Invisible Encryption

Authors: Shahzad Ahmad, Stefan Rass, and Zahra Seyedi

Abstract

This paper introduces Invisible Encryption, a novel cryptographic protocol that integrates threshold secret sharing, steganography, and public-key cryptography to enable covert communication. By embedding a secret share within standard encrypted traffic, specifically by disguising it as a session key or nonce in a hybrid encryption scheme, our method ensures that the transmission of the secret remains undetectable. The secret is reconstructed from shares derived from a public natural language text and the transmitted share, with the selection of shares protected by a secret seed. We provide a formal security analysis, demonstrating that Invisible Encryption achieves confidentiality and plausible deniability under standard cryptographic assumptions, offering a robust solution for applications requiring secure, undetectable communication such as censorship-resistant systems and whistleblower protection.

Overview

This repository contains a Python implementation of an "invisible encryption" technique that:

• Generates cryptographic shares from words in a large text
• Uses Lagrange interpolation for secret sharing/reconstruction
• Hides shares using RSA and AES-CBC encryption
• Provides performance benchmarking for cryptographic operations

The implementation demonstrates how to embed secret shares within innocuous-looking text while maintaining cryptographic security guarantees.

Key Features

• Finite Field Operations: Uses GF(p) with prime p = 2²⁵⁶ - 2³² - 977
• Text-Based Share Generation: Selects words from text to create cryptographic shares
• Threshold Secret Sharing: (k,n) threshold scheme using Lagrange interpolation
• Cryptographic Hiding:
  • Ephemeral RSA key generation (2048-bit)
  • AES-CBC encryption with random IVs
  • Combined RSA + AES encryption protocol
• Performance Measurement: Benchmarks for core operations and different configurations

Requirements

• Python 3.x
• Required packages:

pip install galois cryptography

Usage

1. Clone this repository
2. Install required packages
3. Run the demonstration:

python invisible_encryption.py

Core Functions

# Initialize finite field
GF = galois.GF(2**256 - 2**32 - 977)

# Generate secure values
x_values, x_0 = generate_secure_x_values(num_shares, GF)

# Map text to shares
shares = text_to_shares(large_text, num_shares, x_values, GF)

# Create new share
indices, x_new, s_new = create_new_share(secret, x_values, shares, k, GF, x_0)

# Reconstruct secret
reconstructed = reconstruct_secret(points, GF)

# Hide share with cryptographic protocol
encrypted_payload, ciphertext, private_key = hide_share_in_protocol(s_new, x_0, decoy_payload)

Performance Benchmarks

Table 1: Core Operation Performance

Operation	Mean Time (ms)	Std Dev (ms)	Memory (KB)
Field Initialization	1.345	0.565	226,084
Secure x-value Generation (n=5)	0.400	0.517	226,084
Text-to-Shares Mapping (n=5)	0.200	0.422	226,084
New Share Creation (k=3)	1.700	0.675	226,084
Secret Reconstruction (k=3)	1.601	0.838	226,084
RSA Encryption (2048-bit)	293.057	116.081	226,088
AES-CBC Encryption (decoy, 1KB)	316.110	252.428	226,088

Table 2: Threshold Scheme Performance

Parameters	Share Gen (ms)	New Share (ms)	Secret Recon (ms)	Total (ms)	Overhead (bytes)
k=3, n=5	0.197	2.071	2.140	104.407	544
k=5, n=10	0.300	4.641	3.148	108.090	544
k=7, n=15	0.212	6.713	9.891	116.816	544

Table 3: Decoy Encryption Performance

Payload Size	Encryption (ms)	Decryption (ms)	Ciphertext Size
1 KB	292.504	0.323	1,040 bytes
10 KB	298.280	0.393	10,256 bytes
100 KB	205.628	0.496	102,416 bytes
1 MB	314.813	0.575	1,048,592 bytes

License

This work has been partially supported by the LIT Secure and Correct Systems Lab funded by the State of Upper Austria.

Disclaimer

This code is provided "as-is" for research and educational purposes only. It has not been audited or hardened for production use. Do not use with sensitive data without proper security review.