Cellular automata (CA) are discrete computational models capable of generating complex behaviour from simple local rules, making them a natural candidate for lightweight image encryption on resource-constrained hardware. While prior CA-based encryption schemes have demonstrated strong cryptographic performance, no existing work characterises how that performance is distributed across the full keyspace. This dissertation addresses that gap by implementing a 2D second-order reversible CA-based image encryption scheme and systematically characterising its cryptographic properties across the keyspace of balanced rule-sets.

Confusion and diffusion — Shannon's two criteria for secure encryption — are measured empirically across samples of over 2,000 and 1,000 balanced keys respectively, using images from the USC-SIPI dataset. Novel spatial uniformity metrics, the Local Confusion Distribution (LCD) and Local Diffusion Distribution (LDD), are introduced to supplement global measures and detect spatial bias in the cipher. A theoretical model is derived from first principles to predict confusion convergence behaviour under the second-order recurrence relation.

Results show that approximately 99\% of sampled balanced keys achieve near-optimal confusion within 16 iterations and near-optimal diffusion within 384 iterations, demonstrating that strong cryptographic performance is typical across the keyspace rather than exceptional. A small number of keys are found to never converge regardless of iteration count, with their failure attributed to structural properties of their rule-sets. The theoretical model correctly captures the qualitative S-shaped convergence behaviour but systematically overestimates convergence rate due to idealising independence assumptions, acting as an upper bound rather than a predictor. These findings represent the first systematic keyspace characterisation of a 2D CA-based image encryption scheme.