Laplace transform for Mittag-Leffler function in cryptography

Abstract

The security of information has been a significant part of human civilization since the ancient era. In the information society, the protection of information becomes increasingly crucial for humankind, and new technologies are progressing in an unending stream. Cryptography is one of the greatest methods intended for protecting the transmission of messages and the security of data. For instance, digital commerce, electronic telecommunications such as mobile phone networks, sending personal emails, commercial transactions, paying television, the security of bank cards, cryptocurrency, etc, affect many areas of our everyday lives. Cryptography enables secrecy and protection for secret information by concealing it. It is made through a mathematical method. In this study, we built a new mathematical technique for cryptography in which we applied the Laplace transform (L-Transform) for the Mittag-Leffler function (or E-function) to plain text for encryption and the correspondent inverse L-Transform related to the E-function for decryption. Eventually, we use the Monobit test and correlation test for measuring the security level of encryption and the Python programming language for easily attaining cipher text, the original message, and computations of statistical tests.