• ### On the Application of Nonhomogeneous Differential Equations to a Laplace Transform-based Cryptographic Process

Roberto P. Briones

School of Mathematical and Computer Sciences, Heriot-Watt University Malaysia, 62200, Putrajaya, Malaysia.

Abstract: Hiwarekar [4] introduced a cryptographic scheme which made use of the Laplace transform of the Taylor series of a C^∞ function 𝑡^𝑛𝑓(𝑘𝑡), in the most general sense. However, the functional form more commonly used in literature is 𝑡^𝑛𝑒^𝑘𝑡 mainly due to computational convenience. To transmit an encoded message, the parameters n, k, and f(t) are specified in advance and sent securely. This paper extends the encoding to functions of the form 𝑃(𝑡)𝑒^𝑘𝑡 , where P(t) is an nth degree polynomial with positive integral coefficients, and recognizes the role this function takes as a unique solution to a nonhomogeneous differential equation. Consequently, the representation of all the parameters through a single differential equation and the additional complexity it brings strengthens the security of the ciphertext..

Keywords: Taylor series, non-homogeneous differential equation, particular solution, plaintext, ciphertext.