The security is an important issue in the mobile communications such as LTE/SAE systems, especially the mobile users' authentication and key production process which includes the most important risks. In this paper, we survey and compare authentication and key production solutions, namely the traditional solution EPS-AKA (Evolved Packet Switching -Authentication and key Agreement) which we consider as a benchmark solution and the J-PAKE (Password authenticated Key Exchange by Juggling) mechanism, included in the 4G networks by Cristina-Elena Vintilă et al., which have many advantages such as off-line and on-line dictionary attacks resistance, forward secrecy and Known-key security, so that we can show the strengths and weakness of these solutions.