Encrypted chat over WebID

I've been thinking for some time about WebID based chat.  Also interesting
is the crypto cat spec:

https://project.crypto.cat/documents/spec/spec-rev1.4a.pdf

It seems there's some concern about exposing your private key, in case of
zero day exploits etc.

However it's typical to use PKI to generate a "shared secret" that can be
used, say, to encrypt chat.

Initially it could be possible to communicate a shared secret out of band
(eg i could sent you a mail etc.)

However, I was wondering if there could be a smart way to implement this
using WebID.  Can anyone think of a possible algorithm for this?