Many Petri nets-based methods have been developed and applied to analyze cryptographic protocols. Most of them offer the analysis of one attack trace only. Only a few of them provide the analysis of multiple attack traces, but they are rather inefficient. Similarly, the limitation of the analysis of one attack trace occurs in most model checking methods for cryptographic protocols. Recently, we proposed a simple but practical Petri nets-based model checking methodology for the analysis of cryptographic protocols, which offers an efficient analysis of all attack traces. In our previous analysis, we assume that the underlying cryptographic algorithms are black boxes, and attackers cannot learn anything from cipher text if they do not have a correct key. In this paper, we relax this assumption by considering some algebraic properties of the underlying encryption algorithm. Then, we apply our new method to TMN authenticated key exchange protocol as a case study. Surprisingly, we obtain a very efficient analysis when the numbers of attack traces and states are large, and we discover two new attacks which exploit the algebraic properties of the encryption.