# Cryptanalysis

Imagine you and your friend are passing secret notes in class, and you have a special way to write the notes so that if the teacher intercepts the note, they can’t understand it. This special way of writing the notes is called a “cipher” or “encryption”. The process of making normal messages into secret ones is called “encryption”.

Now, imagine that there’s a third person in the class who’s really good at puzzles. They’ve managed to get hold of a few of your secret notes and they’re trying to figure out what your secret messages say without knowing your special way of writing. This person is doing what’s called “cryptanalysis”.

In more technical terms, cryptanalysis is the study of analyzing information systems in order to study the hidden aspects of the systems. This could include studying how to breach cryptographic security systems and gain access to the contents of encrypted messages, even when the cryptographic key is unknown.

Cryptanalysis uses mathematical analysis and algorithms to decipher the ciphers. It’s used in many areas, including computer security, military intelligence, and even in solving puzzles and games.

In other words, if you’re doing cryptanalysis, you’re trying to crack the code!

**Differential Cryptanalysis**

Differential cryptanalysis is a method of analyzing and breaking cryptographic algorithms (ciphers). It was initially developed for block ciphers, which are a common type of cipher that encrypt data in fixed-size blocks.

In differential cryptanalysis, you don’t look at a single encrypted message and its corresponding decrypted message. Instead, you look at pairs of messages. Here’s how it works in a simplified way:

- You choose two plaintexts (messages before they are encrypted) that have a certain difference. This difference is usually simple, like flipping one specific bit from 0 to 1.
- You encrypt both plaintexts to get two ciphertexts (the encrypted messages).
- Then you look at the difference between the two ciphertexts.

The key idea is that the difference in the ciphertexts can reveal information about the encryption process, and sometimes even about the secret encryption key. If the cipher has certain weaknesses, you might see specific patterns in the differences more often than you would expect by chance. By carefully choosing many pairs of plaintexts, analyzing the resulting differences, and looking for these patterns, you can gather information to help break the cipher.

Differential cryptanalysis is a powerful tool, but it doesn’t work against all ciphers. When developing a new cipher, cryptographers will often use differential cryptanalysis (among other methods) to test whether the cipher is secure. If the cipher is vulnerable to differential cryptanalysis, it’s back to the drawing board.

**Linear Cryptanalysis**

Linear cryptanalysis is another method used to attack cryptographic cipher systems, much like differential cryptanalysis. However, it employs a different strategy. It was first introduced by Mitsuru Matsui in 1993 to attack the **Data Encryption Standard **(DES) cipher.

In linear cryptanalysis, the attacker attempts to find a linear equation that approximates the behavior of the cipher. This linear equation is between the plaintext (the original message), the ciphertext (the encrypted message), and the key. The key point is that the equation is not perfectâ€”it only holds with a certain probability.

Here’s a simplified explanation:

- You would start by making an educated guess about a potential linear equation that relates some bits of the plaintext, some bits of the ciphertext, and some bits of the key.
- Then, you would test this equation against many pairs of plaintext and corresponding ciphertext.
- If the equation is correct more often than what would be expected by chance, then the equation probably has some connection to the secret key.
- By gathering enough plaintext-ciphertext pairs and doing enough statistical analysis, you can increase your chances of correctly guessing the secret key.

One important thing to note is that both linear and differential cryptanalysis are forms of “known plaintext” attacks. This means that in both methods, the attacker needs to have access to both the encrypted message and the original unencrypted message.

And just like with differential cryptanalysis, cryptographers use linear cryptanalysis to test the strength of new ciphers. If a cipher can be broken with linear cryptanalysis, then it’s not secure enough to be used.

**Bringing it all together**

Let’s start with the concept of sending information over the internet. You can think of it like sending a postcard through the mail. Anyone who handles the postcard, from the postal workers to the person who finally delivers it to your mailbox, can read the message because it’s not hidden in any way.

Now, imagine if you could put that postcard in a locked box, and the only person who has the key to open that box is the friend you’re sending the postcard to. Nobody else could read the message, even if they intercept the box. That’s what HTTPS, VPNs, and encrypted messengers do – they lock your information in a box that only the intended recipient can open. This “box” is what we call encryption.

So why are these technologies important? They provide privacy and security. They ensure that your data can’t be easily intercepted and read by others. Whether it’s preventing hackers from stealing your personal information, stopping companies from tracking your online behavior, or protecting your personal conversations from prying eyes, encryption plays a crucial role in keeping your digital life secure.

In the context of cryptanalysis, these encrypted communications represent a challenge. As discussed earlier, cryptanalysis is about trying to break the encryption to read the data without having the key. But with the strong encryption methods used in HTTPS, VPNs, and encrypted messengers, successful cryptanalysis is exceptionally difficult, if not practically impossible with current technology.

**Summary**

Cryptography is an essential part of our digital lives, ensuring the security and integrity of our communications and data. Its two main components are encryption, which is the process of converting plain, understandable information into an unreadable format, and cryptanalysis, which is the art of deciphering this encrypted information without access to the secret key.

Two important techniques in cryptanalysis are differential and linear cryptanalysis. They both provide ways to analyze cryptographic systems and potentially discover the secret key. Differential cryptanalysis involves studying the differences between pairs of plaintext and ciphertext, while linear cryptanalysis involves finding a linear approximation of the encryption function. Both of these techniques require access to pairs of plaintext and corresponding ciphertext, and they can be used to test the security of new cryptographic algorithms.

However, it’s important to note that real-world cryptography and cryptanalysis are complex and require a deep understanding of mathematics and computer science. The examples we discussed are simplified, but they give a glimpse into the fascinating world of cryptography.