caesar’s cipher.

Implement your program in a file called caesar.c in a directory called caesar.
Your program must accept a single command-line argument, a non-negative integer. Let’s call it k for the sake of discussion.
If your program is executed without any command-line arguments or with more than one command-line argument, your program should print an error message of your choice (with printf) and return from main a value of 1 (which tends to signify an error) immediately.
You can assume that, if a user does provide a command-line argument, it will be a non-negative integer (e.g., 1). No need to check that it’s indeed numeric.
Do not assume that k will be less than or equal to 26. Your program should work for all non-negative integral values of k less than 2³¹ - 26. In other words, you don’t need to worry if your program eventually breaks if the user chooses a value for k that’s too big or almost too big to fit in an int. (Recall that an int can overflow.) But, even if k is greater than 26, alphabetical characters in your program’s input should remain alphabetical characters in your program’s output. For instance, if k is 27, A should not become [ even though [ is 27 positions away from A in ASCII, per asciichart.com; A should become B, since B is 27 positions away from A, provided you wrap around from Z to A.
Your program must output plaintext: (without a newline) and then prompt the user for a string of plaintext (using get_string).
Your program must output ciphertext: (without a newline) followed by the plaintext’s corresponding ciphertext, with each alphabetical character in the plaintext "rotated" by k positions; non-alphabetical characters should be outputted unchanged.
Your program must preserve case: capitalized letters, though rotated, must remain capitalized letters; lowercase letters, though rotated, must remain lowercase letters.
After outputting ciphertext, you should print a newline. Your program should then exit by returning 0 from main.

Walkthrough

Usage

Your program should behave per the examples below. Assumed that the underlined text is what some user has typed.

$ ./caesar 1
plaintext:  HELLO
ciphertext: IFMMP

$ ./caesar 13
plaintext:  hello, world
ciphertext: uryyb, jbeyq

$ ./caesar 13
plaintext:  be sure to drink your Ovaltine
ciphertext: or fher gb qevax lbhe Binygvar

$ ./caesar
Usage: ./caesar k

$ ./caesar 1 2 3 4 5
Usage: ./caesar k

Testing

Correctness

check50 cs50/2018/x/caesar

Style

style50 caesar.c

Staff’s Solution

~cs50/pset2/caesar

Hints

This program needs to accept a command-line argument, k, so you’ll want to declare main with:

int main(int argc, string argv[])

Recall that argv is an "array" of strings. You can think of an array as row of gym lockers, inside each of which is some value (and maybe some socks). In this case, inside each such locker is a string. To open (i.e., "index into") the first locker, you use syntax like argv[0], since arrays are "zero-indexed." To open the next locker, you use syntax like argv[1]. And so on. Of course, if there are n lockers, you’d better stop opening lockers once you get to argv[n - 1], since argv[n] doesn’t exist! (That or it belongs to someone else, in which case you still shouldn’t open it.)

And so you can access k with code like

string k = argv[1];

assuming it’s actually there! Recall that argc is an int that equals the number of strings that are in argv, so you’d best check the value of argc before opening a locker that might not exist! Ideally, argc will be 2. Why? Well, recall that inside of argv[0], by default, is a program’s own name. So argc will always be at least 1. But for this program you want the user to provide a command-line argument, k, in which case argc should be 2. Of course, if the user provides more than one command-line argument at the prompt, argc could be greater than 2, in which case, again, your program should print an error and return 1.

Now, just because the user types an integer at the prompt, that doesn’t mean their input will be automatically stored in an int. Au contraire, it will be stored as a string that just so happens to look like an int! And so you’ll need to convert that string to an actual int. As luck would have it, a function, atoi, exists for exactly that purposes. Here’s how you might use it:

int k = atoi(argv[1]);

Notice, this time, we’ve declared k as an actual int so that you can actually do some arithmetic with it.

Because atoi is declared in stdlib.h, you’ll want to #include that header file atop your own code. (Technically, your code will compile without it there, since we already #include it in cs50.h. But best not to trust another library to #include header files you know you need.)

Okay, so once you’ve got k stored as an int, you’ll need to ask the user for some plaintext. Odds are CS50’s own get_string can help you with that.

Once you have both k and some plaintext, p, it’s time to encrypt the latter with the former. Recall that you can iterate over the characters in a string, printing each one at a time, with code like the below:

for (int i = 0, n = strlen(p); i < n; i++)
{
    printf("%c", p[i]);
}

In other words, just as argv is an array of strings, so is a string an array of chars. And so you can use square brackets to access individual characters in strings just as you can individual strings in argv. Neat, eh? Of course, printing each of the characters in a string one at a time isn’t exactly cryptography. Well, maybe technically if k is 0. But the above should help you help Caesar implement his cipher!

Incidentally, you’ll need to #include yet another header file in order to use strlen.

Besides atoi, you might find some handy functions documented at reference.cs50.net under ctype.h and stdlib.h. For instance, isalpha might prove helpful when iterating over plaintext’s characters.

And, with regard to wrapping around from Z to A (or z to a), don’t forget about %, C’s modulo operator. You might also want to check out http://asciichart.com/, which reveals the ASCII codes for more than just alphabetical characters, just in case you find yourself printing some characters accidentally.