Quantum HKDF — Cryptographic Key Generation Through Penrose Tiling

Introduction

When thinking about the world of cryptography, the fusion of mathematical elegance with cryptographic robustness is what will herald a new era of innovation. This detailed walkthrough introduces a different approach that intertwines the intricate Penrose tiling with the principles of cryptography, laying the groundwork for a unique cryptographic key generation and data encryption method.

Penrose Tiling: A Mathematical Marvel

Penrose tiling, named after mathematician Roger Penrose, is renowned for its non-repetitive, aperiodic tiling pattern. This mathematical phenomenon creates an endlessly complex mosaic without recurring motifs, captivating mathematicians and physicists with its simplicity and profundity.

The genesis of the proposed cryptographic method lies in the initialization of Penrose triangles, fundamental elements of the tiling process. The initial configuration is derived through complex number calculations, distributing vertices evenly on a circular path and setting the stage for the ensuing tiling pattern:

v_i = e^(2πi/base), for i = 0, 1, ..., base*2 - 1

This formula ensures the equitable placement of vertices, integral to the formation of the…