Crypto Questions

[Peter Fairbrother]

Two general crypto questions :

1) Is there a way to have reliable authentication that is repudiable? I
think the concepts are too similar, but it would be useful.

2) Does anyone know of a backwards hash, ie an algorithm that gives a
previously specified result from a cyphertext but which is infeasible to
reverse?  How would you generate the cyphertext? No secret keys allowed.

Sounds impossible but I haven't had breakfast yet.

Peter