Information as Geometric Trajectories in Cube State Spaces

This paper proposes a novel cryptographic construction called Cube-Gematria Fractal Cryp
tography, which integrates permutation group dynamics, numerical encoding, and fractal-inspired
nonlinear transformations.
The core idea is to map symbolic input strings into a structured state evolution on a Rubik’s
Cube configuration space, where each elementary operation is represented as a permutation
acting on a 54-element state vector. This discrete dynamical system is further combined with a
gematria-like encoding scheme that transforms operation sequences into numerical representa
tions.
To enhance nonlinearity and diffusion, the model introduces modular arithmetic-based com
pression functions and a fractal-inspired scaling layer motivated by the self-similarity properties
of the Koch curve. Additionally, an optional wave-modulated parameter extension is proposed
to introduce controlled dynamical variability into cryptographic parameters.
The resulting system forms a hybrid construction combining elements from group theory,
discrete dynamical systems, nonlinear arithmetic, and fractal geometry. While the function
exhibits strong structural diffusion and high sensitivity to input perturbations, it is not claimed
to satisfy formal cryptographic security proofs under standard adversarial models.
This work is intended as a theoretical framework exploring the interaction between com
binatorial group actions and nonlinear cryptographic transformations, rather than a finalized
industrial cryptographic primitive.