Enhanced password-based simple three-party key exchange protocol

Recently, Lu and Cao proposed a simple three-party password-based key exchange (STPKE) protocol based on the CCDH assumption. They claimed that their protocol is secure, efficient, and practical. In this paper, unlike their claims, we find that the STPKE protocol is still vulnerable to undetectable on-line password guessing attacks by using formal description, BPR model. These weakness is due to the fact that the messages of the communicants are not appropriately encrypted into the exchanged cryptographic messages. To enhance the security of the STPKE protocol, we suggest a countermeasure to resist our described attacks while the merits of the original protocol are left unchanged.