Text Multilevel Encryption Using New Key Exchange Protocol

Abstract

The technological development in the field of information and communication has been accompanied by the emergence of security challenges related to the transmission of information. Encryption is a good solution. An encryption process is one of the traditional methods to protect the plain text, by converting it into inarticulate form. Encryption implemented can be occurred by using some substitute techniques, shifting techniques, or mathematical operations. This paper proposed a method with two branches to encrypt text. The first branch is a new mathematical model to create and exchange keys, the proposed key exchange method is the development of Diffie-Hellman. It is a new mathematical operations model to exchange keys based on prime numbers and the possibility of using integer numbers. While the second branch of the proposal is the multi-key encryption algorithm. The current algorithm provides the ability to use more than two keys. Keys can be any kind of integer number (at least the last key is a prime number), not necessarily to be of the same length. The Encryption process is based on converting the text characters to suggested integer numbers, and these numbers are converted to other numbers by using a multilevel mathematical model many times (a multilevel process depending on the number of keys used), while the decryption process is a one-level process using just one key as the main key, while the other keys used as secondary keys. The messages are encoded before encryption (coded by ASCII or any suggested system). The algorithm can use an unlimited number of keys with a very large size (more than 7500 bytes), at least one of them a prime number. Exponentiation is also used for keys to increase complexity. The experiments proved the robustness of the key exchange protocol and the encryption algorithm in addition to the security. Comparing the suggested method with other methods ensures that the suggested method is more secure and flexible and easy to implement.

Design a Crime Detection System based Fog Computing and IoT

“…Sensor networks collect data and send it to the cloud via smart gateways for Mechanical and electronic gadgets connected to the web. The data collected from these numerous sources is then used to power the many user-facing services that make up cloud computing [49,50]. Considering Fog's meager resources, a Fog computing communication protocol must be highly effective, lightweight, and flexible.…”

Comparative Study Between a Novel Deterministic Test for Mersenne Primes and the Well-Known Primality Tests

“…This test is considered a generalization for the SST and it is based on a special recursive sequence called Luca's sequence 3,11 . If P and Q are any integers and if 𝛼 = (𝑃 + √𝐷)/2 and 𝛽 = (𝑃 − √𝐷)/2 are the roots of the quadratic equation 𝑥 2 − 𝑃𝑥 + 𝑄 = 0 whose discriminant 𝐷 = 𝑃 2 − 4𝑄 is positive, then the following relations are obtained: 𝑃 = 𝛼 + 𝛽, 𝑄 = 𝛼𝛽, and 𝐷 = (𝛼 − 𝛽) 2 . Assume that 𝐷 ≡ 0 (𝑚𝑜𝑑4), or 𝐷 ≡ 1 (𝑚𝑜𝑑4).…”

“…It is based on selecting the discriminant 𝐷 as the first element in the sequence of the odd positive numbers with common difference 4 and ( 𝐷 𝑛 ) = −1. Then, 𝑃 is selected to be the least odd number greater than 𝐷 1 2 and 𝑄 = (𝑃 2 − 𝐷)/4. For example, if 𝑛 = 5559, it selects 𝐷 = 13 and {𝑃, 𝑄} = {3, −1} where the Lucas test fails.…”

“…The AKS primality test is based on the following theorem found in 17 , and its proof can be found in 16 For example, let 𝑛 = 2017, 𝑎 ∈ [0, log 𝑛], and 𝑟 = 107 such that 𝑂 𝑟 (𝑛) > log 2 𝑛. It is easy to verify that 𝑛 is not a perfect power of 𝑥 for all 𝑏 ∈ [2, log 2 is prime by the AKS test. However, if 𝑛 = 561, then 𝑇(7, 561, 3)(𝑥) = (𝑥 + 7) 561 − 𝑥 561 − 7 ≢ 0 (𝑚𝑜𝑑 𝑥 3 − 1, 561).…”

“…A primality test is a method used to determine whether an input natural number is prime or composite using some number theoretic rules and theorems. Primality testing is mostly used in the fields of cryptography and cybersecurity 1,2 . In general, primality tests are different integer factorization because they only state whether a number is prime or not without giving its prime factors of it.…”