I wrote an article about an ECDH extension for BIP 70:

   https://medium.com/p/cb2f81962c1b

The article is meant for people who don't follow bitcoin-development so
I'll summarise it here:

   - The notion of being able to publish a piece of data once and use it to
   receive lots of payments without any coordination is really useful. This is
   the idea behind the stealth address proposal.

   - Stealth addresses don't fit with the payment protocol, because they're
   a new kind of address (obviously).

   - Stealth addresses are not backwards compatible. If you give someone a
   stealth address and their wallet doesn't support it, they can't pay you,
   not even with worse privacy. Sometimes people may optionally want that
   behaviour but stealth addresses have it all the time.

   - The proposed stealth address design makes huge sacrifices to try and
   keep everything within the block chain. It bloats the chain with OP_RETURN
   stuff that isn't a part of the validation. But more seriously, the only way
   to make it efficient enough for lightweight clients is to reduce the
   "stealthyness". The more efficient you make your address the less private
   it becomes. This is somewhat similar to the dilemma we have with Bloom
   filtering, except Bloom filters are transient and can only be used to link
   addresses by someone who observes them on the wire. Stealth addresses
   record the relationship in the block chain forever.

   - The design makes these sacrifices to avoid moving data around outside
   the block chain. But with BIP 70 that's the direction we're heading in
   anyway. So by adding ECDH to the payment protocol and putting our effort
   into making BIP 70 work really well for everyone, we end up killing
   multiple birds with one stone. The same work that resolves the privacy
   problems inherent in the stealth address design also allows us to attach
   messages to payments and other commonly requested features.

There's a straw man in the article that I recreate here:

message Output {
   optional uint64 amount = 1 [default = 0];
   optional bytes script = 2;
   *optional boolean accept_ecdh = 3;  // Requires script to be a
pay-to-pubkey output.*
}

message Payment {
   optional bytes merchant_data = 1;
   repeated bytes transactions = 2;
   repeated Output refund_to = 3;
   optional string memo = 4;
   *repeated bytes ecdh_nonces = 5;*
}

The way the nonces are combined to arrive at the address could be the same
as in the current stealth address spec. A wallet that doesn't understand
ECDH but does understand raw BIP 70 would deliver the money to the base
address, which receiving wallets would look for too - so it's backwards
compatible. The nonces stay out of the block chain. The transactions are
delivered directly to the recipient so there's no problems with trying to
make it fit with Bloom/prefix filtering.

To make this work there obviously has to be a backchannel from payer to
payee. BIP 70 is mostly used by web shops today so that back channel is
just HTTPS to the website itself, but shops benefit less from ECDH than
others do. So we need a simple email-like store and forward network where
HTTP POSTs to a server get queued up and delivered later (or possibly
forwarded to another store-and-forward network like the Android push
network). Most of the article discusses how best to build such a thing.

The justification for the original stealth address design can be summed up
as "it's easier to [ab]use the Bitcoin network for delivery of short
messages than use a different system". But there are just so many features
we may want to add into the Payment message in future it seems better to
crack the SaF problem earlier rather than continue trying to jam a square
peg into a round hole. There are lots of very reliable SAF networks around
(email, instant messaging, etc) so it doesn't seem infeasible.

Thoughts welcome!