Securely solving simple combinatorial graph problems

Abstract. We investigate the problem of solving traditional combina-torial graph problems using secure multi-party computation techniques, focusing on the shortest path and the maximum flow problems. To the best of our knowledge, this is the first time these problems have been addressed in a general multi-party computation setting. Our study high-lights several complexity gaps and suggests the exploration of various trade-offs, while also offering protocols that are efficient enough to solve real-world problems.