Is there a way to derive a 1024-bit key from the key
pair generated from the DH key agreement algorithm for
use with RSA 1024 encryption?  

More generally, I am looking for a reasonably secure
way to encrypt arbitrary data using a public key from
one of the participants in a successful DH exchange,
or possibly from the shared agreed key generated by
that exchange.  

The goal is that both sides of the exchange could
either use one of the exhanged keys or derive a new
key for use with a block or stream cipher, without
actually sending this new key over the wire.

Mike

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