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In the world of cryptography, understanding the fundamentals is crucial, especially when it comes to its applications in the realm of cryptocurrencies. In this lecture on Bitcoin, Blockchain, and Cryptoassets by the Center for Innovative Finance at the University of Basel, the focus is on Symmetric Cryptography. The lecture covers various aspects of encryption, including the history of encryption methods, the two branches of cryptography (transposition and substitution), and the different types of ciphers used. Viewers are encouraged to engage in open exchanges and provide feedback, ensuring a valuable learning experience for everyone. So, if you’re curious to explore the world of symmetric cryptography and its role in cryptocurrencies, this lecture is the perfect place to start.

A branch of secret writing, cryptography has been used throughout human history with diverse methods of encryption. This lecture delves into the two branches of cryptography, namely transposition and substitution. Through examples such as the Caesar cipher and polyalphabetic substitution, you will learn how letters and words can be substituted to transform plain text into cipher text. And if you’ve ever wondered how computerized encryption works, encoding standards like ASCII or UTF-8, as well as encryption methods like the Data Encryption Standard (DES), will be explained. Additionally, the lecture touches upon the key distribution problem and introduces the concept of asymmetric cryptography, which allows for key exchange without a secure channel. Get ready to unravel the fascinating world of symmetric cryptography and its applications in Bitcoin, Blockchain, and Cryptoassets.

## Symmetric Cryptography

### Definition and Explanation

Symmetric cryptography is a method of encryption where the same key is used for both the encryption and decryption of data. This means that the sender and the recipient both have access to the same secret key, which they use to encrypt and decrypt the message. In symmetric cryptography, the key is shared between the parties involved, hence it is also known as shared-key or secret-key cryptography.

The process of symmetric encryption involves converting plain text into cipher text using the secret key. The sender encrypts the message using the key, and the recipient decrypts it using the same key. This makes symmetric cryptography a faster encryption technique compared to asymmetric cryptography, where different keys are used for encryption and decryption. Symmetric encryption algorithms are generally more efficient and provide a higher level of security.

### Applications of Symmetric Cryptography

Symmetric cryptography has a wide range of applications in various fields. It is commonly used in securing data transmissions over networks, such as internet banking, online shopping, and email communication. Symmetric encryption ensures that the data is secure during transmission and can only be accessed by authorized parties possessing the secret key.

Another popular application of symmetric cryptography is in securing stored data. It is used to encrypt sensitive information stored on computers, servers, or other storage devices. This ensures that even if the data is compromised or accessed without authorization, it remains unintelligible without the corresponding secret key.

Furthermore, symmetric cryptography is utilized in securing communication between different software systems and devices. For example, it is widely used in secure communication protocols, such as SSL/TLS, to establish secure connections between web browsers and servers. Symmetric encryption ensures that the data exchanged between the browser and server remains confidential and integrity is maintained.

Overall, symmetric cryptography plays a crucial role in various aspects of data security and communication, providing a robust and efficient method for encrypting and decrypting sensitive information.

## Cryptography Throughout History

### Introduction to Cryptography

Cryptography, derived from the Greek words “kryptos” (hidden) and “graphein” (writing), is the practice of securing information by transforming it into an unreadable format to protect it from unauthorized access. The art of cryptography dates back thousands of years and has been employed by civilizations throughout history.

Cryptography has been used for different purposes, ranging from military communications to diplomatic correspondences. The primary objective of cryptography is to ensure confidentiality, authenticity, and integrity of the information being transmitted or stored. It has played a crucial role in maintaining secrecy during wars, securing sensitive governmental communications, and protecting trade secrets.

### Different Methods of Encryption

Over time, various methods of encryption have been developed to encode information. These methods can be broadly classified into two categories: transposition and substitution.

Transposition encryption involves rearranging the characters or blocks of the message without changing the actual characters themselves. It aims to obfuscate the structure of the message and make it difficult to decipher. Examples of transposition encryption methods include rail fence cipher and columnar transposition cipher.

On the other hand, substitution encryption involves replacing characters in the message with other characters, numbers, or symbols. This method changes the content of the message and obscures its meaning. Examples of substitution encryption methods include Caesar cipher, Vigenere cipher, and one-time pad cipher.

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## Substitution Cryptography

### Code Substitution

Code substitution is a form of substitution encryption where each character or group of characters in the plaintext is replaced by another character or group of characters in the ciphertext according to a predetermined code. The codebook contains the mapping between the original characters and their corresponding substitutions.

Code substitution can be an effective method of encryption if the codebook is kept secret. However, if the codebook falls into the wrong hands, the encryption can be easily broken. Therefore, maintaining the security of the codebook is crucial in code substitution cryptography. This method was commonly used in military operations and espionage before the advent of more sophisticated encryption techniques.

### Cipher Substitution

Cipher substitution is another type of substitution encryption where each character in the plaintext is replaced by a fixed rule or pattern in the ciphertext. This rule can be a simple one-to-one mapping, such as shifting each letter by a fixed number of positions in the alphabet. Examples of cipher substitution include Caesar cipher and Vigenere cipher, which we will explore in more detail later.

