Subject: [bitcoin-dev] Generalized Commitments

From: Peter Todd <[email-masked]>
Date: Wed, 22 Feb 2017 20:26:11 -0500

On Tue, Feb 21, 2017 at 02:00:23PM -0800, Bram Cohen via bitcoin-dev wrote:
> When one side of a node is empty and the other contains exactly two things
> the secure hash of the child is adopted verbatim rather than rehashing it.
> This roughly halves the amount of hashing done, and makes it more resistant
> to malicious data, and cleans up some implementation details, at the cost
> of some extra complexity.

Note that this is a use-case specific concept of an idea I'm calling a
"generalized commitment"

A commitment scheme needs only have the property that it's not feasible to find
two messages m1 and m2 that map to the same commitment; it is *not* required
that it be difficult to find m given the commitment. Equally, it's not required
that commitments always be the same size.

So a perfectly reasonable thing to do is design your scheme such that the
commitment to short messages is the message itself! This adds just a single bit
of data to the minimum serialized size(1) of the commitment, and in situations
where sub-digest-sized messages are common, may overall be a savings.

Another advantage is that the scheme becomes more user-friendly: you *want*
programmers to notice when a commitment is not effectively hiding the message!
If you need message privacy, you should implement an explicit nonce, rather
than relying on the data to not be brute-forcable.

1) The more I look at these systems, the more I'm inclined to consider
bit-granularity serialization schemes... Heck, sub-bit granularity has
advantages too in some cases, e.g. by making all possible inputs to the
deserializer be valid.

-- 
https://petertodd.org 'peter'[:-1]@petertodd.org