Cube Cryptography — 3D Lattice Permutation Cipher

An interactive, physical group theory stream cipher and peer-to-peer secure messaging application built on Astryx Design System (@astryxdesign/core + @astryxdesign/theme-neutral) and Three.js.

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Overview

Cube Cryptography models cryptographic entropy through the $4.33 \times 10^{19}$ permutation state space of a Rubik's cube lattice. Unlike traditional linear feedback shift registers (LFSR), Project Cube constructs non-linear keystreams via physical 3D spatial rotations, Continuous Cipher Feedback (CFB), and discrete spatial sensor extraction.

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Built with Astryx Design System

The application is built on Astryx components and design tokens wrapped under a custom dark neutralTheme:

• Chat System: Built using @astryxdesign/core/Chat (ChatMessageList, ChatMessage, ChatMessageBubble, ChatSystemMessage, and ChatSendButton).
• Navigation & Layout: TopNav, TopNavItem, Divider, Theme, and responsive drawer triggers with IconButton.
• Form & Parameter Controls: TextInput, TextArea, CheckboxInput, Slider, and SegmentedControl.
• Progressive Disclosure & Feedback: TabList, Tab, CollapsibleGroup, Collapsible, Tooltip, Kbd, StatusDot, Dialog, and DialogHeader.
• Design Tokens: Complete color, radius, spacing, and typography token integration via @astryxdesign/theme-neutral.

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Application Suite

1. Architectural Overview (index.html)

• Physical Permutation Engine: Interactive group theory introduction.
• Live Centerpiece Visualizer: Dual-mode (Encrypt/Decrypt) synchronized telemetry stream displaying Plaintext -> Keystream -> Ciphertext in real-time.
• Pipeline Walkthrough: 4-stage interactive walkthrough powered by Astryx TabList.
• Theoretical Specification: Mathematical breakdown with Astryx CollapsibleGroup.

2. Cryptographic Lab (lab.html)

• 3D Permutation Studio: Full WebGL camera controls with real-time state hashing.
• Step-by-Step Operator: Live algebraic readout inspecting (Input ± Sensor ± StepConstant) % 53 = Output.
• Speed & Animation Controls: Real-time rotation speed adjustments via Astryx Slider.
• Research Guide: Modal walkthrough powered by Astryx Dialog.

3. P2P Secure Chat (chat.html)

• Real-time WebRTC Mesh: Serverless peer-to-peer transmission via PeerJS with global STUN/TURN fallback.
• Live 3D Lattice Encryption: Outgoing messages mechanically rotate the sender's cube, transmitting the ciphertext stream; incoming messages physically rotate the receiver's cube during decryption.
• Channel Collision Detection: Prevents state desynchronization with automatic alerts.

4. Project Lore & Origins (lore.html)

• Story Archive: The origin story of the speedcubing accident, lost mouse incident, and the Eureka moment.

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Mathematical Specification

1. The Permutation Group

The cipher machine operates over the Rubik’s permutation group $G = \langle U, D, L, R, F, B \rangle$. A shared secret seed permutes the initial baseline state across 43 quintillion possible configurations: $$\text{Lattice}_0 = \text{Permute}(\text{SeedKey}) \in G$$

2. Spatial Sensor Extraction

Before encoding character $i$, the engine samples the cubie at the Front-Top-Right $(1, 1, 1)$ coordinate: $$K_i = \text{Lattice.Sample}(x=1, y=1, z=1) \in [0 \dots 52]$$

3. Cipher Feedback (CFB) Rotation

The generated ciphertext character $C_i$ mechanically rotates the lattice before character $i + 1$: $$\text{Move}_{i+1} = \text{MovesList}[\text{ASCII}(C_i) \pmod 6] \in {U, U', R, R', F, F'}$$

4. Modulo-53 Character Transformation

$$C_i = (P_i + K_i + RC_i) \pmod{53} \quad \Big| \quad P_i = (C_i - K_i - RC_i) \pmod{53}$$

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Tech Stack

• UI Framework: React 19
• Design System: @astryxdesign/core & @astryxdesign/theme-neutral
• 3D Graphics Engine: Three.js
• P2P Transport: PeerJS (WebRTC)
• Build Tool: Vite

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Getting Started

1. Clone the Redesign Branch

git clone -b astryx-redesign https://github.com/Geervan/Cube-Cryptography-Sim.git
cd Cube-Cryptography-Sim

2. Install Dependencies

npm install

3. Start Development Server

npm run dev

Open http://localhost:5173 to explore the suite.

4. Production Build

npm run build

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Author

• Geervan — LinkedIn • GitHub