Applying Laplace transforms to cryptography using Bessel and exponential functions and performing detailed time and memory analysis

Authors : Hüseyin Demir, Hatice Muti, Hünkar Acar

Pages : 1244-1256

Doi:10.17714/gumusfenbil.1780179

View : 157 | Download : 191

Publication Date : 2025-12-15

Article Type : Research Paper

Abstract :This paper explores a novel application of the Laplace transform in cryptographic schemes by employing a linear combination of Bessel functions and exponential functions. By leveraging the transform’s properties, we develop an encryption-decryption framework that is computationally efficient and highly secure against certain types of cryptographic attacks. The exponential decay observed in Laplace-transformed domains and the complex behaviour of Bessel functions are powerful tools for data encoding and concealment. Analytical and numerical results validate the method’s effectiveness, showcasing its potential for modern cryptographic systems. Cryptography has long been a cornerstone of secure communication, with its methods evolving in tandem with technological advancements. While traditional schemes rely on number theory or algebraic structures, this paper explores an alternative approach that combines Laplace transforms with special functions. Specifically, we focus on employing Bessel functions in conjunction with exponential functions to construct an encryption algorithm. The Laplace transform’s unique properties, such as linearity, time-shifting, and frequency domain representation, offer a fertile ground for developing innovative cryptographic methods. Then the algorithm described in this study generates a dynamic cipher by processing plaintext using polynomial, exponential, and factorial-based operations. The four fundamental steps comprising the computational process are text preprocessing, dynamic coefficient calculation, encryption packaging, and reverse analysis. The computational cost of each step varies depending on the number of characters processed. The symbol for this character quantity is n. The cryptographic analysis of the problem is discussed in detail.
Keywords : Bessel fonksiyonu, Kriptografi, Laplace dönüşümü, Zaman & bellek

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