🔐Quantum Cryptography Unit 3 – Classical Cryptography

Key Concepts and Terminology

• Cryptography involves techniques for secure communication in the presence of adversaries
• Plaintext refers to the original message or data before encryption
• Ciphertext is the result of encrypting plaintext using an encryption algorithm and key
• Encryption is the process of converting plaintext into ciphertext to protect its confidentiality
• Decryption reverses the encryption process, converting ciphertext back into plaintext using the appropriate key
• Cryptanalysis encompasses techniques used to break or bypass cryptographic security without access to the secret key
• Ciphers are algorithms used for performing encryption and decryption
  • Substitution ciphers replace each letter or group of letters with another letter or symbol
  • Transposition ciphers rearrange the order of letters in the plaintext without changing the letters themselves

Historical Context of Classical Cryptography

• Classical cryptography dates back to ancient times, with early examples found in Egyptian hieroglyphs and Roman military communications
• Julius Caesar employed a simple substitution cipher (Caesar cipher) to protect military messages
• During the Middle Ages, cryptography evolved with the development of more complex substitution ciphers (Vigenère cipher)
• The invention of the telegraph in the 19th century led to increased use of cryptography for secure long-distance communication
• World War I and World War II saw significant advancements in cryptography, including the use of mechanical encryption devices (Enigma machine)
• The development of computers in the mid-20th century marked a turning point, enabling more sophisticated cryptographic techniques

Basic Encryption Techniques

• Substitution involves replacing each letter or group of letters in the plaintext with another letter, symbol, or group of symbols
  • Monoalphabetic substitution uses a single substitution alphabet throughout the encryption process
  • Polyalphabetic substitution employs multiple substitution alphabets, switching between them based on a specific pattern or key
• Transposition rearranges the order of letters in the plaintext without changing the letters themselves
  • Simple columnar transposition writes the plaintext in rows and reads the ciphertext by columns
  • Double transposition applies the transposition process twice to increase security
• One-time pads use a unique key that is as long as the plaintext and is only used once, providing theoretically unbreakable security when used correctly

Common Classical Ciphers

• Caesar cipher is a simple substitution cipher that shifts each letter in the plaintext by a fixed number of positions in the alphabet
• Atbash cipher is a monoalphabetic substitution cipher that maps each letter to its reverse position in the alphabet (A to Z, B to Y, etc.)
• Vigenère cipher is a polyalphabetic substitution cipher that uses a keyword to determine the shifting pattern for each letter in the plaintext
• Playfair cipher is a digraph substitution cipher that encrypts pairs of letters using a 5x5 matrix derived from a keyword
• Hill cipher is a polygraphic substitution cipher that uses matrix multiplication to encrypt groups of letters
• Enigma machine was a complex electromechanical device used by Nazi Germany during World War II, employing a series of rotors and plugboards for encryption

Cryptanalysis Methods

• Frequency analysis examines the frequency of letters or groups of letters in the ciphertext to deduce the original plaintext
  • In many languages, certain letters (E, T, A in English) appear more frequently than others
  • Comparing letter frequencies in the ciphertext to known language statistics can help break substitution ciphers
• Known plaintext attack occurs when the attacker has access to both the plaintext and its corresponding ciphertext
  • By comparing the plaintext and ciphertext, the attacker can deduce the encryption key or algorithm
• Ciphertext-only attack involves attempting to break the cipher using only the intercepted ciphertext
  • Statistical analysis and pattern recognition techniques are employed to identify weaknesses in the cipher
• Brute-force attack exhaustively tries all possible keys until the correct one is found
  • The feasibility of a brute-force attack depends on the key space (number of possible keys) and available computing power

Strengths and Weaknesses of Classical Cryptography

• Classical ciphers provided a foundation for secure communication, protecting sensitive information from unauthorized access
• Substitution ciphers, when used with a large key space, can be resistant to frequency analysis attacks
• Transposition ciphers can effectively obscure the original plaintext, making it difficult to recognize patterns
• One-time pads, when used correctly, offer theoretically unbreakable security
• However, classical ciphers often rely on the secrecy of the encryption algorithm itself (security through obscurity), which is a weak form of security
• Many classical ciphers are vulnerable to frequency analysis and other cryptanalytic techniques
• The key distribution problem arises when communicating parties need to securely share the encryption key over an insecure channel
• Classical ciphers lack the computational security provided by modern cryptographic algorithms

Transition to Modern Cryptography

• The development of computers in the mid-20th century revolutionized cryptography
• Modern cryptography relies on mathematical algorithms and computational complexity to provide security
• Symmetric-key cryptography uses the same key for both encryption and decryption (AES, DES)
  • Provides fast and efficient encryption for large amounts of data
  • Requires secure key exchange between communicating parties
• Public-key cryptography (asymmetric cryptography) uses a pair of keys: a public key for encryption and a private key for decryption (RSA, ECC)
  • Eliminates the need for secure key exchange, as the public key can be freely distributed
  • Enables digital signatures and key exchange protocols
• Cryptographic hash functions (SHA-256, MD5) generate fixed-size digests of input data, providing integrity and authentication
• Modern cryptography aims to provide provable security based on well-defined computational assumptions

Relevance to Quantum Cryptography

• Quantum cryptography leverages principles of quantum mechanics to enable secure communication
• Quantum key distribution (QKD) allows for the secure exchange of encryption keys over untrusted channels
  • QKD protocols (BB84, E91) use properties of quantum states to detect eavesdropping attempts
  • Any attempt to intercept or measure the quantum states alters them, alerting the communicating parties
• Quantum computers, when fully realized, could break many classical cryptographic algorithms (RSA, ECC) that rely on integer factorization or discrete logarithm problems
• Post-quantum cryptography focuses on developing cryptographic algorithms that are resistant to attacks by both classical and quantum computers
  • Lattice-based cryptography, code-based cryptography, and multivariate cryptography are promising candidates for post-quantum security
• Understanding the limitations of classical cryptography is crucial for developing quantum-resistant cryptographic systems
• Quantum cryptography aims to provide unconditional security, moving beyond the computational security offered by classical cryptography