## CS 150 - Assignment 3 - Encryption

#### Due: Wednesday 3/8 at the beginning of class

For this assignment, we're going to be playing with basic cryptography. Cryptography is a field at the intersection of math and computer science that studies ways of securely communicating information. Throughout history, it has played an important role in a variety of cultures in a variety of contexts. We'll play with some basic encryption techniques, but there is a wealth of information on modern encryption out there (Wikipedia is a good place to start if you're interested). In cryptography, the two key functions are encryption, where we take a message and encrypt it, and decryption, where we take an encrypted message and recover the original message. In this assignment, we'll play with a few different ways of doing this.

http://xkcd.com/538/

### 1   Starter

An important skill for any programmer is the ability to utilize and extend previously written code. For this assignment, I'm going to give you some code to get you started. This code has some variables and functions written for you already and you will be filling in some of the details.

Right-click on the above link, select "Save as...", and save the file in a new folder for this assignment. Then open Spyder and open the saved file. This file does not have any syntax errors, however, until you fill in some of the details not all of the functions will run.

### 2   Warming up

To get you warmed up we're going to try a very simple method for encryption. You have a friend who says she has a great idea for encrypting a message. To encrypt it, you repeat each letter 3 times. To decrypt it, you reverse the process. For example:

"secret message" would become "ssseeecccrrreeettt   mmmeeessssssaaagggeee"

Write a function called fools_encrypt that takes the message as a parameter and returns the message encrypted using this scheme. (Hint: remember the '*' operation for strings.)

If you want a challenge (not required), try to write a function called fools_decrypt that decrypts this. For example, you could type:

```>>> fools_decrypt("ssseeecccrrreeettt   mmmeeessssssaaagggeee")
'secret message'
>>> secret = fools_encrypt("secret message")
>>> secret
'ssseeecccrrreeettt   mmmeeessssssaaagggeee'
>>> fools_decrypt(secret)
'secret message'
```
If you're not up for the challenge but want to test decrypting the results of your encryption function, you can copy my sample solution decryption function into your file: fools_decrypt.py (really, though, give it a try before you click on this!).

### 3   Caesar's method

Now, let's try to implement Caesar's encryption scheme. If you need a review of how it works, take a look at the prelab again. In the starter, I've given you a function called shift_letter. Play with this function and try some different letters (lowercase letters only) and different number offsets to make sure you understand how it works. Notice that you can also pass it negative numbers to shift the other direction.

#### Encryption

Once you're comfortable with how shift_letter works, write a function called caesar_encrypt that takes two parameters: the message to be encrypted and the number offset for the encryption. You will very likely want to utilize the shift_letter function.

#### Decryption

One of the nice things about this encryption scheme is that we can use the same function for encrypting and decrypting a message. Before reading on, think about how we could do this... I really mean it, think about it...

To decrypt a message, we can use our caesar_encrypt function, but now, give it a negative number. Encrypt a message or two and make sure that you can decrypt them.

Decrypt the following message with number offset 5:

'htruzyjwexhnjshjenxestertwjefgtzyehtruzyjwxeymfsefxywtstrcenxefgtzyeyjqjxhtujx'

It's a quote from a famous computer scientist (Dijsktra). You don't have to write it down, but it's a good check to make sure you've got things working.

Warning: our encryption schemes will only work for lowercase letters (specifically the letters a-z and space), so make sure that your message doesn't have any other characters otherwise, it won't work correctly.

### 4   Substitution ciphers

Caesar's method is just an example of a more general type of encryption scheme called substitution ciphers. For a general substitution cipher a key is used. The key has all of the same letters as the alphabet, but the order has been shuffled.

When encrypting, you encrypt a letter at a time. For each letter in the message you find that letter in the alphabet and then replace it with the corresponding letter in the key. For example, say you have following alphabet and key (I've put the indices in to make it easier to understand):

```alphabet: a b c d e f g h i j k  l  m  n  o  p  q  r  s  t  u  v  w  x  y  z  ' '
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
key:      h v i e k s y r b d a  j  q  w  n  c  x  m  g  u  f  l  t  p ' ' o  z
```
and you see the character 'k', you look that up in the alphabet and notice that it is at index 10. You then use this index in the key to get 'a' as the letter. This process is repeated for each letter in the message until you have encrypted the entire message. Make sure you understand this process before moving on to the coding.

