💻 computer science

Intelligent Adaptive Hybrid Encryption Based on Unimodular Hill Cipher, RSA-OAEP, and Chaotic Logistic Maps for Universal Digital File Security

This paper proposes an AI-driven adaptive hybrid cryptosystem that dynamically allocates Unimodular Hill Cipher and RSA-OAEP encryption based on file characteristics, utilizing Logistic Chaotic Maps for key generation to achieve robust, efficient, and lossless security for universal binary files.

Original authors: Samsul Arifin

Published 2026-07-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Samsul Arifin

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Digital Locksmith's Dilemma

Imagine your digital life as a massive, bustling city where every file you send—a photo, a song, a secret note, or a complex database—is a package traveling through the streets. To keep these packages safe from thieves, we use "encryption," which is essentially a magical lock that scrambles the contents so only the person with the right key can unscramble them. For decades, we've had two main types of locksmiths. The first type uses a super-fast, mechanical gear system (like a standard lock) that can process huge piles of packages quickly, but if someone figures out how the gears turn, they can open everything. The second type uses a heavy, unbreakable vault door (like a high-security safe) that is incredibly strong but takes forever to open and close, making it terrible for moving thousands of packages at once.

The big challenge in the world of digital security is that most files today aren't just simple letters; they are "binary files"—complex streams of data that look like random noise to a computer. Traditional methods often struggle to handle these diverse file types efficiently without slowing everything down or leaving cracks in the armor. This is where the science of "hybrid encryption" comes in. It's the idea of using the fast gear system for the heavy lifting and the heavy vault door only for the most critical parts, trying to get the best of both worlds. But what if the lock itself could look at the package, decide how big it is, and automatically choose the perfect mix of speed and strength? That is the question this research team set out to answer.

The Smart, Shape-Shifting Lock

In this study, a researcher named Samsul Arifin from the Institut Teknologi Sains Bandung proposes a new, "intelligent" way to lock up digital files. Instead of using a one-size-fits-all approach, the team built a system that acts like a curious detective. Before it even starts locking the file, it takes a quick look at the data to see how "random" or "complex" it is. Think of it like a bouncer at a club who checks your ID and outfit; if you look like a VIP (a small, sensitive file), they treat you differently than if you look like a regular guest (a huge, messy file).

The system uses three main tools to do its job. First, it has a "Unimodular Hill Cipher," which is a fancy name for a mathematical puzzle using a grid of numbers (a matrix) to shuffle data around. It's incredibly fast, like a conveyor belt that can spin thousands of items in a blink. However, to make sure this conveyor belt doesn't get stuck or lose pieces, the researchers use a special kind of grid that is guaranteed to be reversible—meaning you can always get the original items back out. Second, they use "RSA-OAEP," the heavy vault door, but only for a tiny, specific slice of the data. This adds a layer of super-strong protection without slowing down the whole process. Third, to make sure the keys they use are truly unpredictable, they use a "Chaotic Logistic Map." Imagine a butterfly flapping its wings in a way that creates a storm; this mathematical tool takes a tiny seed (like a password) and turns it into a wild, chaotic sequence of numbers that is nearly impossible to guess.

The "intelligent" part of the system is its ability to decide how much of the file to send through the fast conveyor belt versus the heavy vault. In their experiments, they tested this on a real PDF file that was about 1,783,994 bytes in size. The system analyzed the file and found it was already quite random (with an entropy score of 7.996689, which is very close to the maximum possible randomness). Because of this, the system decided to send 98.5% of the file through the fast conveyor belt and only 1.5% through the heavy vault. This is a smart move because it saves time; if they had used the heavy vault for the whole thing, it would have taken much longer.

The results of their simulations were quite impressive. When they locked the file, the resulting "ciphertext" looked like pure, random noise. The researchers measured this using a tool called "Chi-Square," which checks if the data looks like a fair roll of the dice. The original file had a score of 8159.84, indicating it had some patterns, but the encrypted file dropped to a score of 269.85, meaning it looked almost perfectly random. They also checked the "correlation" between the original and the locked file, which was nearly zero (-0.000152), proving that the two looked completely unrelated.

Perhaps the most important finding was that the system didn't lose anything. After locking and unlocking the file, the researchers checked the "SHA-256 hash," which is like a digital fingerprint. The fingerprint of the original file and the decrypted file were identical, confirming that the system could perfectly reconstruct the original document without any missing pieces or errors. They also tested how the system handled different "passwords" and matrix sizes. They found that changing the matrix size from 9 to 2026 made the encryption take longer (from 0.1498 seconds to 11.2176 seconds for encryption, and up to 95.0922 seconds for decryption), but it also made the system more complex and harder to crack.

The paper suggests that this approach offers a balanced solution: it is fast enough for large files, strong enough to protect sensitive data, and smart enough to adapt to whatever kind of file it is given. While the researchers note that larger matrix sizes slow things down significantly, the system successfully demonstrated that it could handle real-world binary files like PDFs, turning them into secure, unreadable data and then perfectly restoring them. The study concludes that this adaptive, hybrid method is a promising step forward for keeping our digital files safe in a world where data comes in all shapes and sizes.

