# [bitcoin-dev] Scaling by Partitioning

Dave Scotese dscotese at litmocracy.com
Thu Dec 10 04:14:17 UTC 2015

```Edit:
"... as well as those blocks with hashes for which the last B bits match
any of the next N bit patterns where *N is largest* integer for which the
claimed output is not *greater* than (subsidy+fees)*(N/(2^B)).

On Wed, Dec 9, 2015 at 8:08 PM, Dave Scotese <dscotese at litmocracy.com>
wrote:

> If we partition the work using bits from the TxID (once it is no longer
> malleable) or even bits from whatever definition we use for "coin," then
> every transaction may have to use all the other partitions to verify that
> the incoming coin is good.
>
> If all partitions are involved in validating and storing every
> transaction, then we may be doing more work in total, but any one node will
> only have to do (and store) a fraction of what it is now.  We would want
> the current situation to be identical to one in which all the participants
> are handling all the partitions.  So how can we break up the work so that
> any participant can handle whatever fraction of the work he or she wants?
> One idea is to use the last bits of the address that will receive the
> subsidy and fees.  You solve the block for your partition by determining
> that all transactions in the block are valid against the subset of blocks
> whose hashes end with the same bits.
>
> This solution is broadcast in the hope that others will start attempting
> to validate that same block on their own partition. If they are mining the
> same partition, they simply change their subsidy address to work on a
> different partition.  Each time a new-but-not-last partition is solved,
> everyone working on the block adds the new solver's output address to their
> generation transaction with the appropriate fraction of the
> reward-plus-subsidy.  In this way, several miners contribute to the
> solution of a single block and need only store those blocks that match the
> partitions they want to work on.
>
> Suppose we use eight bits so that there are 256 partitions and a miner
> wishes to do about 1/5 of the work. That would be 51 partitions.  This is
> signaled in the generation transaction, where the bit-pattern of the last
> byte of the public key identifies the first partition, and the proportion
> of the total reward for the block (51/256) indicates how many partitions a
> solution will cover.
>
> Suppose that the last byte of the subsidy address is 0xF0.  This means
> there are only 16 partitions left, so we define partition selection to wrap
> around.  This 51/256 miner must cover partitions 0xF0 - 0xFF and 0x00 -
> 0x23. In this way, all mining to date has covered all partitions.
>
> The number of bits to be used might be able to be abstracted out to a
> certain level.  Perhaps a miner can indicate how many bits B the
> partitioning should use in the CoinBase. The blocks for which a partition
> miner claims responsibility are all those with a bit pattern of length B at
> the end of their hash matching the the bits at the end of the first
> output's public key in the generation transaction, as well as those blocks
> with hashes for which the last B bits match any of the next N bit patterns
> where for the largest integer N for which the claimed output is not less
> than (subsidy+fees)*(N/(2^B)).
>
> If you only store and validate against one partition, and that partition
> has a solution already, then you would start working on the next block
> (once you've validated the current one against your subset of the
> blockchain).  You could even broadcast a solution for that next block
> before the previous block is fully solved, thus claiming a piece of the
> next block reward (assuming the current block is valid on all partitions).
>
> It seems that a miner who covers only one partition will be at a serious
> disadvantage, but as the rate of incoming transactions increases, the
> fraction of time he must spend validating (being about half of all other
> miners who cover just one more partition) makes up for this disadvantage
> somewhat.  He is a "spry" miner and therefore wins more rewards during
> times of very dense transaction volume.  If we wish to encourage miners to
> work on smaller partitions, we can provide a difficulty break for smaller
> fractions of the work.  In fact, the difficulty can be adjusted down for
> the first solution, and then slowly back up to full for the last
> partition(s).
>
> This proposal has the added benefit of encouraging the assembly of blocks
> by miners who work on single partitions to get them out there with a
> one-partition solution.
>
> On Wed, Dec 9, 2015 at 2:35 PM, Andrew via bitcoin-dev <
> bitcoin-dev at lists.linuxfoundation.org> wrote:
>
>> Hi Akiva
>>
>> I sketched out a similar proposal here:
>> https://bitcointalk.org/index.php?topic=1083345.0
>>
>> with segregated witness, as it might mess up some things, but will take a
>> closer look.
>> On Dec 9, 2015 7:32 AM, "Loi Luu via bitcoin-dev" <
>> bitcoin-dev at lists.linuxfoundation.org> wrote:
>>
>>> Dear Akiva,
>>>
>>> Its Loi Luu, one of the authors of the SCP protocol (
>>> http://eprint.iacr.org/2015/1168.pdf ).
