Computer Science (9645) | Basic encryption methods

🔐 Chapter 3.5.7: Basic Encryption Methods – Keeping Secrets Safe

Welcome to one of the most exciting topics in Computer Science: cryptography! In the section "Representing data," we've looked at how data is stored. Now, we learn how to scramble that data so that even if it falls into the wrong hands, it remains unreadable. This is the foundation of modern internet security, banking, and private communication.

Don't worry if this feels like spycraft; we'll break down the concepts into simple, manageable steps. By the end of these notes, you'll understand the difference between ancient, easily cracked codes and truly secure modern methods!

1. Fundamental Concepts of Encryption

Before we dive into the specific methods, we need to speak the language of spies (cryptographers!).

Key Definitions

Encryption:

Encryption is the process of using an algorithm (a set of steps) to convert readable data (plaintext) into an unreadable format (ciphertext). This ensures that a third party who intercepts the data cannot easily understand it, unless they know both the method and the encryption key.

Plaintext:

This is the original, readable message or data. Think of it as the message you type before pressing 'send'.

Ciphertext:

This is the encrypted, scrambled message. It looks like nonsense, but it contains the plaintext hidden within.

Cipher:

The cipher is the specific algorithm or method used to perform the encryption and decryption (e.g., the Caesar cipher or the Vernam cipher).

Key:

A Key is a secret value (like a specific number, word, or sequence of bits) that is applied by the cipher to the plaintext to produce the ciphertext. The key is essential for both encrypting and decrypting the message.

Analogy: Imagine sending a locked box across the ocean. The message inside is the Plaintext. The box itself is the Ciphertext. The type of lock used is the Cipher. The actual combination/tool used to open the lock is the Key.

2. The Caesar Cipher (A Simple Substitution)

The Caesar cipher is one of the oldest and simplest forms of encryption, famous for being used by Julius Caesar.

How the Caesar Cipher Works

The Caesar cipher is a substitution cipher, meaning each letter in the plaintext is replaced by a letter some fixed number of positions down the alphabet.

The Key is the number of positions to shift.

Step-by-Step Encryption (Shift 3):

1. Identify the Plaintext: A P P L E

2. Apply the Key (Shift 3):

   • A shifts 3 places forward → D

   • P shifts 3 places forward → S

   • L shifts 3 places forward → O

   • E shifts 3 places forward → H

3. The Ciphertext is: D S S O H

To decrypt, the receiver simply shifts each letter 3 places backward.

Why the Caesar Cipher is Easily Cracked

The Caesar cipher offers very little security, making it unsuitable for modern use. It is easily cracked because:

• Limited Key Space: There are only 25 possible unique keys (shifts of 1 through 25). An attacker can simply try every single shift until a readable message appears (this is called a brute-force attack).

• Frequency Analysis: The frequency of letters in the ciphertext directly corresponds to the frequency of letters in the plaintext. For example, in English, 'E' is the most common letter. An attacker can find the most common letter in the ciphertext and assume it represents 'E', revealing the shift (key) immediately.

• Known Shift: Once the shift for one letter is identified, the shift applied to all letters is known because the key is constant throughout the entire message.

3. The Vernam Cipher (The One-Time Pad)

The Vernam cipher (also known as the one-time pad cipher) is theoretically the strongest possible encryption method.

How the Vernam Cipher Works

In the Vernam cipher, a random key, usually represented as a sequence of bits, is combined mathematically with the plaintext message (also represented as bits) to produce the ciphertext.

The key must be used only once, hence the name 'one-time pad'.

Perfect Security

The Vernam cipher is the only cipher that achieves Perfect Security. A cipher is perfectly secure if absolutely nothing about the original plaintext can be learned from examining the ciphertext.

To achieve this guaranteed level of security, the Vernam cipher must meet four extremely strict conditions:

1. The key must be chosen completely randomly. (Truly random, not pseudo-random.)

2. The key must be at least as long as the plaintext. (If the message is 1,000 characters long, the key must also be 1,000 characters long.)

3. The key must be used only once (a "one-time pad").

4. The key must be known only to the sender and receiver.

Did you know? Because producing, distributing, and securely managing keys that are as long as the data itself is very difficult, the Vernam cipher is rarely used for large volumes of data, but it has historically been used for highly sensitive communications between governments (e.g., during the Cold War).

4. Security Levels: Computational vs. Perfect

Computational Security

Most ciphers used by computers today (like AES or RSA) do not offer perfect security; they rely on Computational Security.

A cipher is computationally secure if:

• Information about the plaintext could theoretically be learned from the ciphertext.

• BUT, the algorithms required to crack the cipher would take an unfeasible amount of time to complete (even using the fastest supercomputers), OR the probability of cracking it is extremely low.

Think of it this way: You could eventually brute-force a modern code, but it would take longer than the age of the universe. Therefore, for practical purposes, it is secure.

Comparison Summary:

• Caesar Cipher: Minimal Security (Easily cracked in seconds).

• Vernam Cipher: Perfect Security (Impossible to crack if conditions are met).

• Modern Ciphers (e.g., AES): Computational Security (Feasible to use, infeasible to crack).

5. Symmetric and Asymmetric Ciphers & The Key Exchange Problem

Symmetric Ciphers

A symmetric cipher uses the same key to both encrypt and decrypt the data.

• Both the Caesar cipher and the Vernam cipher are examples of symmetric ciphers.

The Key Exchange Problem

The biggest challenge with symmetric ciphers is the key exchange problem: How do the sender and receiver secretly share the key without it being intercepted by a third party?

If you email the key, an eavesdropper might intercept both the key and the later encrypted message, rendering the encryption useless.

Asymmetric Ciphers

An asymmetric cipher (also known as public-key encryption) uses two different, mathematically related keys:

• A Public Key (used by anyone to encrypt data).

• A Private Key (kept secret by the receiver to decrypt the data).

Since the encryption key (Public Key) can be openly shared without risk, the key exchange problem is solved!

Important Note: Asymmetric ciphers use different keys for encryption and decryption, therefore the key exchange problem does not apply to them.