Question regarding Confidential Transactions
5 messages, 9 to 13 Feb 2016. Started by Henning Kopp.
Henning Kopp (2), Jeremy Papp (2), waxwing/ AdamISZ
Hi all,
I am trying to fully grasp confidential transactions.
When a sender creates a confidential transaction and picks the blinding values correctly, anyone can check that the transaction is valid. It remains publically verifiable. But how can the receiver of the transaction check which amount was sent to him? I think he needs to learn the blinding factor to reveal the commit somehow off-chain. Am I correct with this assumption? If yes, how does this work?
All the best Henning
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.
Although, since I think the range proof is optional for single output transactions (or at least, one output per transaction doesn't require a range proof since there's only one possible value that it can be to make the whole thing work, and that value must be in range, I'm not entirely sure how 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.
Jeremy Papp
On 2/9/2016 7:12 AM, Henning Kopp via bitcoin-dev wrote:
Quoted text (16 lines)
> Hi all, > > I am trying to fully grasp confidential transactions. > > When a sender creates a confidential transaction and picks the blinding > values correctly, anyone can check that the transaction is valid. It > remains publically verifiable. > But how can the receiver of the transaction check which amount was > sent to him? > I think he needs to learn the blinding factor to reveal the commit > somehow off-chain. Am I correct with this assumption? > If yes, how does this work? > > All the best > Henning >
Hi Jeremy,
Quoted text (3 lines)
> 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.
Quoted text (4 lines)
> Although, since I think the range proof is optional for single output > transactions (or at least, one output per transaction doesn't require a > range proof since there's only one possible value that it can be to make the > whole thing work, and that value must be in range, I'm not entirely sure how
I understand and agree.
Quoted text (6 lines)
> 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.
Best Henning
On Tue, Feb 09, 2016 at 04:12:37PM -0600, Jeremy Papp via bitcoin-dev wrote:
Quoted text (40 lines)
> 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. > > Although, since I think the range proof is optional for single output > transactions (or at least, one output per transaction doesn't require a > range proof since there's only one possible value that it can be to make the > whole thing work, and that value must be in range, I'm not entirely sure how > 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. > > Jeremy Papp > > On 2/9/2016 7:12 AM, Henning Kopp via bitcoin-dev wrote: > >Hi all, > > > >I am trying to fully grasp confidential transactions. > > > >When a sender creates a confidential transaction and picks the blinding > >values correctly, anyone can check that the transaction is valid. It > >remains publically verifiable. > >But how can the receiver of the transaction check which amount was > >sent to him? > >I think he needs to learn the blinding factor to reveal the commit > >somehow off-chain. Am I correct with this assumption? > >If yes, how does this work? > > > >All the best > >Henning > > > > _______________________________________________ > bitcoin-dev mailing list > bitcoin-dev@lists•linuxfoundation•org > https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev >
On 2/10/2016 5:53 AM, Henning Kopp wrote:
Quoted text (8 lines)
> 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.)
Quoted text (13 lines)
>> 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
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:
Quoted text (45 lines)
> 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