Cryptography

Introduction to Cryptography

Cryptography is the art and science of concealing meaning, derived from the Greek words "kryptos" (hidden) and "graphein" (writing). It is the foundation of modern information security, enabling confidentiality, integrity, and authentication of digital communications.

Cryptographic Terminology

Basic Terms

• Plaintext: The original, readable message or data
• Ciphertext: The encrypted, unreadable message
• Cipher: The algorithm used for encryption/decryption
• Key: The secret parameter used in encryption
• Encryption: Converting plaintext to ciphertext
• Decryption: Converting ciphertext back to plaintext

A Cryptosystem

A cryptosystem is formally defined as a 5-tuple (E, D, M, K, C):

• E: Encryption function
• D: Decryption function
• M: Message space (all possible plaintexts)
• K: Key space (all possible keys)
• C: Ciphertext space (all possible ciphertexts)

Classical Ciphers

The Caesar cipher is a simple substitution cipher where letters are shifted by a fixed number (the key):

Plain:  A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Cipher: D E F G H I J K L M N O P Q R S T U V W X Y Z A B C

With key = 3: "HELLO" → "KHOOR"

Symmetric Encryption

Also known as secret-key or shared-key encryption, symmetric encryption uses the same key for both encryption and decryption.

Types of Symmetric Ciphers

Block Ciphers

• Encrypt data in fixed-size blocks (typically 64 or 128 bits)
• Modes: ECB, CBC, CTR, GCM
• Examples: DES, AES, Blowfish

Stream Ciphers

• Encrypt data one byte or bit at a time
• Generate a keystream combined with plaintext
• Examples: RC4, ChaCha20, Salsa20

Advantages & Disadvantages

Asymmetric Encryption

Also known as public-key cryptography, asymmetric encryption uses a pair of mathematically related keys: a public key and a private key.

Key Uses

• Encryption: Encrypt messages using recipient's public key
• Digital Signatures: Sign messages using sender's private key
• Key Exchange: Securely exchange symmetric keys

Advantages & Disadvantages

Common Encryption Algorithms

Symmetric Algorithms

DES (Data Encryption Standard)

• 56-bit key, 64-bit block size
• Developed by IBM and NSA in 1977
• Now considered insecure (brute-forceable)
• 3DES (Triple DES) uses three rounds for better security

AES (Advanced Encryption Standard)

• 128, 192, or 256-bit key sizes
• 128-bit block size
• Selected as the standard in 2001
• Used worldwide, considered secure

Asymmetric Algorithms

RSA (Rivest-Shamir-Adleman)

• Based on difficulty of factoring large primes
• Typical key sizes: 2048, 4096 bits
• Most widely used public-key algorithm
• Used for encryption, digital signatures, key exchange

Elliptic Curve Cryptography (ECC)

• Based on elliptic curve discrete logarithm problem
• Smaller keys than RSA for equivalent security
• Used in mobile devices due to efficiency
• Examples: ECDSA, ECDH

Key Distribution

Key distribution is one of the most challenging problems in cryptography. How do you securely share a secret key with someone you can't meet in person?

Symmetric Key Distribution Methods

• Manual Distribution: Physically meeting to exchange keys
• Key Distribution Centers (KDC): Trusted third party distributes keys
• Key Encapsulation: Encrypt key with recipient's public key

Hybrid Approach

Most practical systems use both symmetric and asymmetric encryption:

1. Use asymmetric encryption to securely exchange a symmetric key
2. Use symmetric encryption for the actual data (for speed)