# Securely Computing the Manhattan Distance under the Malicious Model and Its Applications
## 5 The MPC Protocol of Computing Manhattan Distance under the Malicious Model
### Specific Protocol
This research was funded by NSFC, grant numbers 92046001 and 61962009; Inner Mongolia Natural Science Foundation, grant number 2021 MS06006; 2022 Basic Scientific Research Project of Direct Universities of Inner Mongolia, grant number 20220101; 2022 Fund Project of Central Government Guiding Local Science and Technology Development, grant number 20220175; 2022 \"Western Light\" Talent Training Program \"Western Young Scholars\" Project; Inner Mongolia Discipline Inspection and Supervision Big Data Laboratory Open Project Fund, grant number IMDBD202020; Baotou Kundulun District Science and Technology Plan Project, grant number YF2020013; the 14 th Five Year Plan of Education and Science of Inner Mongolia, grant number NGJGH2021167; Inner Mongolia Science and Technology Major Project, grant number 2019 ZD025; 2022 Inner Mongolia Postgraduate Education and Teaching Reform Project, grant number 20220213; the 2022 Ministry of Education Central and Western China Young Backbone Teachers and Domestic Visiting Scholars Program, grant number 20220393; Basic Scientific Research Business Fee Project of Beijing Municipal Commission of Education, grant number 110052972027; Research Startup Fund Project of North China University of Technology, grant number 110051360002. This article does not contain any studies with human participants performed by any of the authors. Not applicable. The authors approve that data used to support the finding of this study are included in the article. In the process of completing the manuscript, I got the help of many people. First of all, I should thank [PERSON] for giving me many valuable opinions and providing me with the greatest support in thought and action. Second, I thank [PERSON] for making a lot of amendments and suggestions to the manuscript. Finally, I want to thank my family, classmates, and friends for their support and encouragement. The authors declare no conflict of interest. ## Abbreviations \begin{tabular}{l l} \(N\) & \(N=pq\), Both \(p\) and \(q\) are large primes \\ \(m\) & Plaintext \\ \(c\) & Ciphertext \\ \(pk(A)/sk(A)\) & The public and private keys of [PERSON]'s GM encryption system \\ \(pk(B)/sk(B)\) & The public and private keys of [PERSON]'s GM encryption system \\ \((g_{a},N_{a})\) & The public key of [PERSON]'s Paillier encryption system \\ \((g_{b},N_{b})\) & The public key of [PERSON]'s Paillier encryption system \\ \(\lambda_{a}\) & The private key of [PERSON]'s Paillier encryption system \\ \(\lambda_{b}\) & The public key of [PERSON]'s Paillier encryption system \\ \end{tabular} 

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