[bitcoin-dev] Updates on Confidential Transactions efficiency

Gregory Maxwell greg at xiph.org
Tue Nov 14 10:38:33 UTC 2017

On Tue, Nov 14, 2017 at 9:11 AM, Peter Todd <pete at petertodd.org> wrote:
> I _strongly_ disagree with this statement and urge you to remove it from the
> paper.

I very strongly disagree with your strong disagreement.

> The worst-case risk of undetected inflation leading to the destruction of a
> currency is an easily quantified risk: at worst any given participant loses
> whatever they have invested in that currency. While unfortunate, this isn't a
> unique or unexpected risk: cryptocurrencies regularly lose 50% - or even 90% -
> of their value due to fickle markets alone. But cryptocurrency owners shrug
> these risks off. After all, it's just money, and diversification is an easy way
> to mitigate that risk.
> But a privacy break? For many users _that_ threatens their very freedom,
> something that's difficult to even put a price on.

Its important that people know and understand what properties a system has.

Perhaps one distinction you miss is that perfectly hiding systems
don't even exist in practice: I would take a bet that no software on
your system that you can use with other people actually implements a
perfectly hiding protocol (much less find on most other people's
system system :)).

In the case of practical use with CT perfect hiding is destroyed by
scalability-- the obvious construction is a stealth address like one
where a DH public key is in the address and that is used to scan for
your payments against a nonce pubkey in the transactions.   The
existence of that mechanism destroys perfect hiding.  No scheme that
can be scanned using an asymmetric key is going to provide perfect

Now, perhaps what you'd like is a system which is not perfect hiding
but where the hiding rests on less "risky" assumptions.  That is
something that can plausibly be constructed, but it's not itself
incompatible with unconditional soundness.

As referenced in the paper, there is also the possibility of having a
your cake and eating it too-- switch commitments for example allow
having computational-hiding-depending-on-the-hardness-of-inverting-hashes
 (which I would argue is functionally as good as perfect hiding, esp
since hiding is ultimately limited by the asymmetric crypto used for
discovery)  and yet it retains an option to upgrade or block spending
via unsound mechanisms in the event of a crypto break.

> Furthermore, the risk of inflation is a risk that's easily avoided:

Sounds like you are assuming that you know when there is a problem, if
you do then the switch commitments scheme works and doesn't require
any selling of anything. Selling also has the problem that everyone
would want to do it at once if there was a concern; this would not
have good effects. :) Without switch commitments though, you are just
hosed.  And you cannot have something like switch commitments without
abandoning perfect hiding ( though you get hiding which is good enough
(tm), as mentioned above).

On Tue, Nov 14, 2017 at 10:07 AM, Peter Todd <pete at petertodd.org> wrote:
> Re: the unprunable accumulators, that doesn't need to be an inherent property
> of Zcash/Monero style systems.
> It'd be quite feasible to use accumulator epochs and either make unspent coins
> in a previous epoch unspendable after some expiry time is reached - allowing

Miners to reduce coin supply, enhancing the value of their own
holdings, by simply not letting near-expiry ones get spent...
(This can be partially mediated by constructing proofs to hide if a
coins in near expiration or not.)

> or make use of a merkelized key-value scheme with transaction provided proofs to shift the costs of
> maintaining the accumulator to wallets.

Yes, that they can do-- though with the trade-offs inherent in that.
It is worse than what you were imagining in the Bitcoin case because
you cannot use one or two time-ordered trees, the spent coins list
needs search-insertion; so maintaining it over time is harder. :(  The
single time ordered tree trick doesn't work because you can't mutate
the entries without blowing anonymity.

I think it's still fair to say that ring-in and tree-in approaches
(monero, and zcash) are fundamentally less scalable than
CT+valueshuffle, but more private-- though given observations of Zcash
behavior perhaps not that much more private.  With the right smart
tricks the scalablity loss might be more inconvenient than fatal, but
they're still a loss even if they're one that makes for a good

As an aside, you shouldn't see Monero as entirely distinct now that
we're talking about a framework which is fully general:  Extending
this to a traceable 1 of N input for monero is simple-- and will add
size log() in the number of ring inputs with good constant factors.
One could also store inputs in a hash tree, and then have a
bulletproof that verified membership in the tree.  This would provide
tree-in style transactions with proofs that grow with the log() of the
size of the tree (and a spent coins accumulator); the challenge there
would be choosing a hash function that had a compact representation in
the arithmetic circuit so that the constant factors aren't terrible.
Effectively that's what bulletproofs does:   It takes a general scheme
for ZKP of arbitrary computation, which could implement a range proof
by opening the commitments (e.g. a circuit for EC point scalar
multiply) and checking the value, and optimizes it to handle the
commitments more directly. If you're free to choose the hash function
there may be a way to make a hash tree check ultra efficient inside
the proof, in which case this work could implement a tree-in scheme
like zcash-- but with larger proofs and slower verification in
exchange for much better crypto assumptions and no trusted setup.
This is part of what I meant by it opening up "many other interesting

But as above, I think that the interactive-sparse-in (CJ) has its own
attractiveness, even though it is not the strongest for privacy.

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