Radius-Transformed Logistic Maps for High-Dimensional Data Generation: Statistical Characterization, Cryptanalysis, and Authenticated Encryption

The growing use of high-dimensional numerical data has renewed interest in chaos-based generation and encryption, yet nonlinear complexity does not necessarily imply statistical independence or cryptographic security. This study critically reassesses a radius-transformed logistic-map framework through mathematical analysis, reproducible numerical experiments, and cryptanalytic testing. Using a control parameter of 3.8, an initial state of 0.5, and radii of 0.776, 0.876, and 0.881, the investigation examines bifurcation behavior, finite-time Lyapunov exponents, numerical precision, statistical distributions, dimensionality, and encryption vulnerabilities. An exact sliding-window identity shows that adjacent multidimensional vectors share all but one coordinate. Across dimensions of 2, 4, 8, 16, and 32, participation-ratio effective rank increases from 1.913 to 27.862, whereas its normalized fraction decreases from 0.957 to 0.871. The one-, two-, and three-radius XOR keystreams exhibit empirical entropies of 6.99398, 6.99312, and 6.99416 bits per byte, respectively, although modulo-128 quantization limits the maximum to seven bits per symbol. A single plaintext-bit modification changes exactly one ciphertext bit, while deterministic keystream reuse permits recovery from known plaintext