Qusicryslals in Vernam cipher

TL;DR

This work addresses secure key management for the Vernam cipher by proposing a quasicrystal-based one-time pad constructed via the cut-and-project method. A 1D quasicrystal $\Lambda_{\tau}(\Omega)$, defined by irrational slopes $\tau,\tau'$ and an acceptance window $\Omega$, yields a finite set of minimal-distance symbols that serve as a binary pad when mapped to $\{0,1\}$ and applied with modulo-2 addition $($XOR$)$ to the plaintext. The authors provide concrete examples and lay out a practical algorithm where the key consists of a small set of random integers and real parameters $(m,a,b,c,d)$ that uniquely determine the pad; they also discuss partial key transmission and generalizations to higher dimensions or modulo-3 encodings. The approach aims to reduce key storage and transmission overhead while preserving the perfect secrecy hallmark of one-time pads, with potential extensions to image data and quantum-resistant contexts. Overall, the paper establishes a mathematically grounded, compact-key framework for quasicrystal-based encryption and outlines directions for implementation and analysis of stability and scalability.

Abstract

We propose a modification of the classical Vernam cipher based on properties of one-dimensional quasicrystals. The method uses the sequence of quasicrystal minimal distances as an one-time pad. The main advantages are strict aperiodicity of such sets and rather short key that uniquely defines quasicrystal.

Figures (1)

• Figure 1: Construction of one-dimensional quasicrystal from $\mathbb{Z}_2$ lattice