## 3 The Proposed Model
### Secret Image Encryption Using MKHE Technique  
In order to effectually encrypt the secret image before steganography, the MKHE technique is applied. An MKHE is a cryptosystem that permits us for evaluating an arithmetic circuit on cipher-text, maybe encrypting in several keys. Assume that \(\mathcal{M}\) remains the message space with arithmetic infrastructure [19]. An MKHE method has 5 PPT techniques (Eval, Setup, Enc, KeyGen, and Dec). It is considered that all contributing parties have a reference (index) to their public and confidential keys. A multi-key cipher  
Figure 3: Flowchart of COA.  
text implicitly has an arranged set \(T=\{id_{1},\ \ldots,\ id_{k}\}\) of connected references. For instance, a fresh cipher-text \(ct\leftarrow\) MKHE. \(Enc(\mu;pk_{id})\) equals to single-element set \(T=\{id\}\) but the size of references fixed obtains superior to the computation amongst cipher-text in various party developments.
* Setup: \(pp\leftarrow\) MKHE. \(Setup\big{(}1^{\lambda}\big{)}\). Proceeds the secured parameter as input and returned the public parameterization. It can be considered that every other technique implicitly gets \(pp\) as input.
* Key Generation: \((sk,\ pk)\leftarrow\) MKHE. \(KeyGen(pp)\). Resultants a pair of confidential and public keys.
* Encryption: \(ct\leftarrow\) -<KHE.\(Enc(\mu;pk)\). Encrypting a plaintext \(\mu\in\mathcal{M}\) and resultants a cipher-text \(ct\in\{0,1\}^{*}\).
* Decryption: \(\mu\leftarrow\) MKHE. \(Dec(\overline{ct};\{sk_{id}\}_{id\in\overline{T}})\). To provide a cipher-text \(\overline{ct}\) with equivalent order of confidential keys, outcomes a plaintext \(\mu\). The Homomorphic estimation is defined as follows: \[\overline{ct}\leftarrow\text{MKHE.}Eva1(C,\ \big{(}\overline{ct},\ \ldots,\ \overline{ct}_{l}\big{)},\ \{pk_{id}\}_{id\in\overline{T}}).\] (16)  
To provide a circuit \(C\), a tuple of multi-key cipher-text \(\big{(}\overline{ct},\ \ldots,\ \overline{ct}_{l}\big{)}\) and the equivalent group of public keys \(\{pk_{id}\}_{id\in\overline{T}}\), resultants a cipher-text \(\overline{ct}\). Its reference set is union \(T=T_{1}\cup\ \cdots\cup\ T_{\ell}\) of reference sets \(T_{j}\) of input cipher-text \(\overline{ct}_{j}\) for \(1\leq j\leq\ell\).  
Semantic Security. To some 2 messages \(\mu_{0},\mu_{1}\in\mathcal{M}\), the distribution (MKHE. \(Enc\) (\(\mu_{i}\); pk)) for \(i=0,1\) can be computationally indistinguishable whereas \(pp\leftarrow\) MKHE. \(Setup\big{(}1^{\lambda}\big{)}\) and \((sk,\ pk)\leftarrow\) MKHE. \(KeyGen(pp)\). Correctness and Compactness. An MKHE technique was compact once the size of cipher-texts related to \(k\) parties is bounded by poly \((\lambda,\ k)\) to set a polynomial poly \((\cdots)\). For \(1\leq j\leq\ell\), assume \(ct_{j}\) be cipher-text (with reference set \(T_{j}\)) so that MKHE. \(Dec(\overline{ct},\ \{sk_{id}\}_{id\in\overline{T}})=\mu_{j}\) Assume \(C:\mathcal{M}^{\ell}\rightarrow\mathcal{M}\) be circuit and \(\overline{ct}\leftarrow\) MKHE.\(Eval(C,\ \big{(}\overline{ct},\ \ldots,\overline{ct}\big{)},\ \{pk_{id}\}_{id\in\overline{T}})\) for \(T=T_{1}\cup\ \cdots\cup\ T_{\ell}\). Afterward,  
\[\text{MKHE.}\ Dec(\overline{ct},\ \{sk_{id}\}_{id\in\overline{T}})=C(\mu_{1}, \ \ldots,\ \mu_{\ell}). \tag{17}\]  
The equality is replaced by estimated equality same as the Cheon, Kim, Kim and Song (CKKS) technique to estimate arithmetic [16].