Improving the robustness of the affine cipher by using a rainbow antimagic coloring

Nowadays, cryptosystems can be applied in several areas in life. One of them is in transaction data. In transaction data, a very strong cryptosystem is needed so that the transaction data is safe. Cryptosystems are better with a strong keystream. In this case, we use rainbow antimagic as a cryptosystem key to improve the robustness of the keystream by using affine cipher. The algorithm uses the edge weights of rainbow antimagic vertex labeling of graphs as a key for encryption and decryption. In this paper, we found the rainbow antimagic connection number of tadpole graphs and two algorithms to straighten affine ciphers.


Introduction
Nowadays, cryptosystems can be applied in several areas in life. One of them is in transaction data. In transaction data, a very strong cryptosystem is needed so that the transaction data is safe. Cryptosystems are better with a strong keystream. In this case, we use rainbow antimagic as a cryptosystem key to improve the robustness of the keystream.
Cryptosystem consists of two processes, namely the encryption process and the description process. Each process requires a key. The process is intended to make it difficult for others to read the secret message. We can see some of the results of other researchers' research in [2,5,6]. There are several types of encryption and decryption processes in cryptosystems, one of them is an affine cipher. Affine cipher is a technique that uses modulo 26 processes in encryption and decryption processes based on the number of letters in the letter [8].
A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions [4]. Based on [4], there are many kinds of labeling. In [3], they introduce rainbow antimagic coloring of graphs. The rainbow antimagic coloring of graphs is one type of labeling in which assignment of integers to the vertices of graphs to certain conditions for every edge weights becomes a rainbow coloring path.
First of all, we have to understand about labeling of graph which have bijective function f from vertex set V (G) to the integers number 1 until the cardinality of vertex set |V (G)|. We can call the bijective function f as rainbow antimagic vertex labeling if for any two vertices have different edge weights as rainbow path at least one. It means that for every k, m ∈ V (G) have rainbow path k − m for any edges as uv and All Proposition, Lemma and Theorem that we used to prove the theorem in this paper are as follows.

Results
Theorem 2. Let T α,β for α ≥ 3 and β ≥ 1 where α, β is natural number, We know that the tadpole graph contains C α and P β . According to Proposition 1, Proposition 2 and Lemma 1, rac(T α,β ) ≥ α 2 + β.  To realize the equality, let us define a vertex labeling f : Then, the labeling f provides the vertex weights as follows.

Inculcating a affine cipher
After getting rainbow antimagic coloring, we can use it to develop an affine cipher by inculcating it. In the affine cipher, the entire method relies on working for mod m (the length of the alphabet used in the Affine cipher). We define the steps of the affine cipher cryptosystem as follows. • The key system source is collected from edge weights of rainbow antimagic vertex labeling of graphs • The key length regards to edge element of graphs

Role of keystream
We use the rainbow antimagic coloring algorithm for the key To develop an affine cipher. This algorithm uses the edge weights of rainbow antimagic vertex labeling of graphs. The sequence is used as a key for encryption and decryption. By using 26 English language alphabets, the following algorithm gives a procedure of the construction. Algorithm 1. Role of Keystream 1. To use the graph elements, define f 2. If f is a bijection, do 3, and bring it back to 1 otherwise 3. To use the sequence for edge weight for every edge, define z j where j = the number of edge and 1 ≤ j ≤ |E(G)| 4. Add z j and arrange the sequence according to the smaller vertex weights 5. Set k as element of the z j sequence

Encryption and Decryption Algorithm
The keystream generated by algorithm 1 is used to determine encryption and decryption of Affine cipher. The method of encryption and decryption are performed by using the following algorithm.
Algorithm 2. Affine Cipher 1. Given that the plaintext P = (p i ), 1 ≤ i ≤ q 2. Compute the ciphertext using Equation 1 and compute the plaintext blocks using Equation 2.
C n = (P n + K) mod 26 (1) P n = (C n − K) mod 26 (2) where P n , K, and C n are the n-th of plaintext, key sequence, and ciphertext, respectively.
For an illustration of how the algorithms are working, we give the following examples. Given that a plaintext P = U N IV ERSIT ASJEM BER, by means of the two   Table 3. Decryption process.

Concluding remarks
In this paper, we have presented the result of the rainbow antimagic coloring of the tadpole graph. In addition, by using Affine cipher and inculcating affine cipher, we can develop the key efficiently. Since the decryption process will pass the keystream, i.e. by using the rainbow antimagic coloring, we ensure that the key will be obviously hard to be revealed by any intruder. However, we need more work to make those algorithms applicable in real life, especially for the use of IOT, thus we propose the following open problems.
Open Problem 1. Obtain programming based on the two algorithms to create a GUI program for the purpose of handling encryption and decryption process by means of rainbow antimagic coloring.