## 2 Methods: MVL Linked List as the Data Protection Model
### Method of Additional Blocking Product Terms in the Linked List  
This method [19] can prevent from attacks 2,3,6, based on adding of fake constants and excessive Literal parameters, given in Table 2. It uses the scheme to generate blocking product terms \(PT^{-}\), providing subsuming of all illegally added product terms located in the truth table between any two given rows e.g., between entries \(\mathbf{e}_{\text{m}}\) and \(\mathbf{e}_{\text{m}-1}\). In order to apply it, the participants of the protocol should by default use constant \(k-1\) only as the selected parameter for minimization procedures [18], which will always subsume all added product terms with any lower constants. For practice it is more comfort to represent steps4 and 6, which were used in Algorithm 2 in the paper [19], as an Exp. (7) for i-th Literal, where indexed parameters \(a,b\) are written as \(\overline{x}_{i},\)\(\overline{\overline{x}}_{i}\) for both entries:  
\[\overline{X}_{i}\Big{(}\overline{x}_{i},\overline{\overline{x}} \Big{)}=\] \[\left\{\begin{array}{l}X_{i}\Big{(}MIN\left(\overline{x}_{i}, \overline{\overline{x}}_{i}\right)+1,Max\left(\overline{x}_{i},\overline{ \overline{x}}_{i}\right)-1\Big{)},\ if\ Max\left(\overline{x}_{i},\overline{ \overline{x}}_{i}\right)-MIN\left(\overline{x}_{i},\overline{\overline{x}}_{i }\right)\geq 2\\ X_{i}\Big{(}MIN\left(\overline{x}_{i},\overline{\overline{x}}_{i}\right),Max \left(\overline{x}_{i},\overline{\overline{x}}_{i}\right)\Big{)},if\ Max\left( \overline{x}_{i},\overline{\overline{x}}_{i}\right)-MIN\left(\overline{x}_{i}, \overline{\overline{x}}_{i}\right)<2\end{array}\right. \tag{7}\]  
As it is not correct to mix operators of AGA and Boolean logic [18], here operations MIN and MAX are considered as Boolean emulations of exp. (2) combined with adding or subtraction of 1. Then basing on definitions and Algorithm 2[19] one can write logic expression, which combines two real product terms \(PT_{m-1}^{+}\) and \(PT_{m}^{+}\), responding to entries with logic constants equal to numbers \(m\) and \(m-1\), and the blocking term \(PT_{m-1,m}^{-}\) with the logic constant \(k-1\). Final exp. (8) obtained e.g., for 3 variables will be  
\[\begin{array}{l}PT_{m-1}^{+}+PT_{m-1,m}^{-}+PT_{m}^{+}=\\ =h_{m-1}\star X_{1}(\overline{x}_{1},\overline{x}_{1})\star X_{2}(\overline{x} _{2},\overline{x}_{2})\star X_{3}(\overline{x}_{3},\overline{x}_{3})+\\ (k-1)\star\overline{X}_{1}\left(\overline{x}_{1},\overline{\overline{x}}_{2} \right)\star\overline{X}_{2}\left(\overline{x}_{1},\overline{\overline{x}}_{2 }\right)\star\overline{X}_{e,1}\left(\overline{\overline{x}}_{1},\overline{ \overline{x}}_{2}\right)+\\ h_{m}\star X_{1}\Big{(}\overline{\overline{x}}_{1},\overline{\overline{x}}_{1 }\Big{)}\star X_{2}\Big{(}\overline{\overline{x}}_{2},\overline{\overline{x }}_{2}\Big{)}\star X_{3}\Big{(}\overline{\overline{x}}_{3},\overline{ \overline{x}}_{3}\Big{)},\end{array} \tag{8}\]  
where any \(\overline{X}_{i}\Big{(}\overline{x}_{i},\overline{\overline{x}}\Big{)}\) is given by Exp. (7).  
As additional blocking segment \(PT_{m-1,m}^{-}\) will enlarge the overall number of product terms and the computing time for \(\sim\)50%, it may be reasonable to use it as a separate page (or a part) of the MVLL.