Multi-LHL protocol

We present a password-authenticated group key exchange protocol where each user has his/her own password. Advantage of such protocol is in short passwords, which can be easily memorized. On the other hand these protocols face the low password entropy. In the first part we define security model based on models of Abdalla, Fouque and Pointcheval and Bellare, Pointcheval, Rogaway. We construct the MLHL (Multi-LHL) protocol, which is based on the LHL protocol proposed by Lee, Hwang and Lee. However, the LHL protocol is flawed as pointed by Abdalla, Bresson, Chevassut and Choo, Raymond. We prove that our protocol is secure authenticated key exchange protocol with forward secrecy property and that the protocol is resistant against attacks on the LHL protocol.