# 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
As shown in Figure 4, both military sides select military bases in an area, and neither side wants the other party to know where their military bases are located. At the same time, the military exchanges between the two sides are close, and the driving distance between the two military bases should be moderate, that is, the distance should be appropriate. In such an actual scene, the range size of the specified area is equivalent to the given complete set. Both parties just select the appropriate coordinate system in the area, and the location of the military bases of both parties is selected within the range of the complete set. For the suitability of the distance, both parties can jointly calculate the Manhattan distance between two points to make appropriate adjustments. There are many similar scenarios, and there will be many constrained optimization problems in engineering practice, scientific research, and other fields. Therefore, to better solve the optimization constraint problem, it is particularly important to calculate the Manhattan distance between two points. 3. Today, with the development of information, information search and matching have practical application value. The location relationship between the security decision vector and the vector interval is the solution to solve the secure searching and matching. The problem of the relationship between the security decision vector and the vector set can also be solved by computing the Manhattan distance securely. ## 8 Conclusions

Securely computing Manhattan distance is a basic module for designing other MPC geometric protocols, so it has important theoretical significance and application value to study this problem. Given the shortcomings of existing protocols, combining [PERSON]'s

Figure 4: Site selection diagram of military base. algorithm with additive homomorphism and GM encryption algorithm with Xor homomorphism, this paper takes the lead in designing a protocol with high-security performance under the premise of resisting malicious participant attacks. Algorithm 2 used tools such as the cut-choose method to prevent deception. The real/ideal model paradigm method is used to prove the security of the malicious model protocol. Compared with existing protocols, the experimental simulation shows that only Algorithm 2 can resist malicious participants' attacks while maintaining high efficiency. The protocol is close to the reality of the existence of malicious participants and has more practical value. The next step is to improve Algorithm 2, using the homogeneous secret sharing to pass the ciphertext, to improve the protocol efficiency. Conceptualization, X.L. ([PERSON]) and X.L. ([PERSON]); funding acquisition, X.L. ([PERSON]); investigation, X.L. ([PERSON]); methodology, R.Z. ; software, D.L. and G.X. ; validation, G.X. and X.C. ; writing--original draft, [PERSON] ([PERSON]); writing--review and editing, [PERSON] ([PERSON]), G.X., and X.C. All authors have read and agreed to the published version of the manuscript.