Question

Write a program that encrypts its input by XORing it with a keystream. Find or write as good a random number generator as you can to generate the keystream. The program should act as a filter, taking plaintext on standard input and producing ciphertext on standard output (and vice versa). The program should take one parameter, the key that seeds the random number generator.

Short answer

Write a program that seeds an RNG with a key to generate a keystream, then XORs the input data with this keystream and outputs the result. Use Python's `random` module for RNG and `sys` for I/O handling.

Step-by-step solution

Understand the Problem

The task is to write a program that encrypts data by XORing it with a keystream generated by a random number generator (RNG). The program must accept a key to seed the RNG, take plaintext from standard input, and output ciphertext (or decrypt if given ciphertext).

Set Up the Environment

Choose a programming language that can easily handle standard input/output and has libraries for random number generation. Python is a good choice due to its built-in support for such tasks.

Random Number Generator Initialization

Use a pseudo-random number generator initialized with a key (the seed). In Python, you can use the `random` module where the key acts as the seed: `random.seed(key)`.

Generate the Keystream

Create a keystream by continuously generating random bytes. You can do this by calling `random.getrandbits(8)` repeatedly to get byte-sized integers.

XOR Input with Keystream

Read the input data byte by byte, and XOR each byte with each corresponding byte from the keystream. Use the XOR operator (`^`) to do this in Python.

Implement Input/Output Handling

Use standard I/O to handle input and output. In Python, use `sys.stdin.read()` for input and `sys.stdout.write()` for output to handle both encryption and decryption.

Complete the Program

Combine all steps into a complete program that reads a seed, generates a keystream, XORs it with input data, and outputs the result. Keep the logic simple and ensure input/output are handled through standard streams.

Key concepts

XOR Cipher

The XOR cipher is a simple encryption technique often used for encrypting data by combining it with a keystream. It relies on the XOR (exclusive or) operation, represented by the symbol `^` in most programming languages like Python. The XOR operation is applied to each bit of the plaintext with a corresponding bit from the keystream.

• Unique Properties: One important property of XOR is that it is reversible. Applying XOR again with the same keystream recovers the original data. This makes it handy for both encryption and decryption using the same process.
• Simplicity: The XOR cipher’s simplicity is both its strength and weakness. While it's easy to implement, when used with predictable keystreams, it can be vulnerable to attacks.
• Usage: XOR ciphers are common in creating basic cryptographic systems or as a building block in more complex encryption schemes.

Understanding the XOR cipher is crucial because it represents the basic operation at the heart of many modern cryptographic algorithms.

Random Number Generator

A random number generator (RNG) is essential in cryptography and many computer applications for producing sequences of numbers that lack any pattern. In encryption, randomness is key to ensuring data security.

• Types: RNGs are categorized into true random number generators (which rely on physical phenomena) and pseudo-random number generators (which rely on algorithms).
• Applications: RNGs are used not just in encryption but also in simulations, gaming, and anywhere uncertainty is needed.

In our encryption task, the RNG is seeded with a key, making it crucial for producing a unique keystream of random numbers which are essential for effective encryption using the XOR cipher.

Keystream Generation

Keystream generation is the process of creating a sequence of bytes or bits that is used to encrypt or decrypt a message in the XOR cipher technique.

• Process: It involves using an RNG to produce continuous random values which serve as the keystream. This stream is XORed with the plaintext to produce ciphertext.
• Importance: A strong keystream is vital for the security of the XOR cipher. If the keystream is predictable, the encryption can be easily broken.
• Implementation: In our example, using Python, we generate the keystream by repeatedly calling `random.getrandbits(8)`, which yields a series of random byte-sized integers. This keystream should be as random as possible to ensure security.

Without an effective keystream, even the cleverest application of the XOR cipher could become insecure.

Pseudo-Random Number Generator (PRNG)

A pseudo-random number generator (PRNG) is an algorithm that produces sequences of numbers that approximate the properties of random numbers.

• Deterministic Nature: Unlike true RNGs, PRNGs are deterministic, which means they use an initial seed value to generate results. Given the same seed, a PRNG will produce the same sequence of numbers.
• Predictability and Use: This predictability, while making PRNGs less random than ideal, can be advantageous in applications such as debugging, simulations, and cryptography where reproducibility is necessary.
• Application in Encryption: For our encryption program, the PRNG's seed is crucial as it ensures the uniqueness of the generated keystream each time the encrypted message is processed with that seed.

PRNGs are powerful tools in a programmer's arsenal, especially when true randomness is difficult or expensive to achieve.