(week2) - caesar details.txt

Et tu?
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:

plaintext	H	E	L	L	O
+ key	1	1	1	1	1
= ciphertext	I	F	M	M	P
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), pi is the ith character in p, and k is a secret key (i.e., a non-negative integer), then each letter, ci, in the ciphertext, c, is computed as

ci = (pi + 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

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

Pseudocode
First, write in pseudocode.txt at right 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 at right 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 and returns from main a value of 1 (which tends to signify an error) immediately. 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 at right 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 at right 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 (with a return code of 1) 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 at right such that, after validating the key, we prompt the user for a string (using "plaintext: " for the prompt) and then shift all of its characters by 1, printing out "ciphertext: " followed by the result and a newline. Your program should then exit by returning 0 from main. 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.


Best to use the modulo (i.e., remainder) operator, %, to handle wraparound from Z to A! But how?
Things get weird if we try to wrap Z or z by 1 using the technique in the previous section.
Things get weird also if we try to wrap punctuation marks using that technique.
Recall that ASCII maps all printable characters to numbers.
Recall that the ASCII value of A is 65. The ASCII value of a, meanwhile, is 97.
If you’re not seeing any output at all when you call printf, odds are it’s because you’re printing characters outside of the valid ASCII range from 0 to 127. Try printing characters as numbers (using %i instead of %c) at first to see what values you’re printing, and make sure you’re only ever trying to print valid characters!