Subject: [bitcoin-dev] Hiding entire content of on-chain transactions

From: Tony Churyumoff <[email-masked]>
Date: Mon, 8 Aug 2016 18:30:21 +0300

This is a proposal about hiding the entire content of bitcoin
transactions.  It goes farther than CoinJoin and ring signatures, which
only obfuscate the transaction graph, and Confidential Transactions, which
only hide the amounts.

The central idea of the proposed design is to hide the entire inputs and
outputs, and publish only the hash of inputs and outputs in the
blockchain.  The hash can be published as OP_RETURN.  The plaintext of
inputs and outputs is sent directly to the payee via a private message, and
never goes into the blockchain.  The payee then calculates the hash and
looks it up in the blockchain to verify that the hash was indeed published
by the payer.

Since the plaintext of the transaction is not published to the public
blockchain, all validation work has to be done only by the user who
receives the payment.

To protect against double-spends, the payer also has to publish another
hash, which is the hash of the output being spent.  We’ll call this hash *spend
proof*.  Since the spend proof depends solely on the output being spent,
any attempt to spend the same output again will produce exactly the same
spend proof, and the payee will be able to see that, and will reject the
payment.  If there are several outputs consumed by the same transaction,
the payer has to publish several spend proofs.

To prove that the outputs being spent are valid, the payer also has to send
the plaintexts of the earlier transaction(s) that produced them, then the
plaintexts of even earlier transactions that produced the outputs spent in
those transactions, and so on, up until the issue (similar to coinbase)
transactions that created the initial private coins.  Each new owner of the
coin will have to store its entire history, and when he spends the coin, he
forwards the entire history to the next owner and extends it with his own
transaction.

If we apply the existing bitcoin design that allows multiple inputs and
multiple outputs per transaction, the history of ownership transfers would
grow exponentially.  Indeed, if we take any regular bitcoin output and try
to track its history back to coinbase, our history will branch every time
we see a transaction that has more than one input (which is not uncommon).
After such a transaction (remember, we are traveling back in time), we’ll
have to track two or more histories, for each respective input.  Those
histories will branch again, and the total number of history entries grows
exponentially.  For example, if every transaction had exactly two inputs,
the size of history would grow as 2^N where N is the number of steps back
in history.

To avoid such rapid growth of ownership history (which is not only
inconvenient to move, but also exposes too much private information about
previous owners of all the contributing coins), we will require each
private transaction to have exactly one input (i.e. to consume exactly one
previous output).  This means that when we track a coin’s history back in
time, it will no longer branch.  It will grow linearly with the number of
transfers of ownership.  If a user wants to combine several inputs, he will
have to send them as separate private transactions (technically, several
OP_RETURNs, which can be included in a single regular bitcoin transaction).

Thus, we are now forbidding any coin merges but still allowing coin
splits.  To avoid ultimate splitting into the dust, we will also require
that all private coins be issued in one of a small number of
denominations.  Only integer number of “banknotes” can be transferred, the
input and output amounts must therefore be divisible by the denomination.
For example, an input of amount 700, denomination 100, can be split into
outputs 400 and 300, but not into 450 and 250.  To send a payment, the
payer has to pick the unspent outputs of the highest denomination first,
then the second highest, and so on, like we already do when we pay in cash.

With fixed denominations and one input per transaction, coin histories
still grow, but only linearly, which should not be a concern in regard to
scalability given that all relevant computing resources still grow
exponentially.  The histories need to be stored only by the current owner
of the coin, not every bitcoin node.  This is a fairer allocation of
costs.  Regarding privacy, coin histories do expose private transactions
(or rather parts thereof, since a typical payment will likely consist of
several transactions due to one-input-per-transaction rule) of past coin
owners to the future ones, and that exposure grows linearly with time, but
it is still much much better than having every transaction immediately on
the public blockchain.  Also, the value of this information for potential
adversaries arguably decreases with time.

There is one technical nuance that I omitted above to avoid distraction.
 Unlike regular bitcoin transactions, every output in a private payment
must also include a blinding factor, which is just a random string.  When
the output is spent, the corresponding spend proof will therefore depend on
this blinding factor (remember that spend proof is just a hash of the
output).  Without a blinding factor, it would be feasible to pre-image the
spend proof and reveal the output being spent as the search space of all
possible outputs is rather small.

To issue the new private coin, one can burn regular BTC by sending it to
one of several unspendable bitcoin addresses, one address per denomination.
 Burning BTC would entitle one to an equal amount of the new private coin,
let’s call it *black bitcoin*, or *BBC*.

Then BBC would be transferred from user to user by:
1. creating a private transaction, which consists of one input and several
outputs;
2. storing the hash of the transaction and the spend proof of the consumed
output into the blockchain in an OP_RETURN (the sender pays the
corresponding fees in regular BTC)
3. sending the transaction, together with the history leading to its input,
directly to the payee over a private communication channel.  The first
entry of the history must be a bitcoin transaction that burned BTC to issue
an equal amount of BCC.

To verify the payment, the payee:
1. makes sure that the amount of the input matches the sum of outputs, and
all are divisible by the denomination
2. calculates the hash of the private transaction
3. looks up an OP_RETURN that includes this hash and is signed by the
payee.  If there is more than one, the one that comes in the earlier block
prevails.
4. calculates the spend proof and makes sure that it is included in the
same OP_RETURN
5. makes sure the same spend proof is not included anywhere in the same or
earlier blocks (that is, the coin was not spent before).  Only transactions
by the same author are searched.
6. repeats the same steps for every entry in the history, except the first
entry, which should be a valid burning transaction.

To facilitate exchange of private transaction data, the bitcoin network
protocol can be extended with a new message type.  Unfortunately, it lacks
encryption, hence private payments are really private only when bitcoin is
used over tor.

There are a few limitations that ought to be mentioned:
1. After user A sends a private payment to user B, user A will know what
the spend proof is going to be when B decides to spend the coin.
 Therefore, A will know when the coin was spent by B, but nothing more.
 Neither the new owner of the coin, nor its future movements will be known
to A.
2. Over time, larger outputs will likely be split into many smaller
outputs, whose amounts are not much greater than their denominations.
You’ll have to combine more inputs to send the same amount.  When you want
to send a very large amount that is much greater than the highest available
denomination, you’ll have to send a lot of private transactions, your
bitcoin transaction with so many OP_RETURNs will stand out, and their
number will roughly indicate the total amount.  This kind of privacy
leakage, however it applies to a small number of users, is easy to avoid by
using multiple addresses and storing a relatively small amount on each
address.
3. Exchanges and large merchants will likely accumulate large coin
histories.  Although fragmented, far from complete, and likely outdated, it
is still something to bear in mind.

No hard or soft fork is required, BBC is just a separate privacy preserving
currency on top of bitcoin blockchain, and the same private keys and
addresses are used for both BBC and the base currency BTC.  Every BCC
transaction must be enclosed into by a small BTC transaction that stores
the OP_RETURNs and pays for the fees.

Are there any flaws in this design?

Originally posted to BCT https://bitcointalk.org/index.php?topic=1574508.0,
but got no feedback so far, apparently everybody was consumed with bitfinex
drama and now mimblewimble.

Tony