REGISTRO DOI: 10.69849/revistaft/th102412121667
Edinaldo Sá
Resumo
This paper details the methodology applied to data compression and encryption, exploring the efficiency of compression and encryption algorithms in highly variable scenarios. Using detailed benchmarks involving over 500,000 files and approximately 9,450 distinct configurations, evaluations were conducted to test both performance and security of the DRIC (Data Reduction Information Compression) system. This study compares DRIC’s effectiveness with established technologies such as Deflate, AES, RSA, and Blowfish, analysing its relevance in various contexts, ranging from data transmission to secure cloud storage. Furthermore, physical implications related to data flow and entropy are discussed, such as encryption systems based on non-linear correlations and high entropy.
The foundation of this paper is based on the method developed by DRIC, detailed in the patent available at ht- tps://patents.google.com/patent/US20220321141A1. This technology represents the state-of-the-art in data compression, offering an innovative solution combining efficiency and security. Its superior performance compared to traditional approaches positions it as one of the most advanced tools for data compression and encryption, with applications ranging from secure information transmission to optimised storage in cloud systems.
1. Introduction
Data compression and encryption are essential tools for optimising resource usage in data transmissions and for protecting information integrity in high-security contexts. The methodologies involved in this process rely on principles of data reduction and protection mechanisms that use complex mathematical transformations. In this study, we address the principles governing the efficiency of these systems, focusing on compression techniques and cryptographic algorithms used in high-complexity and high-variability data environments. The DRIC system was designed to optimise both compression and encryption without compromising data integrity. To understand this process in depth, it is essential to analyse the physical properties related to entropy, serial correlation, and the impact of compressed data distribution on transmission systems.
2. Data Compression and Security
Data compression deliberately reduces the volume of transmitted or stored data, saving computational resources and network bandwidth. The DRIC system relies on data reduction principles based on mathematical algorithms that act on file entropy. Compression works by identifying repetitive patterns and redundancies in the data, making it possible to eliminate these repetitions without information loss. The basic formula for the compression ratio is given by:
Moreover, the physical laws governing signal propagation in transmission systems play a crucial role in the efficiency of the DRIC system. These laws, especially those related to information theory and thermodynamics, are fundamental to data compression.
Below are some relevant equations:
- Shannon Entropy
Entropy is a measure of uncertainty in a data set and is directly related to the potential for compression:
where H(X) is the entropy of the data set X, p(xi) is the probability of the element xi occurring, and log2 denotes the base-2 logarithm.
- Helmholtz Free Energy
In analogy to thermodynamics, Helmholtz free energy can describe the “available energy” in the data for compression:
- Compressibility Relation
The compressibility of a system is a measure of its ability to reduce volume (or size) without loss of integrity:
- Equipartition Theorem of Energy
The equipartition theorem can be adapted to describe how energy (or information) is distributed among system elements:
- Compression Ratio
The compression ratio can be expressed as:
where C is the compression ratio, Soriginal is the original size of the data, and Scompressed is the size of the compressed data.
Entropy, a measure of data uncertainty or randomness, lies at the core of compression algorithms. When entropy is high, data possesses little redundancy, limiting compression potential. Conversely, data with low entropy tends to exhibit repetitive patterns that can be exploited to maximise volume reduction efficiency.
Serial correlation also plays a significant role. Data with high serial correlation indicates that subsequent elements heavily depend on previous ones, facilitating the application of prediction-based algorithms and redundancy elimination. This reduces the volume of transmitted data while maintaining the necessary integrity for faithful reconstruction at the destination.
These principles establish DRIC as a robust and efficient solution for applications demanding advanced compression and encryption, significantly saving resources and protecting data in highly complex environments.
2.1 Compression Efficiency Across File Types
Tests conducted with the DRIC system indicate that compression efficiency varies considerably depending on the file type. Multimedia files such as videos and images tend to have higher entropy, making their compression less efficient. However, using advanced sliding window techniques combined with Monte Carlo simulations and data dictionaries, the DRIC algorithm can efficiently analyse long bit sequence blocks for redundancies and poorly structured data. In contrast, text files and spreadsheets have a structure that favours compression
due to data repetition. It is important to note that there is an overhead for each execution.
Files with high entropy are less susceptible to efficient compression since the data is more unpredictable.
