[ofriel] Another requirement is that the full public key Y_c is not transmitted 
as part of TLS handshake from client to server. We cannot not use RFC 7250 as 
is. Instead, something like the Known Certificates proposal in cTLS 
https://tools.ietf.org/html/draft-ietf-tls-ctls-01#section-5.1.3 would work.

Is that a primary requirement or a derived requirement?

  I'm not sure of the distinction you're making here.

Well, once again, it seems like the technical requirement is that:

1. You want to authenticate the server to the client (as noted below, I don't 
think that the distinction
you are making between "assurance" and "authenticate" is sufficiently crisp to 
be helpful).
2. The only secret information that the server shares with the client is Y_c.

But this doesn't necessarily preclude the client *sending* Y_c, it merely 
requires that
it not send it to anyone who hasn't proven they know Y_c first. For instance, 
if Y_c
was used as a PSK (as owen suggests), then it might (again, no analysis here)
allow the client to send Y_c in an RFC 7250 certificate message because it would
already be being encrypted under a key that required knowing Y_c.

[ofriel] This makes sense, and should avoid having to use cTLS ‘Known 
Certificates’ for the client’s Certificate RPK.
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