CSH-256: A Modular Cubing–Based Approach toStrengthening the Critical Path in Hash Functions

Parallelizable hash functions enable efficient hardware but may introduceasymmetries exploitable by adversarial parallelization. We present CSH-256, acompression function integrating modular cubing at fixed intervals within aMerkle–Damg˚ard framework. The design leverages the AES S-Box nonlinearity and SHA-256 structure to increase sequential dependency along the criticalpath, limiting parallel attack efficiency. Under explicit assumptions, we analyzethe construction’s indifferentiability from a random oracle and model its parallelcomplexity. The parallel speedup is S(P) = O(W/D), where W and D denotetotal work and critical path depth. For N = 4096 and q = 240, the indifferentiability advantage is negligible, dominated by O((Nq)2/2256). Empiricalevaluations demonstrate a saturation of parallel speedup consistent with thetheory. Unlike memory-hard alternatives (Argon2, scrypt) requiring 16–64 MBfootprints, CSH-256 achieves parallel resistance using only 1.5 KB of memory. Byproviding formal guarantees absent in prior constructions (bcrypt, PBKDF2),our results suggest applicability in resource-constrained authentication contexts.