Caesar

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

$ ./caesar 13
plaintext:  HELLO
ciphertext: URYYB

Background

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.

To be clear, then, here’s how encrypting HELLO with a key of 1 yields IFMMP:

More formally, 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) % 26

wherein % 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. Indeed, for the sake of discussion, think of A (or a) as 0, B (or b) as 1, …, H (or h) as 7, I (or i) as 8, …, and Z (or z) as 25. Suppose that Caesar just wants to say Hi to someone confidentially using, this time, a key, k, of 3. And so his plaintext, p, is Hi, in which case his plaintext’s first character, p₀, is H (aka 7), and his plaintext’s second character, p₁, is i (aka 8). His ciphertext’s first character, c₀, is thus K, and his ciphertext’s second character, c₁, is thus L. Can you see why?

Let’s write a program called caesar that enables you to encrypt messages using Caesar’s cipher. At the time the user executes the program, they should decide, by providing a command-line argument, on what the key should be in the secret message they’ll provide at runtime. We shouldn’t necessarily assume that the user’s key is going to be a number; though you may assume that, if it is a number, it will be a positive integer.

Here are a few examples of how the program might work. For example, if the user inputs a key of 1 and a plaintext of HELLO:

$ ./caesar 1
plaintext:  HELLO
ciphertext: IFMMP

Here’s how the program might work if the user provides a key of 13 and a plaintext of hello, world:

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

Notice that neither the comma nor the space were “shifted” by the cipher. Only rotate alphabetical characters!

How about one more? Here’s how the program might work if the user provides a key of 13 again, with a more complex plaintext:

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

Notice that the case of the original message has been preserved. Lowercase letters remain lowercase, and uppercase letters remain uppercase.

And what if a user doesn’t cooperate?

$ ./caesar HELLO
Usage: ./caesar key

Or really doesn’t cooperate?

$ ./caesar
Usage: ./caesar key

Or even…

$ ./caesar 1 2 3
Usage: ./caesar key

./caesar key

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.
• If any of the characters of the command-line argument is not a decimal digit, your program should print the message Usage: ./caesar key and return from main a value of 1.
• 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 2^31 - 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 http://www.asciichart.com/[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.

How to begin? Let’s approach this problem one step at a time.

Pseudocode

First, write some pseudocode that implements this program, even if not (yet!) sure how to write it in code. There’s no one right way to write pseudocode, but short English sentences suffice. Recall how we wrote pseudocode for finding Mike Smith. Odds are your pseudocode will use (or imply using!) one or more functions, conditions, Boolean expressions, loops, and/or variables.

Counting Command-Line Arguments

Whatever your pseudocode, let’s first write only the C code that checks whether the program was run with a single command-line argument before adding additional functionality.

Specifically, modify caesar.c in such a way that: if the user provides exactly one command-line argument, it prints Success; if the user provides no command-line arguments, or two or more, it prints Usage: ./caesar key. Remember, since this key is coming from the command line at runtime, and not via get_string, we don’t have an opportunity to re-prompt the user. The behavior of the resulting program should be like the below.

$ ./caesar 20
Success

or

$ ./caesar
Usage: ./caesar key

or

$ ./caesar 1 2 3
Usage: ./caesar key

Accessing the Key

Now that your program is (hopefully!) accepting input as prescribed, it’s time for another step.

Recall that in our program, we must defend against users who technically provide a single command-line argument (the key), but provide something that isn’t actually an integer, for example:

$ ./caesar xyz

Before we start to analyze the key for validity, though, let’s make sure we can actually read it. Further modify caesar.c such that it not only checks that the user has provided just one command-line argument, but after verifying that, prints out that single command-line argument. So, for example, the behavior might look like this:

$ ./caesar 20
Success
20

Validating the Key

Now that you know how to read the key, let’s analyze it. Modify caesar.c such that instead of printing out the command-line argument provided, your program instead checks to make sure that each character of that command line argument is a decimal digit (i.e., 0, 1, 2, etc.) and, if any of them are not, terminates after printing the message Usage: ./caesar key. But if the argument consists solely of digit characters, you should convert that string (recall that argv is an array of strings, even if those strings happen to look like numbers) to an actual integer, and print out the integer, as via %i with printf. So, for example, the behavior might look like this:

$ ./caesar 20
Success
20

or

$ ./caesar 20x
Usage: ./caesar key

Peeking Underneath the Hood

As human beings it’s easy for us to intuitively understand the formula described above, inasmuch as we can say “H + 1 = I”. But can a computer understand that same logic? Let’s find out. For now, we’re going to temporarily ignore the key the user provided and instead prompt the user for a secret message and attempt to shift all of its characters by just 1.

Extend the functionality of caesar.c such that, after validating the key, we prompt the user for a string and then shift all of its characters by 1, printing out the result. We can also at this point probably remove the line of code we wrote earlier that prints Success. All told, this might result in this behavior:

$ ./caesar 1
plaintext:  hello
ciphertext: ifmmp

Your Turn

Now it’s time to tie everything together! Instead of shifting the characters by 1, modify caesar.c to instead shift them by the actual key value. And be sure to preserve case! Uppercase letters should stay uppercase, lowercase letters should stay lowercase, and characters that aren’t alphabetical should remain unchanged.

Walkthrough

How to Test Your Code

Execute the below to evaluate the correctness of your code using check50. But be sure to compile and test it yourself as well!

check50 cs50/problems/2019/fall/caesar

Execute the below to evaluate the style of your code using style50.

style50 caesar.c

How to Submit

Execute the below, logging in with your GitHub username and password when prompted. For security, you’ll see asterisks (*) instead of the actual characters in your password.

submit50 cs50/problems/2019/fall/caesar