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Date: Tue, 1 Oct 2013 16:26:03 +0200
From: Adam Back <adam@cypherspace.org>
To: Mark Friedenbach <mark@monetize.io>
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Cc: Bitcoin Dev <bitcoin-development@lists.sourceforge.net>
Subject: [Bitcoin-development] homomorphic coin value (validatable but
 encrypted) (Re: smart contracts -- possible use case? yes or no?)
Precedence: list

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