From Schreier graphs to secure s-boxes using a group-theoretic design framework
Abdul Razaq, Muhammad Ramzan, Qin Xin, Hanan Alolaiyan, Dilshad Alghazzawi · 2026
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Description
Abdul Razaq and four co-authors present a 2026 method for building secure substitution boxes, the nonlinear parts of symmetric ciphers that scramble data during encryption. Their construction starts with the action of the modular transformation group on a projective line over a finite field with 257 elements. That action produces Schreier graphs, and the cycle structure of those graphs forms an initial 8 by 8 substitution box. A non-abelian permutation group then rearranges the box positions to refine the design.
The finished box was checked against standard cryptographic tests, including nonlinearity, differential uniformity, the strict avalanche test, bit independence, and linear approximation odds. It also performed well in an image encryption trial judged by texture measures such as contrast, correlation, energy, homogeneity, and entropy from gray-level co-occurrence matrices. The authors argue the graph-based route gives strong random-looking scrambling for encryption and image work.
Catalog record
| CREATOR | Abdul Razaq, Muhammad Ramzan, Qin Xin, Hanan Alolaiyan, Dilshad Alghazzawi |
|---|---|
| YEAR | 2026 |
| COLLECTION | PAPERS |
| FORMAT | TXT |
| FILE SIZE | 131071 |
| LICENSE | https://creativecommons.org/licenses/by/4.0 |
| RIGHTS | CC BY |
| SOURCE | Europe PMC |