1. Introduction
Nowadays we frequently use Instant Messaging (IM) system for communication. While it provides us convenience to interact with others, there exist some side effects like an invasion of privacy through eavesdropping. Thus, popular IM systems such as Telegram and Threema have strengthened their security by message encryption. It makes the message unreadable to anybody except the sender and the receiver. However, it is still weak in a brute-force attack because the security of cryptosystem depends on the key size which has potential vulnerability to be cracked. There are 2n possible keys with a n-bit key, so the attacker needs to try 2128 operations for cracking 128-bit key. In the case of Password based encryption (PBE), the necessary number of operations for cracking the key are much less by the fact that user-chosen passwords are tend to be weak, which results in the small key space.