Cipher substitution offers a higher level of security compared to code substitution because the rule or pattern used for substitution is not dependent on an external codebook. However, with the advent of more advanced encryption-breaking techniques, cipher substitution on its own may not provide sufficient security and is often combined with other encryption methods for more robust protection.

## Caesar Cipher

### Explanation of Caesar Cipher

The Caesar cipher is one of the simplest and most widely known examples of cipher substitution encryption. It involves replacing each letter in the plaintext with a letter a fixed number of positions down the alphabet.

For example, with a shift of 3, “A” would be replaced by “D”, “B” would become “E”, and so on. The alphabet loops around, so “Z” would be replaced by “C”.

### Shifting Letters

In the Caesar cipher, the key is the number of positions by which the letters are shifted in the alphabet. This key determines the specific substitution rule used in the encryption and decryption process.

The Caesar cipher operates on the principle of modular arithmetic. If the shift value exceeds the total number of letters in the alphabet, 26 in the case of English, the alphabet wraps around and the remaining shifts are performed from the beginning of the alphabet. This ensures that the substitution remains within the bounds of the available characters.

### Example and Demonstration

To illustrate how the Caesar cipher works, let’s use the example of shifting each letter by 3 positions.

If we take the word “HELLO” as the plaintext, applying the Caesar cipher with a shift of 3 would result in the cipher text “KHOOR”. The letter “H” is shifted three positions to the right to become “K”, the letter “E” becomes “H”, “L” becomes “O”, and so on.

This simple demonstration showcases the basic concept of the Caesar cipher and how it transforms the original message into an encrypted form. However, it’s important to note that the Caesar cipher is relatively easy to break, especially with the aid of modern computing power and frequency analysis techniques.

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## Frequency Analysis

### Decrypting Ciphers

Frequency analysis is a technique used to break encryption methods, particularly those based on substitution. By analyzing the frequency of certain letters or patterns in the ciphertext, it is possible to deduce the corresponding letters or patterns in the plaintext.

In the case of the Caesar cipher, frequency analysis involves looking at the frequency of each letter in the encrypted message. Since each letter is shifted by the same number of positions, the relative frequency of each letter in the ciphertext remains the same as in the plaintext. Therefore, by comparing the frequency of letters in the ciphertext with the expected letter frequencies in the English language, it is possible to determine the shift used in the Caesar cipher.

### Letter Frequency Comparison

The frequency of letters in the English language follows a certain pattern. Some letters, such as “E” and “T”, occur more frequently than others like “Z” and “Q”. This frequency pattern provides a basis for frequency analysis in cryptography.

In the case of the Caesar cipher, the most frequent letter in the ciphertext is likely to correspond to the letter “E” in the plaintext. By identifying the most frequent letter and assuming it represents “E”, it is possible to calculate the shift used in the encryption and decrypt the message accordingly.

The success of frequency analysis in breaking the Caesar cipher relies on the accuracy of letter frequency estimates and assumptions. It is most effective when dealing with longer messages and texts that contain a sufficient variety of letters and patterns.

### Techniques and Challenges

While frequency analysis is a powerful technique in decrypting substitution ciphers like the Caesar cipher, it is not foolproof. Sophisticated encryption methods, such as the Vigenere cipher, employ techniques to counter frequency analysis.

To overcome the challenges presented by frequency analysis, techniques like polyalphabetic substitution are used. These methods use multiple alphabets or shifting patterns to provide a higher level of encryption and make frequency analysis more difficult.

Additionally, the success of frequency analysis relies on accurate letter frequency data. The frequency of letters may vary in different texts and languages, so it is essential to use reliable and up-to-date frequency statistics for accurate analysis.

## Polyalphabetic Substitution

### Introduction to Polyalphabetic Substitution

Polyalphabetic substitution is an advanced encryption method that improves upon the weaknesses of simple substitution ciphers like the Caesar cipher. It introduces multiple shifts or alphabets to create a more complex encryption scheme.

In polyalphabetic substitution, each letter in the plaintext can be substituted by multiple different letters depending on its position in the message or a predetermined pattern. This makes the encryption more resistant to frequency analysis, as the same letter in different positions will have different substitutions.

### Using Multiple Alphabets

Polyalphabetic substitution uses multiple alphabets or shifting patterns to enhance the security of the encryption. The key, in this case, determines the rules or patterns used for substitution.

For example, the Vigenere cipher is a well-known polyalphabetic substitution cipher that employs a keyword or phrase as the key. Each letter in the key corresponds to a particular alphabet or shifting pattern. As the encryption progresses, the position of the letters in the keyword determines which alphabet is used for substitution.

By introducing multiple shifting alphabets, polyalphabetic substitution makes frequency analysis more challenging. The same letter will have different substitutions depending on its position in the message, making it difficult to deduce the key or the plaintext through frequency analysis alone.

### Difficulty of Decryption

Polyalphabetic substitution ciphers, such as the Vigenere cipher, are more difficult to decrypt compared to simple substitution ciphers. The complexity lies in correctly identifying the key or the shifting patterns used for substitution.

