Intro to Cryptography

Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.

-Vladimir Arnold, Soviet mathematician

Cryptography is the science of secure communication in the presence of third parties or adversaries. It involves the use of mathematical algorithms to transform messages into unintelligible forms that can only be deciphered by the intended recipients who have the knowledge of the key. Cryptography has been used for centuries, dating back toancient civilizations such as the Greeks and Romans who used simple substitution ciphers to encode their messages. Read more about these ciphers on page 2 of our website!

During World War II, cryptography played a crucial role in the outcome of the war. The Cipher Race, also known as the Code War, was a competition between the Allied and Axis powers to develop and break each other's ciphers. The German Enigma machine was considered unbreakable until British cryptanalysts working at Bletchley Park, including Alan Turing, were able to crack the code, which gave the Allies a significant advantage.

The development of computers and other technologies has revolutionized the field of cryptography. The shift from manual to automated encryption and decryption methods allowed for the creation of more complex ciphers. One of the most famous modern ciphers is the Advanced Encryption Standard (AES), which is widely used in many encryption applications, including online banking and e-commerce.

As ciphers are developed, they are often subject to attacks by adversaries who try to break them. Cryptanalysts use various methods to break ciphers, such as brute-force attacks, which involve trying all possible keys until the correct one is found, or more sophisticated attacks based on mathematical analysis. As a result, ciphers need to be constantly improved and updated to remain secure against these attacks.

In addition to ciphers, other cryptographic techniques include steganography and hashing. Steganography involves hiding messages within other messages, such as hiding text within an image file. Hashing involves forming a fixed-size output string for any size of input data; that string is known as a hash, which can be used to verify the integrity of the original data. Hashing is commonly used in password storage, where the password is hashed and stored rather than the plaintext password itself.

Cryptography has a rich history and has played a vital role in various aspects of society, from ancient civilizations to modern-day applications such as e-commerce and online security. The Cipher Race during World War II exemplifies the importance of cryptography in warfare, and the development of more complex ciphers and automated encryption methods has opened up new opportunities for secure communication. However, as technology advances, so do the methods used to break ciphers, and cryptography needs to adapt and evolve to remain secure.

To learn more about cryptography, we suggest the book Codebreakers by David Kahn!

Check out this table we made for the timeline of cryptography!

Era of cryptography Description
Historical Ciphers (read more) This era covers the early history of cryptography, including ancient ciphers such as the Caesar cipher and Pigpen cipher. These ciphers were used for secrecy and military communication, often relying on substitution and transposition techniques. Nowadays, they are considered incredibly weak since ciphers relying on substitution of one character with another one assigned to it are easily broken with frequency analysis.
Classical Cryptography This era includes the development of classical cryptographic techniques, such as the Vigenère cipher, Hill cipher, and the Enigma machine used during World War II. These ciphers introduced more complex mathematical operations, such as polyalphabetic substitution and modular arithmetic and matrix operations, to enhance security.
Modern Cryptography This era marks the shift towards mathematical-based cryptographic techniques, including the development of symmetric key algorithms like AES and DES for encryption and decryption. Asymmetric key algorithms, such as RSA and Diffie-Hellman, were also introduced during this era, revolutionizing secure communication by allowing for secure key exchange without the need for pre-shared keys.
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Quantum Cryptography This era introduces the use of principles from quantum mechanics to secure communication. Quantum cryptography leverages the properties of quantum particles, such as superposition and entanglement, to achieve secure key exchange, with examples like Quantum Key Distribution (QKD) protocols.
Post-Quantum Cryptography This era focuses on the development of cryptographic techniques that are resistant to attacks by quantum computers, which pose a threat to traditional cryptographic systems. Post-quantum cryptography involves exploring new mathematical approaches, such as lattice-based cryptography, code-based cryptography, and hash-based cryptography, to ensure security in the post-quantum computing era.

Here are some videos you can check out about cryptography!