# Blockchain-Based Decentralised Authentication in Closed Environments
## 4 Results
### GNY Analysis
The freshness postulate F1 was then applied to obtain \(V_{i}\mid\equiv\#(ID_{A},N_{A},H(PWD))\). This implied that nodes \(V_{i}\) believed that the received message and all its components were fresh. Hence, the message was not a replay attack. Nodes \(V_{i}\) could now verify \(H(PWD)\) by checking their blockchain. A consensus was reached at this stage. The recognisability postulate R1 was then applied to show that, by checking the blockchain, nodes \(V_{i}\) recognised the identity of \(A\) and its password, from which we obtained \(V_{i}\mid\equiv\#(ID_{A},N_{A},H(PWD))\). Subsequently, the message interpretation postulate II was applied. This led to nodes \(V_{i}\) to believe that \(A\) had indeed conveyed the message, \(A\) had conveyed the message encrypted with the group key \(K\), and \(A\) also possessed \(K\). Moreover, the postulate I7 was applied to obtain \(V_{i}\mid\equiv A\mid\sim ID_{A},H(PWD)\). This led to nodes \(V_{i}\) to believe that \(A\) had sent its identity and password to \(V_{i}\) for verification. Finally, applying the jurisdiction postulate J1, nodes \(V_{i}\) believed that \(A\) had jurisdiction over all components of the message. This implied that \(V_{i}\) believed in \(A\)'s identify and password. **Message 2:** The being-told postulates T1 and T3 were applied to the message to obtain \(A\triangleleft ID_{V_{i}},ID_{A},N_{A}+1,N_{V_{i}},AutHStatus\), which describes the fact that \(A\) who possessed the group key \(K\) decrypted the message to see all components of the received message. \(A\) could also apply \(K\) to check message integrity. Possession postulate P1 was applied to verify that \(A\) now possessed the identity of \(V_{i}\), newly updated nonce \(N_{A}+1\), new nonce \(N_{V_{i}}\), and authentication status. Based on this, the freshness postulate F1 was applied to show that, after seeing \(N_{A}+1\) and \(N_{V_{i}}\), \(A\) believed that these components were freshly computed and generated. This implied that \(A\) believed the received message to be fresh. In other words, the message was not a replay attack. We then applied the recognisability postulate R1 to show that the message was indeed from a recognisable source because it contained recognisable components, such as \(ID_{A}\) and \(N_{A}+1\). The message interpretation postulate I1 was applied next. This indicated that \(A\) received the message encrypted with the group key \(K\), which \(A\) also possessed and believed that \(K\) was shared with \(V_{i}\). Therefore, this confirmed that \(A\) believed that \(V_{i}\) had indeed conveyed the message and that \(V_{i}\) also possessed the key \(K\). Thus, we applied the postulate I7 to further confirm that \(A\) believed that \(V_{i}\) had sent the authentication status as the reply to \(A\)'s authentication request in message 1. Jurisdiction postulate J1 was the final rule to be applied. This led \(A\) to believe that \(V_{i}\) had jurisdiction over all components of the message. This implied that \(A\) believed in the received identity of \(V_{i}\) and that the authentication status was sent by \(V_{i}\), thus confirming that man-in-the-middle attacks did not occur. The GNY analysis of the messages leads us to conclude that the proposed authentication protocol can achieve mutual authentication and security against a replay attack (from freshness analysis) and a man-in-the-middle attack (from recognisability, message interpretation, and jurisdiction analysis).