While frequency analysis can still be applied to break polyalphabetic substitution ciphers, it becomes significantly more challenging due to the additional shifting alphabets. The repeated patterns required for accurate frequency analysis are concealed by the variations introduced by multiple shifting alphabets.

Decryption of polyalphabetic substitution ciphers often involves identifying patterns in the ciphertext, attempting different key lengths, and performing extensive analysis to deduce the correct key or keyword. As a result, polyalphabetic substitution ciphers provide a higher level of security compared to simpler encryption methods.

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## Vigenere Cipher

### Overview of Vigenere Cipher

The Vigenere cipher is a widely used polyalphabetic substitution cipher that was first described by Giovan Battista Bellaso in the 16th century. It improves upon the drawbacks of simple substitution ciphers by introducing a keyword or phrase as the key.

In the Vigenere cipher, each letter in the plaintext is shifted according to a particular alphabet or shifting pattern associated with a letter in the keyword. The repeating keyword determines the selection of these shifting alphabets, making it harder to decrypt the message through frequency analysis.

### Encryption Using a Code Word

To encrypt a message using the Vigenere cipher, a code word or keyword is selected. This keyword should be easy for the sender and recipient to remember but difficult for others to guess. The length of the keyword should be equal to or longer than the length of the message to ensure secure encryption.

Once the keyword is chosen, each letter in the plaintext is shifted according to the corresponding letter in the keyword to obtain the encrypted message. The repeating keyword determines the selection of different shifting alphabets, providing a higher level of security compared to simple substitution ciphers.

### Strengths and Weaknesses

The Vigenere cipher offers enhanced security compared to simpler encryption methods. The use of multiple shifting alphabets based on a repeating keyword makes frequency analysis more challenging. The same letter in different positions will have different substitutions, making it difficult to deduce the key or the plaintext based on letter frequencies alone.

However, like any encryption method, the Vigenere cipher is not without its weaknesses. If the keyword is short or easily guessable, the encryption can be easily cracked through brute force or by analyzing repeating patterns. Furthermore, the security of the Vigenere cipher relies heavily on the secrecy of the keyword, as knowledge of the keyword allows for decryption of the message.

The Vigenere cipher served as an important breakthrough in encryption during its time and laid the foundation for more advanced encryption techniques that are used today.

## One-Time Pad Cipher

### Unbreakable Encryption

The one-time pad cipher is a type of encryption that is considered unbreakable if used correctly. It was first described by Frank Miller in 1882 and later independently reinvented by Gilbert Vernam in 1917.

In the one-time pad cipher, each character in the plaintext is encrypted by combining it with a character from a random key that is at least as long as the message. The key is typically generated by a true random process, such as radioactive decay or atmospheric noise, to ensure complete randomness and unpredictability.

Since the key is as long as the message and completely random, it provides perfect secrecy. This means that even with unlimited computational power, it is impossible to decipher the message without possessing the exact key used for encryption.

### Use of Unique Keys

The security of the one-time pad cipher lies in the use of unique keys. Each key should be used only once and never reused. This is where the name “one-time pad” originates from. Reusing a key compromises the security of the encryption and makes it vulnerable to analysis and decryption.

To maintain the security of the one-time pad cipher, the keys must be kept completely secret and securely distributed between the sender and recipient. The key should not be susceptible to interception or compromise, as any leakage of the key would render the encryption useless.

### Advantages and Limitations

The one-time pad cipher offers several advantages over other encryption methods. It provides perfect secrecy and is theoretically unbreakable if the key is used only once and kept fully secret. Additionally, the encryption and decryption process is relatively simple and does not require complex algorithms or computations.

However, the one-time pad cipher has certain limitations that restrict its widespread use. Firstly, it requires a key that is as long as the message, making it impractical for encrypting large volumes of data. Secondly, securely distributing and exchanging the keys can be a challenging task, especially in scenarios where secure communication channels are not readily available.

Despite these limitations, the one-time pad cipher remains an important concept in cryptography and serves as a benchmark for measuring the security of other encryption techniques.

## Conclusion

Symmetric cryptography, with its use of a shared secret key, provides an efficient and secure method for encrypting and decrypting data. It has found extensive applications in securing data transmissions, stored data, and communication between different software systems and devices.

Throughout history, various encryption methods have been developed to protect information. Cryptography has played a crucial role in maintaining secrecy, securing communications, and protecting sensitive data.

Substitution cryptography, including code substitution and cipher substitution, has been employed to hide the content and structure of messages. The Caesar cipher, a simple substitution cipher, introduced the concept of letter shifting and demonstrated the vulnerability of basic substitution ciphers to frequency analysis.

Frequency analysis has been a powerful technique in decrypting ciphers, but the introduction of polyalphabetic substitution encryption, such as the Vigenere cipher, made it more difficult. The use of multiple shifting alphabets based on a keyword enhanced the security and complexity of encryption.

The one-time pad cipher, if used correctly and with unique keys, provides unbreakable encryption. However, its practical limitations, such as the size and secure distribution of keys, have restricted its widespread use.

In conclusion, cryptography has evolved over time, and encryption techniques have become more sophisticated. Symmetric cryptography, along with other encryption methods, continues to play a crucial role in protecting sensitive information and ensuring secure communication in the digital age.