Advanced Cryptography through Exponential Functions and Modular Techniques Exponential Functions and Modular Techniques in Advanced Cryptography

Abstract

This study introduced a novel approach to cryptography, leveraging natural transformations through a distinct exponential function, “ ” with a variable “ ” expressed as “ ”. This innovative framework enhances the security of information by employing advanced encryption and digital signature techniques to ensure confidentiality, integrity, and authentication. The proposed method enables secure transactions, reliable communication channels, and robust protection against unauthorized access. The exponential functions improve a layer of difficulty that rises encryption strength and makes it useful to make safe sensitive information in a various field such as healthcare, finance, and national security. The Natural Transformation was introduced in this study, that aids a new term in cryptography which helps to secure data and offer enough security for sensitive information. Encryption and decryption were performed using a newly developed mathematical method that incorporates modular operations, including , along with an extended technique using  for enhanced security. Capital English alphabets to numeric value had been assigned for mod 26 and for hard security.