A Scalable Hybrid Encryption Framework Based on Unimodular Hill Cipher and Chaotic Logistic XOR Stream Cipher for Secure Binary File Protection

Technical Summary: A Scalable Hybrid Encryption Framework Based on Unimodular Hill Cipher and Chaotic Logistic XOR Stream Cipher

Problem Statement
The rapid expansion of digital information exchange across cloud platforms, industrial infrastructures, and governmental systems has intensified the need for cryptographic techniques capable of securing arbitrary binary data. While traditional algorithms like the Hill Cipher offer strong diffusion through matrix multiplication, they suffer from inherent linearity, making them vulnerable to known-plaintext and chosen-plaintext attacks. Conversely, chaotic systems provide nonlinearity and confusion but often lack the structural robustness of matrix-based transformations. Furthermore, many existing hybrid approaches are optimized for image encryption, failing to address the heterogeneous structures, metadata, and compression rules of general binary files (e.g., DOCX, PDF, executables). There is a gap in scalable, format-independent encryption frameworks that simultaneously ensure high statistical security, computational efficiency, and lossless reconstruction for diverse binary file types.

Methodology
The authors propose a hybrid encryption framework that integrates the Unimodular Hill Cipher (UHC) with a Chaotic Logistic Map-based XOR Stream Cipher. The methodology treats all input files as raw byte streams, eliminating the need for format-specific preprocessing. The encryption process consists of two primary layers:

1. Unimodular Hill Cipher (Diffusion Layer):

   • The plaintext is partitioned into fixed-length blocks of 256 bytes ($16 \times 16$ matrix dimension).
   • A key matrix is generated as a unimodular matrix (determinant = $\pm 1$), ensuring invertibility over integer arithmetic without requiring complex modular inverse calculations.
   • The matrix is constructed dynamically using chaotic pseudo-random sequences to populate an upper-triangular matrix, which is then transformed via elementary row operations to maintain unimodularity.
   • Encryption is performed via matrix multiplication modulo 256: $C_i = M \cdot P_i \pmod{256}$.

2. Chaotic Logistic XOR Stream Cipher (Confusion Layer):

   • A Logistic Map ($x_{n+1} = r x_n (1 - x_n)$) generates a pseudo-random keystream.
   • The initial seed ($x_0 = 0.73911$) and control parameter ($r$) are used to produce a sequence of chaotic values, which are quantized into 8-bit bytes.
   • The intermediate ciphertext from the Hill layer undergoes an XOR operation with this keystream: $C'_i = C_i \oplus K_i$.
   • This layer introduces nonlinearity, obscuring the algebraic relationships inherent in the matrix transformation.

Decryption reverses this process: the XOR masking is removed first, followed by multiplication with the inverse unimodular matrix ($M^{-1}$), guaranteeing exact, lossless recovery of the original binary file.

Key Contributions

• Format Independence: The framework processes arbitrary binary files (DOCX, PDF, JPEG) as raw byte streams, requiring no knowledge of internal file structures or metadata.
• Hybrid Security Architecture: The combination of UHC and Logistic XOR addresses the linearity of classical Hill Ciphers and the potential predictability of standalone chaotic streams, creating a system with both strong diffusion and nonlinear confusion.
• Scalability and Efficiency: The design supports linear time complexity ($O(N)$) relative to file size, enabling efficient processing of large datasets (up to 100 MB) without significant throughput degradation.
• Comprehensive Evaluation: The study validates the framework across twelve test files with varying sizes and formats, utilizing a broad suite of security metrics including entropy, correlation, avalanche effect, chi-square tests, and MD5 integrity verification.

Experimental Results
The framework was evaluated using 12 binary files (DOCX, PDF, JPEG) ranging from 1 MB to 100 MB on a standard CPU environment (Intel Xeon 2.20 GHz).

• Statistical Security:

  • Entropy: The average ciphertext entropy reached 7.9999, nearly identical to the ideal value of 8.0, indicating a uniform byte distribution.
  • Correlation: The average correlation coefficient between adjacent bytes was −0.0043, demonstrating negligible statistical dependence.
  • Avalanche Effect: For PDF datasets, the avalanche effect was 50.0020%, confirming that minor input changes result in significant ciphertext variations.
  • Chi-Square Test: A p-value of 0.967092 for PDF datasets indicated that the ciphertext distribution closely follows a uniform random distribution.
  • Key Sensitivity: A sensitivity of 99.6139% was achieved, showing that slight key modifications produce drastically different ciphertexts.

• Performance:

  • Throughput: The system achieved average encryption and decryption throughputs of 24.48 MB/s and 23.83 MB/s, respectively.
  • Scalability: Throughput remained stable as file sizes increased, with linear scalability observed.
  • Overhead: Ciphertext expansion was negligible (e.g., 0.005% for a 815 KB PDF), preserving storage efficiency.

• Integrity: All decrypted files produced MD5 hashes identical to the original plaintexts, confirming 100% lossless reconstruction.

Significance and Claims
The paper claims that the proposed hybrid UHC–Logistic XOR framework effectively balances security, computational efficiency, scalability, and compatibility. By integrating unimodular matrix transformations with chaotic masking, the system achieves near-ideal randomness and strong resistance to statistical attacks while maintaining the ability to encrypt diverse binary file formats without data loss.

The authors acknowledge that while the framework demonstrates strong statistical security, the study is limited to general statistical metrics. They note that resistance to specific advanced cryptanalytic attacks (such as known-plaintext attacks against the linear structure) was not deeply explored in this iteration. Additionally, the current implementation is sequential; future work could explore parallel computing or hyperchaotic systems to further enhance throughput and security complexity. The study positions the framework as a practical solution for modern binary file protection, offering a robust alternative to image-specific or format-dependent encryption schemes.