Password-Based Authenticated Key Exchange

Authenticated Key Exchange protocols enable several parties to establish a shared cryptographically strong key over an insecure network using various authentication means, such as strong cryptographic keys or short (i.e., low-entropy) common secrets. The latter example is definitely the most interesting in practice, since no additional device is required, but just a human-memorable password, for authenticating the players. After the seminal work by Bellovin and Merritt, many settings and security notions have been defined, and many protocols have been proposed, in the two-user setting and in the group setting.