** <math>\Pi^S_i</math> won't have a chance to reach consistency for the messages receives after ''p''

To ensure that the forward secrecy in long living chat session ''(n+1)sec'', provide session key update through the session. Each message sent to the session by each participant contains meta data described in Section XX. Prior to sending any message, ''(n+1)sec'' instance, determines the content of meta data, and piggy back that to the message according to the following algorithm: