ON THE SECURITY OF GENERALIZED MULTILINEAR MAPS BASED ON WEIL PAIRING

In 2017, Tran et al. proposed a multilinear map based on Weil pairings to realize the Boneh-Silverberg scheme. They proposed an algorithm to evaluate the Boneh-Silverberg multilinear map and showed that it could be used to establish a shared key in multipartite key exchange for five users. They claimed their scheme was secure and computable in establishing a shared key between 5 users. Unfortunately, they did not prove that their scheme meets three additional computational assumptions proposed by Boneh and Silverberg. In this paper, with some computational modifications, we show that the algorithm proposed by Tran et al. does not satisfy three security assumptions proposed by Boneh and Silverberg. Therefore, every user involved in this multipartite key exchange can obtain the shared key and other users' secret values. We also show that the computation to obtain a shared key is inefficient because it requires a lot of computation and time.