A review of the password authenticated key exchange protocols vulnerabilities and principles of the SESPAKE protocol construction

We consider a family of protocols permitting the parties sharing a weak key (a password) to generate a strong common key using the unprotected channel. It is supposed that to check the password correctness the adversary should interact with legitimate participants. A review of the known vulnerabilities of the protocols of the family considered is given. This review is used to explain the main principles of the SESPAKE protocol construction.