Technical Summary: Intelligent Adaptive Hybrid Encryption Based on Unimodular Hill Cipher, RSA-OAEP, and Chaotic Logistic Maps

Problem Statement
The rapid expansion of digital communication has created a critical need for robust data protection mechanisms capable of securing heterogeneous binary files (e.g., PDFs, executables, multimedia, and scientific datasets) across diverse environments. Traditional encryption approaches face specific limitations: symmetric algorithms like AES and DES, while efficient, may lack adaptability for dynamic file properties in large-scale environments; conversely, asymmetric schemes like RSA offer strong security but introduce prohibitive computational overhead when applied directly to bulk binary data. Furthermore, existing hybrid systems often rely on static partitioning strategies that fail to account for intrinsic file characteristics such as entropy, size, and structural complexity, leading to inefficient encryption allocation. There is a notable gap in the literature regarding a unified framework that combines unimodular matrix cryptography, asymmetric protection, chaotic key generation, and adaptive intelligence specifically designed for universal binary file security.

Methodology
The proposed framework introduces an intelligent adaptive hybrid cryptographic system that dynamically allocates encryption workloads based on the statistical characteristics of the input file. The methodology consists of five primary stages:

Feature Extraction: The system analyzes the input binary file to extract a feature vector including file size ( $S$ ), Shannon entropy ( $H$ ), mean byte value ( $\mu$ ), standard deviation ( $\sigma$ ), the number of unique byte values ( $U$ ), and file extension category ( $E$ ). Shannon entropy is calculated to determine the randomness and structural complexity of the data.
Adaptive Split Decision: A rule-based AI-driven engine determines the optimal partition ratio between the symmetric and asymmetric encryption layers. Based on heuristics (e.g., files with entropy > 7.5 or size > 500 MB), the system assigns the majority of bulk data to the computationally efficient Unimodular Hill Cipher, while reserving a small, sensitive portion for RSA-OAEP encryption. This dynamic allocation balances speed and security.
Chaotic Key Generation: To ensure high unpredictability, the system employs a Logistic Chaotic Map defined by $x_{n+1} = r x_n (1 - x_n)$ with a control parameter $r=3.923$ . The initial condition $x_0$ is derived from a user password. The resulting chaotic sequence is transformed into a byte stream to populate the elements of the encryption matrix.
Hybrid Encryption:
- Unimodular Hill Cipher: The bulk data is encrypted using matrix multiplication modulo 256 ( $C = K \cdot P \mod 256$ ). The encryption matrix $K$ is constructed to be unimodular (determinant $\pm 1$ ), ensuring it is invertible under modular arithmetic, which guarantees lossless decryption ( $P = K^{-1} \cdot C \mod 256$ ).
- RSA-OAEP: A small, adaptive segment of the data is encrypted using RSA with Optimal Asymmetric Encryption Padding (OAEP) to provide semantic security and resistance against chosen-ciphertext attacks.
Ciphertext Composition and Integrity: The final encrypted file comprises a metadata header (storing partition lengths), the Hill Cipher segment, and the RSA segment. Integrity is verified using SHA-256 hashing before and after the encryption-decryption cycle.

Key Contributions
The paper identifies four primary innovations:

Adaptive Intelligence: Unlike static hybrid systems, this framework utilizes a dynamic split-ratio mechanism driven by file statistics (entropy, size, etc.) to optimize encryption allocation.
Unimodular Matrix Construction: The study employs unimodular matrices generated via elementary row operations to solve the invertibility constraints common in modular matrix cryptography, ensuring reliable decryption without numerical instability.
Chaotic Integration: The integration of Logistic Chaotic Maps for dynamic matrix generation enhances key randomness and sensitivity to initial conditions, strengthening resistance against brute-force and known-plaintext attacks.
Universal Binary Compatibility: The system operates directly on 8-bit unsigned integer arrays, enabling the encryption of arbitrary file formats without requiring file-specific preprocessing or semantic decoding.

Experimental Results
The framework was evaluated using binary PDF datasets under various matrix dimensions and password configurations. Key findings include:

Statistical Security: The encrypted files achieved a ciphertext entropy of 7.999891 (approaching the theoretical maximum of 8 for 8-bit data) and a Chi-Square statistic reduction from 8159.84 (plaintext) to 269.85 (ciphertext), indicating a near-uniform byte distribution.
Diffusion and Confusion: The Pearson correlation coefficient between plaintext and ciphertext was −0.000152, demonstrating a near-zero linear relationship and strong diffusion.
Lossless Recovery: SHA-256 hash values of the original and decrypted files were identical, confirming perfect data reconstruction.
Performance: Encryption and decryption times varied with matrix dimensions (e.g., decryption time increased from ~0.39s for a $9 \times 9$ matrix to ~95s for a $2026 \times 2026$ matrix), reflecting the $O(n^3)$ complexity of matrix inversion. However, the adaptive strategy kept RSA overhead minimal by processing only ~1.5% of the data asymmetrically.
Robustness: The system demonstrated high sensitivity to key changes; different matrix dimensions and password inputs produced entirely distinct ciphertexts and MD5 hashes.

Significance and Claims
The authors claim that this study provides a unified synthesis of chaotic dynamics, linear algebra, and asymmetric cryptography into a scalable architecture for heterogeneous binary file security. The significance of the work lies in its ability to offer a balanced combination of computational efficiency, statistical security strength, and dynamic adaptability. By avoiding dependencies on semantic file structures, the framework is presented as suitable for diverse deployment scenarios, including cloud storage, secure archival, digital forensics, and IoT environments. The paper concludes that the proposed adaptive hybrid cryptosystem successfully transforms structured binary data into highly randomized ciphertext while maintaining deterministic reconstruction accuracy, offering a robust solution for universal digital file protection.

The Digital Locksmith's Dilemma

The Smart, Shape-Shifting Lock

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