3.3 Stream ciphers and pseudo-random number generators

Stream ciphers are a crucial part of symmetric key cryptography, encrypting data bit by bit using a key stream. They're fast and efficient, making them ideal for real-time applications or resource-limited devices. Understanding how they work is key to grasping modern encryption methods.

Pseudo-random number generators (PRNGs) are the heart of stream ciphers, creating the key stream that scrambles the data. These generators must be unpredictable and produce long, non-repeating sequences to ensure security. Knowing PRNG principles helps you appreciate the complexity behind seemingly simple encryption processes.

Stream cipher principles

Key characteristics and operation

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• Stream ciphers encrypt plaintext one bit or byte at a time, unlike block ciphers which operate on fixed-size blocks
• Key stream generation uses a pseudo-random number generator (PRNG) initialized with a secret key and initialization vector (IV)
• Encryption combines key stream with plaintext using bitwise XOR operation
• Security depends on unpredictability and non-repeatability of the key stream
• Two main categories exist:
  • Synchronous stream ciphers generate key stream independently of plaintext/ciphertext
  • Self-synchronizing stream ciphers generate key stream based on previous ciphertext bits
• Offer faster performance and lower computational requirements compared to block ciphers (suitable for resource-constrained environments or high-speed applications)

Security requirements and considerations

• Critical security requirement prohibits reusing the same key stream more than once (prevents two-time pad attack vulnerability)
• Key stream must be indistinguishable from truly random sequences
• Requires large internal state to resist reconstruction attacks (typically twice the size of desired security level in bits)
• Forward secrecy protects past outputs even if current state compromised
• Common designs incorporate:
  • Linear feedback shift registers (LFSRs)
  • Non-linear feedback shift registers (NLFSRs)
  • Combinations with additional non-linear components

Pseudo-random number generators in stream ciphers

PRNG fundamentals and requirements

• PRNGs produce sequences of numbers that appear random but generate through deterministic mathematical process
• Seed or initial state derives from secret key and initialization vector
• Cryptographically secure PRNGs must have long period (sequence should not repeat for very large number of generated bits)
• Statistical randomness crucial for generated sequences to pass various randomness tests
• Internal state size must be sufficiently large to resist state reconstruction attacks

PRNG properties for stream cipher security

• Unpredictability of output sequence critical for overall cipher security
• Long period prevents repetition of key stream
• Statistical randomness ensures generated sequences indistinguishable from truly random data
• Large internal state size increases resistance to state reconstruction attacks
• Forward secrecy protects past outputs even if current state compromised

Stream cipher security and cryptanalysis

Common attack vectors

• Known-plaintext attacks reveal portions of key stream with sufficient plaintext-ciphertext pairs
• Distinguishing attacks differentiate cipher output from truly random data (indicates design weakness)
• Correlation attacks exploit statistical weaknesses in key stream generator to deduce internal state or secret key
• Algebraic attacks express cipher as system of equations to solve for secret key or internal state
• Time-memory trade-off attacks (Babbage-Golic attack) recover internal state through precomputation and data storage
• Initialization attacks target weaknesses in key and IV setup process
• Side-channel attacks exploit information leaked through physical implementation (power analysis, timing attacks)

Security considerations and defenses

• Unpredictability and non-repeatability of key stream form primary security basis
• Proper key and IV management prevents key stream reuse
• Strong PRNG design resists various cryptanalytic techniques
• Large internal state increases resistance to reconstruction attacks
• Careful implementation mitigates side-channel attack risks
• Regular security audits and updates address newly discovered vulnerabilities

Stream cipher implementation

Encryption and decryption process

• Initialize PRNG with secret key and IV
• Generate key stream as needed for encryption or decryption
• Encryption combines key stream with plaintext using bitwise XOR
• Decryption applies same key stream generation process and combines with ciphertext
• Synchronization between sender and receiver ensures same key stream used for encryption and decryption
• Error propagation limited (bit error in ciphertext only affects corresponding plaintext bit during decryption)

Implementation considerations

• Never reuse same key stream (requires careful IV or nonce management)
• Optimize PRNG for target platform (use platform-specific instructions or parallelization techniques)
• Implement secure key and IV management protocols
• Ensure proper synchronization between encryption and decryption processes
• Consider trade-offs between performance and security based on application requirements
• Regularly update and patch implementations to address newly discovered vulnerabilities