Re: [bitcoin-dev] Question regarding Confidential Transactions

[Adam Gibson <ekaggata@gmail.com>]

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In case it helps:
The elements alpha sidechain uses a different address format, which
includes an ECDH pubkey used for creating an ECDH shared secret.
That shared secret is used to seed a RFC6979 prng, which allows both
sides to generate the blinding factors used in the rangeproof.

So the situation is: both sides can generate the blinding factors, but
also the fake signatures used in the rangeproof (the basic idea there
is to have N signatures in a ring, but only one of them real; the rest
are forged and can be (must be) entirely random numbers. I say 'basic'
because the Borromean sig design is to link together several rings,
not just one). This allows the sender to embed the amount into one of
those fake signatures (usually the last one) using xor, with certain
formatting details.

It would be possible to not bother to embed the amount in this way;
the receiver, knowing the stream of fake/real signatures (again -
because he knows the seed for the prng), could simply observe which
ones are real and therefore know the digits of the amount. But if he
did it this way, it would not be possible to embed any other data into
the range proof (such as: auditing related information) using xor as
above.

I did some detailed explanation/investigation of this in sections 3.3
and 3.4 of
https://github.com/AdamISZ/ConfidentialTransactionsDoc/blob/master/essayonCT.pdf
; with apologies for any errors, it was just an investigation I did
last summer.


On 02/10/2016 06:39 PM, Jeremy Papp via bitcoin-dev wrote:
> On 2/10/2016 5:53 AM, Henning Kopp wrote:
>> Hi Jeremy,
>> 
>>> My understanding of the paper is that the blinding factor would
>>> be included in the extra data which is incorporated into the
>>> ring signatures used in the range proof.
>> Yep, that is a possibility. The blinding factor could be
>> encrypted with the public key of the receiver. Thus it is only
>> visible for the receiver who can then check that the correct
>> amount has been sent.
> ECC doesn't work like RSA; you can't encrypt directly with a
> public key.  That's why you generate a shared secret between sender
> and receiver.  See also, ECDH. (Basically, if (m, M = m*G) is your 
> private/public key pair, and (n, N = n*G) is your recipient's
> private public key pair, you can both generate shared secret S =
> m*N = n*M = m*n*G without revealing your private keys to each
> other, and without revealing the secret to anyone else as long as
> they don't know either private key. You then use S as the basis for
> the key to some symmetric algorithm.)
>>> you'd transmit it then, though in any case, since using it
>>> will pretty much require segwit, adding extraneous data isn't
>>> much of a problem.  In both cases, I imagine the blinding
>>> factor would be protected from outside examination via some
>>> form of shared secret generation... Although that would require
>>> the sender to know the recipient's unhashed public key; I don't
>>> know of any shared secret schemes that will work on hashed
>>> keys.
>> Here you lost me. Why do we need to create a shared secret? Is
>> this shared secret used as the blinding factor? Also I think the
>> sender knows the unhashed public key of the receiver. The only
>> reason not to include it in the transaction script is that an 
>> external observer is unable to see the receiver directly in the 
>> blockchain.
> Normal Bitcoin transactions are made to the hash of a public key
> because once the public key is known, it becomes easier to break it
> if we ever develop quantum computers. That's why it's recommended
> that you only spend from a particular address once (if possible)
> since its only in spending that you are required to reveal your
> public key.   Since you can't do a shared secret with a public key
> hash, AFAIK, you'd have to know the public key of your recipient to
> be able to do ECDH.
> 
> Jeremy Papp _______________________________________________ 
> bitcoin-dev mailing list bitcoin-dev@lists.linuxfoundation.org 
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
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