Caesar

Problem to Solve

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 instead. 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

wherein \(\%\space26\) 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, \(p_0\), is H (aka 7), and his plaintext’s second character, \(p_1\), is i (aka 8). His ciphertext’s first character, \(c_0\), is thus K, and his ciphertext’s second character, \(c_1\), is thus L. Make sense?

In a file called caesar.c in a folder called caesar, write a program 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, 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.

Demo

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 asciitable.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: (with two spaces but without a newline) and then prompt the user for a string of plaintext (using get_string).
• Your program must output ciphertext: (with one space but 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.

Advice

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

Pseudocode

First write, try to write a main function in caesar.c that implements the program using just pseudocode, even if not (yet!) sure how to write it in actual code.

int main(int argc, string argv[])
{
    // Make sure program was run with just one command-line argument

    // Make sure every character in argv[1] is a digit

    // Convert argv[1] from a `string` to an `int`

    // Prompt user for plaintext

    // For each character in the plaintext:

        // Rotate the character if it's a letter
}

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 main in caesar.c in such a way that, if the user provides no command-line arguments, or two or more, the function prints "Usage: ./caesar key\n" and then returns 1, effectively exiting the program. If the user provides exactly one command-line argument, the program should print nothing and simply return 0. The program should thus behave per the below.

$ ./caesar
Usage: ./caesar key

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

$ ./caesar 1

Checking the Key

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

Add to caesar.c, below main, a function called, e.g., only_digits that takes a string as an argument and returns true if that string contains only digits, 0 through 9, else it returns false. Be sure to add the function’s prototype above main as well.

Then modify main in such a way that it calls only_digits on argv[1]. If that function returns false, then main should print "Usage: ./caesar key\n" and return 1. Else main should simply return 0. The program should thus behave per the below:

$ ./caesar 42

$ ./caesar banana
Usage: ./caesar key

Using the Key

Now modify main in such a way that it converts argv[1] to an int. You might find atoi, declared in stdlib.h, to be helpful, per manual.cs50.io. And then use get_string to prompt the user for some plaintext with "plaintext: ".

Then, implement a function called, e.g., rotate, that takes a char as input and also an int, and rotates that char by that many positions if it’s a letter (i.e., alphabetical), wrapping around from Z to A (and from z to a) as needed. If the char is not a letter, the function should instead return the same char unchanged.

Then modify main in such a way that it prints "ciphertext: " and then iterates over every char in the user’s plaintext, calling rotate on each, and printing the return value thereof.

Walkthrough

How to Test

Correctness

check50 cs50/problems/2023/fall/caesar

debug50 ./caesar KEY

debug50 ./caesar

Style

style50 caesar.c

How to Submit

1. Download your caesar.c file by control-clicking or right-clicking on the file in your codespace’s file browser and choosing Download.
2. Go to CS50’s Gradescope page.
3. Click Problem Set 2: Caesar.
4. Drag and drop your caesar.c file to the area that says Drag & Drop. Be sure it has that exact filename! If you upload a file with a different name, the autograder likely will fail when trying to run it. Ensuring you have uploaded files with the correct filename is your responsibility!
5. Click Upload.

You should see a message that says “Problem Set 2: Caesar submitted successfully!”