Cryptography Study Guide Notes

Randomness

• Randomness is crucial in cryptography for several applications, including:

  • Secure key generation.

  • Initialization Vectors (IVs).

  • Nonces (number used once).

• There are different types of randomness:

  • True randomness: Generally considered the best and most unpredictable.

  • Pseudo-randomness: Algorithms that generate seemingly random numbers but are deterministic.

Stream Cipher

• A stream cipher encrypts data one bit or byte at a time.

• It combines a keystream with the plaintext using the XOR operation.

• Example of stream cipher encryption: $ciphertext = ''.join(chr(ord(p) ^ ord(k)) for p, k in zip(plaintext, key))$

  • This code iterates through the plaintext and key, XORs the ordinal value of each character, and joins the resulting characters to form the ciphertext.

Block Cipher

• A block cipher encrypts data in fixed-size blocks (e.g., 64-bit blocks).

DES (Data Encryption Standard)

• DES is an outdated block cipher.

• It's considered insecure due to its relatively short 56-bit key length.

Hash Algorithms

• Hash algorithms map an input of arbitrary size to a fixed-size output (hash or digest).

• They are primarily used for verifying data integrity.

Password Management

• A secure password management technique involves using salted hashes.

• Salting adds a unique random value to each password before hashing, making it more resistant to rainbow table attacks.

HMAC (Hash-based Message Authentication Code)

• HMAC combines a hash function with a secret key.

• It provides both message authenticity and integrity.

Diffie-Hellman Key Exchange Protocol

• The Diffie-Hellman key exchange protocol allows two parties to create a shared secret over an insecure channel.

• The process involves:

  • Two parties, typically called Alice and Bob, agree on a large prime number $p$ and a base $g$.

  • Alice chooses a secret integer $a$ and computes $A = g^a \, mod \, p$.

  • Bob chooses a secret integer $b$ and computes $B = g^b \, mod \, p$.

  • Alice sends $A$ to Bob, and Bob sends $B$ to Alice.

  • Alice computes the shared key as $shared_key = B^a \, mod \, p$.

  • Bob computes the shared key as $shared_key = A^b \, mod \, p$.

  • These two keys are equal because $B^a \, mod \, p = (g^b)^a \, mod \, p = g^{ab} \, mod \, p = (g^a)^b \, mod \, p = A^b \, mod \, p$.

RSA Encryption

• RSA is an asymmetric encryption algorithm.

• It uses a public key for encryption and a private key for decryption.

• The security of RSA is based on the difficulty of factoring large prime numbers.

Blockchain

• A blockchain is an immutable ledger.

• Each block contains:

  • The hash of the previous block.

  • Data (e.g., transactions).

  • A timestamp.

• Issues with blockchains:

  • Centralization of mining.

  • RPCA (Remote Procedure Call Authentication).

Cryptography Principles

• Cryptography aims to provide:

  • Confidentiality: Protecting data from unauthorized access.

  • Integrity: Ensuring that data has not been altered.

  • Authentication: Verifying the identity of a user or device.

  • Key Management: Securely managing cryptographic keys.

Python Functions for Cryptography

• ord(char): Converts a character to its integer representation.

• chr(num): Converts an integer to its character representation.

• secrets.randbelow(100): Securely generates a random integer less than 100.

• Example of generating ciphertext from XORing plaintext with a key:
  $ciphertext = ''.join(chr(ord(p) ^ ord(k)) for p, k in zip(plaintext, key))$

One-Time Pad

• Encrypting a message using a randomly generated key of the same length as the message.

• import random

  key = random.randint(0, 255)

  ciphertext = ''.join(chr(ord(c) ^ key) for c in message)

RSA Implementation Example

• Using the Crypto.PublicKey library to generate RSA keys.

• Example:

from Crypto.PublicKey import RSA

key = RSA.generate(2048)
public_key = key.publickey().export_key()
private_key = key.export_key()

SHA256

• SHA (Secure Hash Algorithm): A family of cryptographic hash functions used to ensure data integrity and authenticity; commonly utilized in digital signatures and certificates.

• from hashlib import sha256

  digest = sha256(message.encode()).hexdigest()