# A Multi-Objective Optimization of Secure Pull Manufacturing Systems
## 3 Methodology
### BioGamal Secure Algorithm
#### 3.1.1 BioGamal Technique  
The BioGamal technique is implemented by joining the DNA algorithm and ElGamal cryptosystem. Both algorithms are applied in the encryption and decryption cycle. To scramble the hash estimation of the information in the Kanban card, DNA cryptography is used in first level. In data science, the two states, 0 or 1, are used to encode the paired computerized coding. DNA cryptography relies upon the DNA rationale word; they utilize just two digits, 0 and 1, to make four nucleic acid bases--A, C, G, and T--which are denoted by Adenine, Cytosine, Guanine, and Thymine, respectively [13]. In DNA, double chains of nucleic acids are arranged in a double helix arrangement. Hence, each chain is a complement to the previous one. T and A are paired duos; C and G are elective matched couples. The 0 and 1 are a supplement pair in double activities; in this manner, 0 and 1 are a supplement pair, and 0 1 and 1 0 are another supplement pair. In the wake of utilizing these ATGC sequences, 16 distinct keys are framed, which are given in Table 1[12].  
Figure 4: Flowchart of Proposed Algorithm for security system.  
The algebraic properties of modular exponentiation, with the discrete logarithm problem, are the two essential factors to generate the ElGamal digital signature algorithm. The algorithm is executed in three main phases: generation of the key, encryption of the message, and finally, decryption of the message. In order to generate keys, a public key and private key pair are employed. Using a private key, a digital signature can be produced for a message, and, additionally, a digital signature can be confirmed by using the signer's public key. Digital signatures allow the recipient to verify the message's authenticity, message integrity, and message non-repudiation by providing message authentication, integrity, and message non-repudiation, with the sender unable to fraudulently state that they did not sign the message. A digital signature algorithm, based on ElGamal, is implemented as follows:  
**Phase 1: Generation of key**  
* Create a large prime number \(p\) and primitive group where \(Z_{p}^{*}\) are relatively prime to \(p\)
* Generate another primitive element \(g\) and free element \(\alpha\in\{0,\,1,\,\dots,\,p-2\}\) to produce public and private key.
* Public key is molded by three pair of parameters as: \[\beta=g^{\alpha}\text{mod}p\] where, \(\alpha\) is the private key that is secret value.  
**Phase 2: Encryption of message**  
* The algorithm uses public key and random secret integer \(k,k\in\{0,\,1,\,\dots,\,p-2\}\)
* Encrypt each character in the message using dissimilar \(k\) number.
* Compute \(r\) and \(t\) values as follow \[r=g^{k}\text{mod}p\] \[t=\beta^{k}M\text{mod}p\]
* Cipher text achieved as \((r,\,t)\).  
**Phase 3: Decryption of message**  
* Utilize secret key \(\alpha\) and public keys \((p,g,\beta)\) to perform the decryption phase. From received cipher text \((r,\,t)\), plaintext is performed as: \[M=tr^{-a}\text{mod}p\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Pattern** & **Key Combination** & **Value** \\ \hline
0000 & AA & 0 \\
0001 & AT & 1 \\
0010 & AG & 2 \\
0011 & AC & 3 \\
0100 & TA & 4 \\
0101 & TT & 5 \\
0011 & TG & 6 \\
0111 & TC & 7 \\
1000 & GA & 8 \\
1001 & GT & 9 \\
1010 & GG & 10 \\
1011 & GC & 11 \\
1100 & CA & 12 \\
1101 & CT & 13 \\
1110 & CG & 14 \\
1111 & CC & 15 \\ \hline \hline \end{tabular}
\end{table}
Table 1: DNA Key Combination.