Question

( simple Encryption) Some information on the Internet may be encrypted with a simple algorithm known as "rot13," which rotates each character by 13 positions in the alphabet. Thus, 'a' corresponds to 'n', and 'x' corresponds to 'k'. rot13 is an example of symmetric key encryption. With symmetric key encryption, both the encrypter and decrypter use the same key. a. Write a program that encrypts a message using rot13. b. Write a program that decrypts the scrambled message using 13 as the key. c. After writing the programs of part (a) and part (b), briefly answer the following question: If you did not know the key for part (b), how difficult do you think it would be to break the code? What if you had access to substantial computing power (e.g., supercomputers)? In Exercise 18.26 we ask you to write a program to accomplish this.

Short answer

Rot13 can be broken easily without the key by trying all 25 other shifts; it's not secure.

Step-by-step solution

Understanding Rot13 Encryption

Rot13 is a simple substitution cipher where each letter is replaced by the letter 13 positions ahead in the alphabet. For example, 'a' becomes 'n', 'b' becomes 'o', up to 'z', which becomes 'm'. This can be used for both encryption and decryption since applying rot13 twice returns the original message.

Writing the Encryption Program

To implement a rot13 encryption program in Python, a function is created that loops through each character in the message. In Python, the ord() function converts a character to its ASCII value. If a character is a letter, 13 is added, and if this goes beyond 'z' or 'Z', it wraps around by subtracting 26. Here is a basic implementation: ```python def rot13_encrypt(message): encrypted = [] for char in message: if 'a' <= char <= 'z': encrypted.append(chr((ord(char) - ord('a') + 13) % 26 + ord('a'))) elif 'A' <= char <= 'Z': encrypted.append(chr((ord(char) - ord('A') + 13) % 26 + ord('A'))) else: encrypted.append(char) return ''.join(encrypted) ``` This processes the input message by shifting each letter by 13 positions in both upper and lower cases.

Writing the Decryption Program

Creating a decryption program is similar to the encryption process, as applying rot13 to an already rot13 encrypted message decrypts it. Use the same function, as rot13 is its own inverse: ```python def rot13_decrypt(message): # Since rot13 is symmetric, you use the same function as encryption return rot13_encrypt(message) ``` This program takes the encrypted message and applies rot13 again to decrypt it back to the original message.

Evaluating the Difficulty of Breaking Rot13 without the Key

Rot13 is a straightforward substitution cipher, acting as just a basic Caesar cipher with a fixed shift of 13. Without the key, it would not be difficult to break rot13 since there are only 25 other possibilities for the shift, which allows a brute-force approach by trying all shifts. With substantial computing power, this process would be instantaneous. Therefore, rot13 is not considered secure encryption.

Key concepts

Substitution Cipher

A substitution cipher is a method of encoding where each letter or group of letters is replaced with another. This technique hides the original message by disguising it with a predetermined pattern of replacement.
Substitution ciphers come in various types, each with a unique way of substituting characters.

The overarching concept is to take a message and replace its elements according to a specific set of rules:

• Simple Substitution: Each letter in the plaintext is replaced with another letter. An example is the ROT13 cipher where each letter is shifted by 13 places.


• Homophonic Substitution: Each letter in the plaintext can map to multiple letters in the ciphertext. This enhances complexity compared to a direct letter-to-letter transformation.


• Polyalphabetic Substitution: Utilizes multiple substitution alphabets to substitute the letters in the plaintext. The Vigenère cipher is a classic example.

Substitution ciphers are relatively easy to understand and implement but often lack strong security due to their predictability. Today's secure communication systems have evolved to more complex algorithms.

Symmetric Key Encryption

Symmetric Key Encryption refers to methods where the same key is used to both encrypt and decrypt the data. It's a fundamental pillar of cryptography, widely used due to its efficiency and simplicity.
The shared key, known only to the sender and receiver, secures the communication between them:

• Speed: The process of symmetric encryption is relatively fast, making it ideal for encrypting large volumes of data.


• Shared Secret: Both parties involved must have access to the key and keep it private.


• Examples: In addition to ROT13, there are other algorithms like AES (Advanced Encryption Standard) which are commonly used in many security protocols.

However, symmetric key encryption comes with challenges. The complexity of secure key distribution and management becomes more challenging as the number of users increases in a network.
Understanding symmetric key encryption is crucial for grasping how basic encryption systems work and why key management is so important.

Caesar Cipher

The Caesar Cipher is one of the simplest and oldest forms of encryption. Named after Julius Caesar, who reportedly used it to protect his communications, this cipher shifts the letters of the alphabet a fixed number of spaces along.
The key in a Caesar Cipher is the number of positions each letter is shifted. For example:

• Shift of 1: 'A' becomes 'B', 'B' becomes 'C', and so on.


• Shift of 3: 'A' becomes 'D', 'B' becomes 'E', etc. This was historically used by Caesar in his messages.

The ROT13 cipher is a special case of the Caesar Cipher where the shift is 13. This shift is exactly half of the 26 letters in the English alphabet, meaning applying ROT13 again to an ROT13-encrypted message returns the original text.
Although easy to implement, the Caesar Cipher is not secure by modern standards. The limited number of possible shifts makes it vulnerable to brute force attacks, where adversaries simply try all possible shifts. It's a fascinating example for educational purposes, illustrating core principles of cryptography effectively.