Cryptography Unit 3 - Comprehensive Study Notes

What is Cryptography?

Cryptography is the practice and study of techniques for secure communication in the presence of third parties.
Aim: ensure that a given message is read by the reader and the receiver exclusively.

In modern applications it is crucial to communicate securely, such as:
- transferring funds electronically,
- storing users' information in databases (e.g., Facebook, Twitter).
With blockchain technologies (Bitcoin, Ethereum), secure communication remains essential.

Plaintext:
- Any readable data, including binary files.
- It is the input into a crypto system.
- Plaintext can be utilized without the need for decryption algorithms (or a key).
Ciphertext:
- The result of encryption performed on plaintext using an algorithm.
- Ciphertext is not human readable.
- We need a decryption algorithm (and usually a key) to recover plaintext.

Encryption: the process of encoding a given message so that only authorized parties can access it.
Decryption: the inverse operation, decoding a message to recover the plaintext.
Key: a sequence required for both encryption and decryption.

Encryption: ciphertext = f(plaintext, key)
Decryption: plaintext = f^{-1}(ciphertext, key)
Represented as:
- \text{ciphertext} = f(\text{plaintext}, \text{key})
- \text{plaintext} = f^{-1}(\text{ciphertext}, \text{key})

Uses a single key for both encryption and decryption:
- \text{ciphertext} = f(\text{plaintext}, \text{key})
Why called a "private key" or "symmetric" cryptosystem.
Main problem: the private key must be exchanged securely, and there are many keys in a network (one per pair of communicating users).

If there are N users in a network and each pair uses a unique private key to communicate, how many unique private keys are needed?
Options:
- A. N/2
- B. N
- C. N+N
- D. NXN
- E. I don’t want to let you know my answer.
Correct count (theoretically): \binom{N}{2} = \frac{N(N-1)}{2}
Note: None of the given options in the slide match this, highlighting the complexity of key management in symmetric networks.

Uses different keys for encryption and decryption:
- Ciphertext = f(plaintext, public_key)
- Decryption uses the private key: plaintext = f^{-1}(ciphertext, private_key)
This is why it is called a public key cryptosystem or asymmetric cryptosystem.

Private key: must be kept private by the owner.
Public key: can be known by anyone in the network.
Example workflow:
- Alice wants to send a message to Bob.
- Alice encrypts the message using Bob's public key.
- Bob decrypts the message using his own private key.

Q1: What is a key in cryptography?
- Options (summary): The encrypted message; A sequence needed for encryption and decryption; The decrypted message.
- Correct notion: The key is a sequence needed for both encryption and decryption.
Q2: A cryptosystem that uses the same key for encryption and decryption is called:
- Symmetric (private key) cryptography.
Q3: The cryptosystem that uses two keys (private and public) is:
- Public key cryptography (asymmetric encryption).

Objective: Create a Python program to perform encryption and decryption using XOR.
Encryption rule: To encrypt, XOR a plaintext message M with a private key K: E = M^K
Decryption rule: To decrypt, XOR the encrypted message E with the same key K: M = E^K
Important: the same operation (XOR) can be used for both encryption and decryption.
Operation details:
- XOR (exclusive OR) is a binary operation that yields true when the inputs differ.
- In Python, XOR is represented by the caret symbol: ^.
- The operation can be performed between elements from bytearrays, not just strings.
Practical notes for Lab 1:
- Example syntax reference: A ^ B, where A and B are elements from bytearrays.
- Encoding: 'I am the king of the north'.encode('utf-8') converts a string to a bytearray.
- Decoding: bytearray_value.decode('utf-8') converts a bytearray back to a string.
- Pay attention to indentation in Python programs.

plaintext as input to a cryptosystem corresponds to data intended for secure handling.
ciphertext as output of encryption corresponds to protected data.
Plaintext can be binary or text; ciphertext is not human-readable until decrypted.
The security of symmetric systems heavily depends on secure key exchange and key secrecy.

Cryptography underpins secure online transactions, data privacy, and authentication.
In real-world systems, hybrid approaches are common: symmetric encryption for data at rest or in bulk, with asymmetric crypto used for secure key exchange (e.g., TLS).
Public-key cryptography enables digital signatures and identity verification in addition to confidentiality.

The balance between strong cryptographic protections and user accessibility.
Trade-offs between performance (speed of symmetric vs asymmetric) and key management complexity.
Implications for surveillance, privacy rights, and security governance.

Encryption function and decryption function: \text{ciphertext} = f(\text{plaintext}, \text{key}), \text{plaintext} = f^{-1}(\text{ciphertext}, \text{key})
Symmetric key concept: single key for both encryption and decryption; key must be kept secret and shared securely only with intended recipients.
Asymmetric key concept: pairs of keys (publickey, privatekey) where the public key is distributed openly and the private key is kept secret.

World War II cryptography: Enigma and Colossus illustrate the historical importance of secure communications.
Modern secure communications include financial transactions and social media data protection.
Blockchain technologies reinforce the importance of secure communication channels.
Lab 1 emphasizes XOR-based symmetric encryption and Python-related implementation notes, including byte-level operations and string encoding/decoding.