Year: 2026
Type: article
Abstract: MD-Hill-SPN is the first Hill-based construction to combine a multi-tier diffusion mix layer, a memory-hard KDF, and a simultaneous multi-metric empirical evaluation. Two independent runs of the full metric suite yield: (a) full plaintext avalanche from round 1 (mean 63.97–64.67 of 128 bits, ideal 64); (b) the differential-probability sampling floor of 2×10⁻⁵ reached at round 4 (50,000 of 50,000 output differences distinct, both sessions); (c) algebraic-degree lower-bound saturation at the maximum observable value from round 1; (d) linear bias indistinguishable from random (combined exceedance 4.40%, below the 4.55% noise floor); and (e) branch numbers at the Singleton (MDS) bound for every tier (B = 5 for 4×4, B = 9 for 8×8, B = 17 for 16×16), computed exhaustively over weight-1 inputs. MD-Hill-SPN therefore moves beyond theoretical construction to a construction that passes a defined empirical evaluation suite: avalanche, differential sampling, linear-bias probing, algebraic-degree lower bounds, and MDS branch numbers under single-key, known-plaintext conditions with fixed parameters, an evaluation no prior Hill cipher variant has reported in full.
DOI: 10.3390/jcp6030104
Author: Porter E. Coggins
Institution: Bemidji State University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,207
OpenAlex ID: W7164996704