# Enabling Horizontal Collaboration in Logistics Through Secure Multi-Party Computation
## 2 Preliminaries
### Introduction to MPC
The idea is that any secret value \(x\) can be \"split\" into \(n\) elements \(x_{1},\ldots,x_{n}\) called _shares_ using a secret sharing scheme [24], in such a way that no \"small\" coalition of parties can recover any information on \(x\) based on the shares in their possession, while larger coalitions can completely reconstruct \(x\) given their set of shares. This sharing system is also supposed to support the evaluation of sums and products, meaning that given shares of two values \(x\) and \(y\), it is possible to compute shares of \(x+y\) and of \(x\cdot y\) without revealing any information on \(x\) nor \(y\). The idea is then to express the function \(f\) as a circuit, compute shares of each input value, and evaluate the circuit on these shares; once shares of the output value \(f\Big{(}x^{(1)},\ldots,x^{(n)}\Big{)}\) are obtained, parties can then reveal these shares and reconstruct the output. Security is guaranteed under the assumption that the adversary can only control a \"small\" coalition. Comparison to Other Privacy-Preserving Technologies  
In addition to MPC, a variety of other privacy-enhancing technologies (PETs) has been introduced in the academic literature and found various applications in different domains in the real world. Thus, we will next briefly justify the choice for our MPC-based solution presented in the subsequent sections. The main alternative paradigm for secure computation besides MPC is that of fully homomorphic encryption (FHE), which enables computations on encrypted data without decrypting them, hence preserving privacy throughout the process. This allows data owners to outsource sensitive data processing, such as to cloud services, while keeping the underlying information confidential. The encrypted results can then be decrypted only by the data owner's secret key. Since its conceptual introduction by [PERSON] et al. [33] and its first practical realization in 2009 [34], FHE has seen many advances but remains computationally expensive and slower than working with plaintext data. In the context of our scenario, protecting sensitive business information is crucial. Yet, while FHE could theoretically allow computations on encrypted inputs from multiple parties, it is not a fully natural choice here, as the master secret key (needed for decrypting the final computation result) needs to be handled securely, thus again requiring either a trusted entity managing the key--the avoidance of which is the main ambition of this work--or a distributed setup resembling to MPC. Another main approach used for federated computations, especially in the context of federated learning, is that of differential privacy (DP) [35]. This is a technique for protecting individual data entries in a dataset by adding carefully calibrated randomness to the output of computations. It ensures that the inclusion or exclusion of a single data point does not significantly affect the result, thereby providing strong privacy guarantees. DP is particularly well-suited for statistical analysis, aggregate queries, and releasing anonymized datasets. However, in collaborative logistics optimization--where multiple hauliers aim to jointly optimize truck utilization--DP is not ideal: our use case requires precise, per-instance decisions (e.g., matching specific orders to trucks), where even small inaccuracies introduced by DP noise can degrade the quality of the solution.