Comparing Chaotic Maps as Pseudorandom Generators for Stream Cipher Encryption
TL;DR
A comparative study of five well-known chaotic maps as keystream generators for a basic XOR stream cipher confirms that mathematical chaos alone does not guarantee cryptographic randomness, and that map selection, parameterisation, and output-extraction method are critical design choices for chaos-based stream ciphers.
Abstract
Chaos theory offers a compelling foundation for cryptographic pseudorandom number generation owing to the extreme sensitivity of chaotic dynamical systems to initial conditions. This paper presents a comparative study of five well-known chaotic maps—Logistic, Tent, Sine, Piecewise Linear Chaotic Map (PWLCM), and Hénon—as keystream generators for a basic XOR stream cipher. Each map is evaluated under identical conditions using five statistical metrics: keystream bit balance, 8-bit Shannon entropy, adjacent-byte Pearson correlation, compression ratio, and avalanche bit error rate (BER). Results show substantial variation in cryptographic suitability. The tent map produces keystreams closest to ideal randomness across all metrics, exhibiting near-perfect bit balance, the highest entropy (7.95 bits/byte), near-zero byte correlation, and incompressible ciphertext. The logistic map shows strong bit bias; PWLCM displays high adjacent-byte correlation; and the Hénon map produces compressible ciphertext with the lowest entropy, suggesting finite-precision periodicity. All five maps demonstrate strong key sensitivity (BER ≈ 0.50). These findings confirm that mathematical chaos alone does not guarantee cryptographic randomness, and that map selection, parameterisation, and output-extraction method are critical design choices for chaos-based stream ciphers.