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Date: Mon, 7 Oct 2013 21:01:03 +0200
From: Adam Back <adam@cypherspace.org>
To: Mark Friedenbach <mark@monetize.io>
Message-ID: <20131007190103.GA6811@netbook.cypherspace.org>
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Cc: Bitcoin Dev <bitcoin-development@lists.sourceforge.net>
Subject: Re: [Bitcoin-development] homomorphic coin value (validatable but
 encrypted) (Re: smart contracts -- possible use case? yes or no?)
Precedence: list

An update on the homomorphic coins, some more math validation & a test
implementation needs to be done, but a surprisingly good outcome so far of
predicted 2.5kB homomorphic valued coin.  Only coin splitting has to incur
the 2.5kB range proof.  Coin adding, full spending and mining is "free",
because adding existing range proofed and validated coins cant overflow by
definition (21 mil coin cap).  You can also (obviously I guess) add a
homomorphicaly encrypted "0" value to a few other peoples coin balance to
get a kind of taint mitigation.

https://bitcointalk.org/index.php?topic=305791.msg3294618#msg3294618

Adam

On Tue, Oct 01, 2013 at 09:11:43PM +0200, Adam Back wrote:
>Err actually not (efficient) I made a mistake that came out when I started
>writing it up about how the t parameter in the proof relates to bitcoin
>precision and coin representation (I thought t=2, but t=51).  Damn!  Back to
>the not so efficient version (which is more zerocoin-esque in size/cost), or
>the more experimental Schoenmaker non-standard p, q non EC one, or other
>creative ideas to change the coin representation to simplify the proof (of
>which this was a failed attempt).  See the bitcointalk thread for details.
>
>https://bitcointalk.org/index.php?topic=305791.new#new
>
>Adam
>
>On Tue, Oct 01, 2013 at 04:26:03PM +0200, Adam Back wrote:
>>On Sun, Sep 29, 2013 at 10:49:00AM -0700, Mark Friedenbach wrote:
>>>This kind of thing - providing external audits of customer accounts
>>>without revealing private data - would be generally useful beyond
>>>taxation. If you have any solutions, I'd be interested to hear them
>>>(although bitcoin-dev is probably not the right place yet).
>>
>>Thanks for providing the impetus to write down the current state, the
>>efficient version of which I only figured out a few days ago :)
>>
>>I have been researching this for a few months on and off, because it seems
>>like an interesting construct in its own right, a different aspect of
>>payment privacy (eg for auditable but commercial sensistive information) but
>>also that other than its direct use it may enable some features that we have
>>not thought of yet.
>>
>>I moved it to bitcointalk:
>>
>>https://bitcointalk.org/index.php?topic=305791.new#new
>>
>>Its efficient finally (after many dead ends): approximately 2x cost of
>>current in terms of coin size and coin verification cost, however it also
>>gives some perf advantages back in a different way - necessary changes to
>>schnorr (EC version of Schnorr based proofs) allow n of n multiparty sigs,
>>or k of n multiparty sigs for the verification cost and signature size of
>>one pair of ECS signatures, for n > 2 its a space and efficiency improvement
>>over current bitcoin.
>>
>>Adam