## 2 Methods: MVL Linked List as the Data Protection Model
### MVL Scheme of the Linked List  
Principally, initial MVLL scheme [19] includes two protective tools:  
(1) duplicating notation of the same message in the last and in the previous entries like in BC schemes [25; 26], and (2) the approval of data by quasi-random values of the hash function, assigned by the set of external distant nodes. Any attempt to modify data in the MVLL will need to modify at least two rows in the truth table of the linked list, approved before by two sets of externally assigned hash values. That is why the first way to use MVLL is to detect attacks 1,4,5 in Table 2 by comparison of entries, written in internal and different external parts of the linked list. The second way is to use blocking terms [19] preventing from 2,3,6, types of attacks. In order to write the new entry \(\mathbf{e}\) to MVLL [19], the mobile agent (called the prover in route verification tasks [41]) declares the new entry to \(Q\) collaborating nodes (or verifiers) by sequential mailing according to the list of participants of the protocol. First of them assigns the time stamp \(t\), and each of verifiers should assign its quasi-random hash value \(h\) to the received entry \(\mathbf{e}\). These hash values are to be preliminary generated by QKD lines and accumulated in nodes in order to provide maximal unpredictability of data. One of assigned hash values should be used as the output value of the MVLL function, confirming every entry in the MVLL. After the acquisition of external hash values, mobile agent sends the complete set of data \(m\), \(t\), \(\mathbf{e}_{m}=\{e_{1,m},\ldots,e_{n,m}\}\), and \(h=\{h_{1}\,,\ldots,h_{Q}\}\) to external participants (i.e., \"witnesses\") for their backup storage copies, formed individually according to known common rules. The absence of the verifier's reply due to faults and switched-off mode is to be fixed by zero. In general case one can form the linked list function \(F_{ll}\)[19] by product terms, containing pairs of entries obtained at different time moments \(t_{m}\) and \(t_{m-s}\), where \(m\) is the number of the last entry; \(s\) is the shift of the number for the previous entry. Function \(F_{ll}\) responds to Definition 1 and Exp. (5). \begin{table}
\begin{tabular}{c c c} \hline \hline
**N** & **Attack Type** & **Consequences, Scheme of Protection** \\ \hline
5. & Replacement of the logic & Result: Values of fake C* are assigned to correct values of a,b: \\  & constant C by fake C* \(\
eq 0\) in & \(PT_{fake}=C^{*}\,\,X_{1}(2,4)*X_{2}(75,77)*X_{3}(31,\,34)\). \\  & some PT, parameters \(a,b\) are & Protection: Monitoring of sets of real constants C and parameters \(a,\ b\). \\  & real. & \\
6. & Replacement of real \(a,\ b\) by fake ones \(a^{*},\ b^{*}\) in Literals & Result: Incorrect values of C are assigned to fake values. \\  & \(X_{i}(a,b)\) of one PT. & Possible protection: Method of blocking logic terms for \(a^{*},\ b^{*}\) beyond the real band. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Cont. **Definition 2**. : cited from [19]. _Logic ledger function or a linked list of logic entries is given within AGA as a hash function_  
\[ \begin{array}{l}h^{(out)}=\\ F_{ll}\big{(}m,s,\ t,e_{1,m}\,\ldots,e_{p,m},\ e_{1,m-s}\,\ldots,e_{p,m-s},\ \ h_{1,m},\ldots,h_{Q,\ m},\ \ h_{1,m-s},\ldots,h_{Q,\ m-s}\big{)},\end{array}  \tag{5}\]  
or in the compact notation \(h^{(m,s)}=F_{ll}(m,s,t,e_{m},\ e_{m-s},h_{m},h_{m-s})\). In Exp. (5) \(m\) is the number of the last entry; \(s\) is the shift of the number for the previous entry; \(t\) is the time stamp corresponding to the last entry; \(e_{1,m}\,\ldots,e_{p,m}\) are the parameters of the last entry \(e_{m}\); \(e_{1,m-s}\,\ldots,e_{p,m-s}\) refer to parameters of the earlier received entry \(e_{m-s};h_{1,m},\ldots,h_{Q,\ m}\) are the hash values assigned by network verifiers to the last entry \(e_{m}\); \(h_{1,m-s},\ldots,h_{Q,\ m-s}\) are the hash values of the earlier received entry \(e_{m-s}\); and \(q\) is the number of a verifier, \(q=1,\ldots,Q\). All these parameters are natural numbers.