# Universally Composable Oblivious Transfer with Low Communication
## 7 Conclusions  
This paper constructs a UC-secure OT protocol on lattice based on the Mod-LWR difficult problem. The protocol obtains universally composable security under the random oracle machine model and can resist static adversary attacks. Besides, the comparison with other UC-secure OT protocols shows that the protocol has constant interaction rounds and low communication costs.  
Depending on the attack strategy of the adversary, it can be classified as a static adversary, dynamic adversary, or proactive adversary. Therefore, the following research focuses on an OT protocol that can resist other types of attacks.  
Conceptualization, [PERSON]; formal analysis and investigation, [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON]. ([PERSON]); writing--original draft preparation, [PERSON]; writing--review and editing, [PERSON]; visualization, [PERSON]; supervision, [PERSON]; [PERSON], [PERSON] ([PERSON]), [PERSON] and [PERSON]. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Scheme**} & \multicolumn{1}{c}{**Assumption**} & \multicolumn{1}{c}{**Model**} & \multicolumn{1}{c}{**Security**} & \multicolumn{1}{c}{**Strategy**} & \multicolumn{1}{c}{**Rounding**} & \multicolumn{1}{c}{**Communication**} & \multicolumn{1}{c}{**Computational**} \\  & & & & & & & & **Cost** & \\ \hline Peikert [16] & LWE & CRS & UC & Static & At least 2 & \(O\big{(}n^{2}\text{lgn}\big{)}\big{(}Z_{q}\big{)}\) & \(O\big{(}n^{3}\text{lgn}\big{)}(\times)\) \\ [PERSON] [23] & RLWE & ROM & UC & Static & 3 & \(O\big{(}n^{2}\big{)}\big{(}Z_{q}\big{)}\) & \(O\big{(}n^{3}\big{)}(\times)\) \\ [PERSON] [24] & LWE & CRS & UC & Static & 2 & \(O\big{(}n^{2}\text{lgn}\big{)}\big{(}Z_{q}\big{)}\) & \(O\big{(}n^{3}\text{lgn}\big{)}(\times)\) \\ Our & Mod-LWR & ROM & UC & Static & 3 & \(O\big{(}n^{2}\big{)}(R_{t}\big{)}\) & \(O\big{(}n^{3}\text{lgn}\big{)}(+)\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison with other OT protocols.  
**Funding:** This research was supported in part by the National Natural Science Foundation of China (61370188), in part by the Beijing Municipal Education Commission Scientific Research Project (KM202010015009), in part by the Beijing Municipal Education Commission Scientific Research Project Funding (KM202110015004), in part by the Beijing Institute of Graphic Communication Doctoral Funding Project (27170120003/020), in part by the Beijing Institute of Graphic Communication Research Innovation Team Project (Eb202101), in part by the Intramural Discipline Construction Project of Beijing Institute of Graphic Communication (21090121021), in part by the Key Educational Reform Project of Beijing Institute of Graphic Communication under (22150121033/009), in part by the BICC (Ec202201), in part by the Beijing Institute of Graphic Communication Doctoral Funding Project (27170122006), and in part by the general research project of Beijing Association of Higher Education (MS2022093).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data available on request from the authors.  
**Conflicts of Interest:** The authors declare no conflict of interest.