Analysis of the empirical complexity of Advanced Encryption Standards - 128 statistically

Abstract

Algorithm analysis stands as a cornerstone in the field of theoretical computer science, captivating researchers with its focus on dissecting and understanding the operational complexity of various algorithms. This intricate process is pivotal for acquiring deeper insights into the practical performance of algorithms, beyond what is discernible from theoretical analysis alone. A relatively novel and increasingly relevant approach in this realm is the concept of empirical complexity. This method diverges from traditional theoretical analysis by placing emphasis on the practical execution of an algorithm across a spectrum of varying and escalating input sizes. Such a hands-on approach is instrumental in predicting the complexity of the algorithm in real-world scenarios. The empirical data thus obtained undergoes rigorous statistical analysis, enabling a more nuanced and concrete understanding of the algorithm’s behavior and performance. This approach not only enriches our comprehension of algorithms but also plays a crucial role in optimizing and refining their application in practical computing environments. • Background: In the realm of digital security, cryptographic algorithms are indispensable for protecting applications and safeguarding sensitive information, be it of national significance or personal confidentiality. The efficiency of these algorithms in contemporary, high-velocity computational environments is paramount. Such algorithms typically incorporate intricate mathematical operations. This study delves into the computational intricacies of AES-128, a predominant cryptographic algorithm, scrutinizing its computational complexity. • Method: This study applies a thorough empirical complexity framework to establish the asymptotic limits of AES-128 accurately. It then conducts a detailed regression analysis with closed boundaries to measure AES-128’s empirical complexity with precision. • Result: The investigation reveals that the empirical complexity of AES-128 adheres to an Oemp (n) notation, where ‘n’ represents the size of the input data. • Conclusion: The research establishes that AES-128’s time complexity for both encryption and decryption processes aligns with O(n), a finding supported through both empirical evidence and theoretical analysis. Furthermore, a statistical model has been crafted to accurately forecast the execution time based on any specified input size for AES-128’s encryption and decryption activities. This advancement aids in predicting performance outcomes prior to the actual encoding process.