```Thanks Peter for the paper!

I'm just going to restate your 'simple explanation' to make sure I got
it...```
```
The payee publishes a public key of theirs, which will be a long-standing
identifier, public key = 'Q', corresponding private key = 'd'.

To pay them, payee generate a keypair, private key = 'e' public key of
'P'. Publish 'P' in the transaction.

The payer can calculate S = eQ, where S is a shared secret between
payer/payee. The payee calculates the same S as S = dP. So the payee sees
'P' in a transaction, and multiplies by their private key, to get S.

Now that we have the shared secret, either side can calculate an offset to
Q which becomes the pay-to-address. When you say BIP32-style derivation,
Q' = H(S) + Q, does this mean Q + SHA256(33-byte S)?

A payee has to check each transaction (or every transaction of a fixed
prefix) with 'P', calculate Q' = Q + H(dP) and see if that transaction
pays to Q'. If the address matches, then the payee can spend it with
private key of d + H(dP).

One downside is that you have to hold your private key in memory
unencrypted in order to identify new payments coming in. So
stealth-addresses may not be suitable for receiving eCommerce payments,
since you can't implement a corresponding watch-only wallet, e.g. there's
no way to "direct-deposit into cold storage."

Hope I got that right...

On Mon, 06 Jan 2014 04:03:38 -0800, Peter Todd <p...@petertodd.org> wrote:

> Using Elliptic curve Diffie-Hellman (ECDH) we can generate a shared
> secret that the payee can use to recover their funds. Let the payee have
> keypair Q=dG. The payor generates nonce keypair P=eG and uses ECDH to
> arrive at shared secret c=H(eQ)=H(dP). This secret could be used to
> derive a ECC secret key, and from that a scriptPubKey, however that
> would allow both payor and payee the ability to spend the funds. So
> instead we use BIP32-style derivation to create Q'=(Q+c)G and associated
> scriptPubKey.
>
> As for the nonce keypair, that is included in the transaction in an
>    RETURN <P>

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