Secure linear system computation in the presence of malicious adversaries

In this paper, we study the system of linear equation problems in the two-party computation setting. Consider that P1 holds an m × m matrix M1 and an m-dimensional column vector B1. Similarly, P2 holds M2 and B2. Via executing a secure linear system computation, P1 gets the output x (or ⊥) conditioned on (M1 + M2)x = (B1 + B2), and the rank of matrix M1 + M2, while P2 gets nothing. This also can be used to settle other cooperative linear system problems. We firstly design an efficient protocol to solve this problem in the presence of malicious adversaries, then propose a simple way to modify our protocol for having a precise functionality, in which the rank of matrix M1+M2 is not necessary. We note that our protocol is more practical than these existing malicious secure protocols. We also give comparisons with other protocols and extensions to similar functions.