# Novel Designated Ownership Transfer with Grouping Proof
## 3 Security Analysis  
Table 2 presents a comparison of the security features. \(\mathbf{O}\) denotes that a method listed in the comparison is capable of a feature; \(\mathbf{X}\) denotes that a method fails to achieve the feature; and \(\triangle\) means that the method can achieve the feature when certain circumstances are satisfied. In addition, we use \(\mathbf{OT}\) as an abbreviation for ownership transfer and \(\mathbf{GP}\) for grouping proof to indicate which vulnerabilities are present in these two protocols. For example, the replay attack can take place in both protocols, whereas the denial of proof vulnerability is unique to grouping proof protocols.  
In the method proposed by [PERSON] and [PERSON]. [3], the messages are transmitted without random numbers or any counters to prevent old messages from being replayed.  
In addition to the legitimacy of the generated proof, the previously proposed protocols [3; 5; 24] do not authenticate the responses received from the tags. Therefore, if the response messages are generated by tags that do not belong to the current tag group, the verifier will reject and discard the proof, leading to denial of proof. Concurrent attacks can occur when several readers simultaneously attempt to generate grouping proofs for the same tag, which prevents the proofs from being generated because the contents of the previous tags are overwritten by subsequent readers. The protocol proposed by [PERSON] and [PERSON] [3] requires the tags and readers to be written multiple times to generate the grouping proof, which can cause a problem in a scenario in which previously written information can be overwritten by other readers. In [PERSON]'s protocol [5], the reader must read the tags more than twice to generate a proof. Although [PERSON] et al.'s protocol [24] does not overwrite proofs when the tags are read by different readers during inspection, the random numbers are not subject to the same security check and might therefore be overwritten.  
[PERSON] and [PERSON] [26] proved that [PERSON]'s protocol [22] is vulnerable to the desynchronization attack, which causes a tag to lose synchronization with the new owner, resulting in DoS. In Sections 3.1-3.7, we analyze our proposed protocol, which prevents all the aforementioned threats.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Protocol** & **Replay Attack\({}^{*}\)** & **Denial of Proof** & **Concurrency Attack** & **Denial of Service** & **Forward Secrecy** & **Backward Secrecy** \\  & **(OT/GP)** & **(GP)** & **(GP)** & **(OT)** & **(OT)** & **(OT)** \\ \hline [PERSON] [22] + [PERSON] and [PERSON] [5] & \(O/O\) & \(\times\) & \(\times\) & \(\times\) & \(\circ\) & \(\circ\) \\ [PERSON] [22] + [PERSON] and [PERSON] [3] & \(O/\times\) & \(\times\) & \(\times\) & \(\times\) & \(\circ\) & \(\circ\) \\ [PERSON] [22] + [PERSON] et al. [24] & \(O/O\) & \(\times\) & \(\triangle\) & \(\times\) & \(\circ\) & \(\circ\) \\ [PERSON] [22] + [PERSON] et al. [25] & \(O/O\) & \(\triangle\) & \(\circ\) & \(\times\) & \(\circ\) & \(\circ\) \\ Our Protocol & \(O/O\) & \(\circ\) & \(\circ\) & \(\circ\) & \(\circ\) & \(\circ\) \\ \hline \hline \end{tabular}
* Denotes replayed transmission from either reader to tag or from tag to reader.  
\end{table}
Table 2: Comparison of security features of different protocols.