3. Data Encryption and Security
Encryption is the process of encoding information to protect it from unauthorised access. In the DRIC system, encryption is applied after data compression, ensuring both bandwidth efficiency and transmission security. The cryptographic algorithms used in the system include AES (Advanced Encryption Standard), RSA (Rivest-Shamir-Adleman), and Blowfish.
Each of these algorithms has a distinct encryption approach. For example, AES uses 128-bit blocks and keys of 128, 192, or 256 bits, depending on the desired security level. The basic equation describing the symmetric encryption process is:
where C is the ciphertext, EK is the encryption function using the keyK, and P is the original plaintext. For asymmetric encryption, such as RSA, the basic encryption equation is:
where e is the public key, and n is the product of two large prime numbers. The DRIC system combines these principles with efficient compression, allowing not only secure transmission but also resource savings.
4. Security and Performance Evaluation
The performance evaluation of the DRIC system includes measuring compression and encryption efficiency in different test scenarios. Three hardware configurations were used, ranging from 2GB to 16GB of RAM and from 1.5GHz to 3.6GHz CPU. Results indicate that although compression and encryption time increases with data volume, integrity and security are not compromised. Ampère-Maxwell’s Law, describing the generation of magnetic fields from electric currents, finds an analogy in the data transmission process. The variation in the electric field over time is essential to maintaining the integrity of data packets transmitted in an encryption system, ensuring that the received data has not been tampered with. Furthermore, post-decompression quality metrics such as VMAF (Video Multi-Method Assessment Fusion) show that Cambridge Large Two 3 files maintain their integrity and visual quality, with minimal variations after compression and decompression.
5. Related Physical Applications
The physical functions involved in the study of data compression and encryption are directly related to the principles of energy conservation and the Second Law of Thermodynamics, which states that the entropy of a closed system tends to increase over time. This implies that although it is possible to reduce data volume, there is a theoretical limit to efficient compression without data loss. The application of quantum mechanics in encryption, through quantum cryptography, is also discussed as a promising future for systems like DRIC. Using photons for transmitting cryptographic keys, for example, can eliminate the possibility of undetected interception, dramatically increasing the security of communication systems.
6. Conclusion
The DRIC system proves to be an effective solution for both data compression and encryption, combining efficiency and security in an optimised package for various file types and environments. The physical implications of the methodologies used, such as entropy, serial correlation, and energy conservation in compression systems, corroborate the robustness of the system. These factors make DRIC a suitable solution for high-security demand scenarios, such as data transmission in distributed networks and cloud storage.
References
The equations presented are based on thermodynamic and information theory concepts adapted to the context of data compression, with the main reference being the DRIC patent. Below are the patent and key books used as references:
- Lisboa, R. F., Freijanes, R. S., and Cassinera, A. D. File Compression System. US Patent Application US20220321141A1, 2022.
Description: This patent describes systems and methods for file compression, based on frequency trees and segment encoding, optimising data storage and processing. - Callen, H. B. Thermodynamics and an Introduction to Thermostatistics. 2nd Edition, Wiley, 1985.
Description: This book provides a comprehensive overview of the fundamental principles of thermodynamics, including Helmholtz free energy and the equipartition theorem. - Cover, T. M., and Thomas, J. A. Elements of Information Theory. 2nd Edition, Wiley, 2006.
Description: An essential reference on information theory, presenting Shannon entropy and its mathematical implications. - Kittel, C., and Kroemer, H. Thermal Physics. 2nd Edition, W. H. Freeman, 1980.
Description: A solid introduction to thermal physics, including concepts such as entropy and energy distribution. - Reif, F. Fundamentals of Statistical and Thermal Physics. Waveland Press, 2009.
Description: Presents the statistical and thermal fundamentals that connect thermodynamics with statistical physics, including compressibility and entropy. - Zemansky, M. W., and Dittman, R. H. Heat and Thermodynamics. 7th Edition, McGraw-Hill, 1997.
Description: Detailed coverage of classical thermodynamics and its applications in physical systems.
Federal University of Rio Grande – FURG, Brazil / Faculty of Physics, University of Warsaw, Poland
Autor para correspondência: Edinaldo E-mail: Edinaldo@furg.br / e.porto-de-sa@uw.edu.pl.