Block Geometry in Chaos-Based Image Encryption: Security and Throughput Trade-Offs of a Four-Round Arnold Cat–Logistic Map Cipher

Image streams carried by surveillance networks, clinical imaging systems and IoT sensing platforms are routinely stored and transmitted over channels their owners do not control, so confidentiality has to be provided by the data itself rather than by the network. Chaos-based ciphers answer that need cheaply, but the block geometry of their permutation stage is usually fixed by fiat and never examined. This paper reports a four-round confusion–diffusion cipher that pairs block-wise Arnold Cat Map permutation with S-box substitution and a combined SHA-256/logistic-map XOR diffusion, and measures what the choice of block geometry actually costs and buys. Five block sizes (16 to 256) and three overlap ratios (0%, 50% and 75%) were evaluated on the 24-image Kodak Lossless True Color Image Suite against histogram, entropy, correlation, differential, key-sensitivity, keystream-randomness and integrity criteria. Overlap raised encryption time by up to 86% while leaving entropy, correlation, NPCR and UACI statistically unchanged, so the non-overlapping $128\times 128$ configuration was adopted. That configuration reaches an information entropy of 7.9998 bits (pooled across the three color channels), a mean chi-square of 253.44 against an ideal of 255, adjacent-pixel correlation near zero, and differential scores of NPCR $99.61\%$ and UACI $33.46\%$ against ideals of $99.609\%$ and $33.464\%$, with a 128-bit key space and sensitivity to parameter perturbations of ${10}^{-14}$ under a 128-bit key. Decryption is exactly lossless (MSE $=0$, CC $=1$) and throughput reaches a mean of $6.79$ MB/s (${10}^6$ bytes/s) with a keyed HMAC-SHA-256 tag that makes any ciphertext tampering detectable with overwhelming probability: across salt-and-pepper noise, Gaussian noise, occlusion and clipping at every tested level, not one damaged ciphertext passed verification.