>>>
>>> Before SCP, we had been thinking hard about how to do sharding
>>> efficiently without degrading any security guarantee. A simple solution
>>> which splits the coins, or TXs in to several partitions will just not work.
>>> You have to answer more questions to have a good solutions. For example, I
>>> wonder in your proposal, if a transaction spends a "coin" that ends in "1"
>>> and creates a new coin that ends in "1", which partition should process the
>>> transaction? What is the prior data needed to validate that kind of TXs?
>>>
>>> The problem with other proposals, and probably yours as well,  that we
>>> see is that the amount of data that you need to broadcast immediately to
>>> the network increases linearly with the number of TXs that the network can
>>> process. Thus, sharding does not bring any advantage than simply using
>>> other techniques to publish more blocks in one epoch (like Bitcoin-NG,
>>> Ghost). The whole point of using sharding/ partition is to localize
>>> the bandwidth used, and only broadcast only a minimal data to the network.
>>>
>>> Clearly we are able to localize the bandwidth used with our SCP
>>> protocol. The cost is that now recipients need to  themselves verify
>>> whether a transaction is double spending. However, we think that it is a
>>> reasonable tradeoff, given the potential scalability that SCP can provides.
>>>
>>> Thanks,
>>> Loi Luu.
>>>
>>> On Wed, Dec 9, 2015 at 12:27 AM, Akiva Lichtner via bitcoin-dev <
>>> bitcoin-dev at lists.linuxfoundation.org> wrote:
>>>
>>>> Hello,
>>>>
>>>> I am seeking some expert feedback on an idea for scaling Bitcoin. As a
>>>> brief introduction: I work in the payment industry and I have twenty years'
>>>> experience in development. I have some experience with process groups and
>>>> ordering protocols too. I think I understand Satoshi's paper but I admit I
>>>> have not read the source code.
>>>>
>>>> The idea is to run more than one simultaneous chain, each chain
>>>> defeating double spending on only part of the coin. The coin would be
>>>> partitioned by radix (or modulus, not sure what to call it.) For example in
>>>> order to multiply throughput by a factor of ten you could run ten parallel
>>>> chains, one would work on coin that ends in "0", one on coin that ends in
>>>> "1", and so on up to "9".
>>>>
>>>> The number of chains could increase automatically over time based on
>>>> the moving average of transaction volume.
>>>>
>>>> Blocks would have to contain the number of the partition they belong
>>>> to, and miners would have to round-robin through partitions so that an
>>>> attacker would not have an unfair advantage working on just one partition.
>>>>
>>>> I don't think there is much impact to miners, but clients would have to
>>>> send more than one message in order to spend money. Client messages will
>>>> need to enumerate coin using some sort of compression, to save space. This
>>>> seems okay to me since often in computing client software does have to
>>>> break things up in equal parts (e.g. memory pages, file system blocks,) and
>>>> the client software could hide the details.
>>>>
>>>> Best wishes for continued success to the project.
>>>>
>>>> Regards,
>>>> Akiva
>>>>
>>>> P.S. I found a funny anagram for SATOSHI NAKAMOTO: "NSA IS OOOK AT MATH"
>>>>
>>>>
>>>> _______________________________________________
>>>> bitcoin-dev mailing list
>>>> bitcoin-dev at lists.linuxfoundation.org
>>>> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>>>>
>>>>
>>>
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>>>
>>>
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>>
>
>
> --
> I like to provide some work at no charge to prove my value. Do you need a
> techie?
> I own Litmocracy <http://www.litmocracy.com> and Meme Racing
> <http://www.memeracing.net> (in alpha).
> I'm the webmaster for The Voluntaryist <http://www.voluntaryist.com>
> which now accepts Bitcoin.
> I also code for The Dollar Vigilante <http://dollarvigilante.com/>.
> "He ought to find it more profitable to play by the rules" - Satoshi
> Nakamoto
>

--
I like to provide some work at no charge to prove my value. Do you need a
techie?
I own Litmocracy <http://www.litmocracy.com> and Meme Racing
<http://www.memeracing.net> (in alpha).
I'm the webmaster for The Voluntaryist <http://www.voluntaryist.com> which
now accepts Bitcoin.
I also code for The Dollar Vigilante <http://dollarvigilante.com/>.
"He ought to find it more profitable to play by the rules" - Satoshi
Nakamoto
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