Data Encryption Based on Exponential Numbers
Ho‐Hsuan Chang · Journal of Physics Conference Series · 2019
Abstract A novel data encryption scheme using a set of exponential numbers is proposed in this paper which aims at achieving secure communications over public networks. The study begins with the definition of pattern of exponential number, where the decimal pattern of an exponential number g e is the result of taking e − 1 times multiplication the base element g by itself. The multiplication operation of two large integers involves the complicated carry conditions in each step, which is digit-dependence and can only be analyzed case by case. This implies that the pattern of a large exponential number is unpredictable. Next, we prove that nature number can be spanned by a set of exponential numbers, and there exists numerous spanning sets for one nature number, demonstrating that the expression of nature number using a set of exponential numbers is not unique. The unpredictable nature of exponential patterns and the abundant available sets of exponential numbers can contribute the concealment of information when data streams are encrypted by the exponential numbers. In addition, we prove that the base elements of a set of exponential numbers applied for spanning a nature number can be arbitrarily assigned. With this property, we can distribute a secret key sequence in advance as the base elements for data encryption, or this secret key can be shared using the Diffie-Hellman Key-Exchange system over public network. Finally, the encrypted message consists of a sequence of exponents and the index data, which indicates the relationship between the base elements and the secret key for decryption. The ciphertext is transmitted via the public channel to the receiver end; however, it can only be decrypted by those who own the secret key. Some examples are shown for demonstration the feasibility of the proposed encryption scheme.