#### Key generation

Before we can actually encrypt anything, we first need to generate a key. We could do this by hand, but it's a pain. In the starter code, I've included a function called keygen. This function takes any string as a parameter and generates a random key based on that input string (think of it like a password). I've given you all the code for this function except it relies on the splice function, which needs to be implemented. Fill in the details of the splice function.

When you're done, you should be able to generate random keys using the keygen function. Try out a few examples and make sure that it is a permutation of all of the letters in the alphabet and that you get the same thing back if you give it the same password. For example:

```>>> keygen("doglover")
'deyvhaflcirmtjsgoxbpzukwnq '
>>> keygen("doglover")
'deyvhaflcirmtjsgoxbpzukwnq '
```
(Note: due to various computer specific factors you may not get the exact same keys as I have included here, however, if you call keygen twice with the same string, you should get the same string back.)

#### Encryption

Now that you can generate random keys, you're ready to encrypt something. Write a function called subst_encrypt that takes two parameters: the message to be encrypted and the key (not the password). The function should return the message encrypted using the key. Notice that there is a constant called ALPHABET which has all of the letters and space in order. You'll likely need to use this.

#### Decryption

For a general substitution cipher we also need to write a decryption method. Write a function called subst_decrypt that takes two parameters: the encrypted message and the key (not the password). The function should return the message decrypted using the key (i.e. the original message before encryption). This function should be very similar to the encryption function with just one or two minor changes (it's the same basic idea, but in the other direction). When you're done, you can generate a new key then encrypt and decrypt messages. For example:
```>>> key = keygen("mypassword")
>>> encrypted = subst_encrypt("this is a secret message", key)
>>> encrypted
'hsiwdiwdqdwfxcfhdvfwwqgf'
>>> subst_decrypt(encrypted, key)
'this is a secret message'
```
(As before, note that keygen might work differently on your machine, so your encrypted text might look different.)

Decrypt the following message using the password "i like cs"

```'ao us jauaoiwpuxsrtauxusrrf xwuiju g wuiduqrtuxh uyhrwpuqrtuxh urwfqurddusquxusia'
```
(Note: If it doesn't work, check to see if you random key is 'xscl dpoimkfzwrevhjatgynqbu'. If it's not, it's most likely just a difference in computers. Try your decrypt message with this key then to make sure it works).

Again, you don't have to write it down, but it's a good check to make sure you've got things working.

### 5   Extra points

If you do extra points, please include a comment at the top stating what you did.
• [1 point] Caesar's method can actually be written using our code for the general substitution cypher. Write a function called shift that takes as input a number. The function should return a key that is the inorder alphabet shifted up by the number input. For example:
```>>> shift(3)
'defghijklmnopqrstuvwxyz abc'
```
If you then use this key with your subst_encrypt function you should get the same answer as if you'd used your caesar_encrypt method with the number offset

• [1 point] Write a pair of functions my_encrypt and my_decrypt that implement your own encryption algorithm. You may rely on whatever input you would like, but make it clear in the documentation how they should be run. Points will be awarded based on difficulty and creativity.

### 6   When you're done

When you're all done you should have three different encryption/decryption methods and a method for generating random keys. Make sure that your program is properly commented:
• You should have comments at the very beginning of the file stating your name, course (including section number), assignment number and the date.
• Each function should have an appropriate docstring
• Other miscellaneous comments to make things clear
In addition, make sure that you've used good style.

#### What to hand in:

You should have implemented:
• fools_encrypt
• caesar_encrypt
• splice
• subst_encrypt
• subst_decrypt
Submit your .py file online using the digital submission link on the course web page. You must have submitted it online before the beginning of class on Wednesday.