Applications of Fourier Transformation with the help of Cryptography

Abstract

Cryptography is used for the investigation of mathematical skills that interlink with the aspects of data integrity, individual authentication, and information security. Cryptography is the fundamental basis of modern electronic communication. The Encryption means converting a file into secret keys, while decryption means converting an encrypted message into normal language. Numeric values from 0 to 25 and 26 to 51 will be assigned to small and capital alphabets, respectively. The special case of Taylor series will be considered for exponential and simple functions. Fourier transformation will be used to code and decode a message. For better calculation of encryption and decryption, the modulus 57 will be used with 4 special characters. Many researchers have utilized different transformations such as Laplace and natural transformations. However, Fourier transformation with exponential function has provided authentic results compared to other transformations. The key factor of this work is the generalized key that decodes the special information, including ATM cards transmitting financial information and computer passwords. Cryptography is the study of mathematical skills related to information security aspects such as confidentiality, data integrity, data authentication, and personal authorship. Fourier Transforms, a powerful mathematical tool used to analyze and manipulate signals in the frequency domain, have found numerous applications in the field of cryptography. By transforming data between the time and frequency domains, Fourier methods offer unique advantages for encryption, decryption, and the design of cryptographic algorithms