First time posting here, please be gentle.

I'm doing a research project about blockchain timestamping. There are many such projects, including the fantastic OpenTimestamps.

All of the projects essentially save some data in a block, and rely on the block timestamp as a proof that this data existed at some specific time.

But how accurate are Bitcoins timestamps?

I didn't find any discussion or research regarding Bitcoin timestamp accuracy (also not in the history of this mailing list). I share here a simple analysis of timestamp accuracy, and a suggestion how to improve it.

Basic observations and questions:

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1. It seems to me that the timestamp is not the time that the block was created. Ideally, it's the time that the miner started to try to mine the block. However, as timestamps may also be used as a source of variety for hashes, the exact meaning of its value is unclear.

If this is true, then there's a strange phenomena to observe in blockchain.info and blockexplorer.com: the timestamps of blocks equals the receiving times.

Am I wrong in my understanding, or is there a mistake in those websites?

2. Timestamps are not necessary to avoid double-spending. A simple ordering of blocks is sufficient, so exchanging timestamps with enumeration would work double-spending wise. Permissioned consensus protocols, such as hyperledger, indeed have no timestamps (in version 1.0).

As far as I could tell, timestamps are included in Bitcoin's protocol *only* to adjust the difficulty of PoW.

Direct control of timestamp accuracy:
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The only element in the protocol that I found to control timestamp accuracy is based on the network time concept.

The Bitcoin protocol defines “network time” for each node. The network time is the median time of the other clients, but only if
    1. there are at least 5 connected, and
    2. the difference between the median time and the nodes own system time is less than 70 minutes.

Then new blocks are accepted by the peers if their timestamps is
    1. less than the network time plus 2 hours, and
    2. greater than the median timestamp of previous 11 blocks.

The first rule supplies a 2 hour upper bound for timestamp accuracy.

However, the second rule doesn't give a tight lower bound. Actually, no lower bound is given at all if no assumption is made about the median. If we assume the median to be accurate enough at some timepoint, then we're only assured that any future timestamp is no bigger than this specific median, which is not much information.

Further analysis can be made under different assumptions. For example, what's the accuracy if holders of 51% of the computational power create honest timestamps? But unfortunately, I don't see any good reason to work under such an assumptions.

The second rule cannot be strengthened to be similar to the first one (i.e., nodes don't accept blocks less than network time minus 2 hours). The reason is that nodes cannot differentiate if it's a new block with dishonest timestamp, an old block with an old timestamps (with many other blocks coming) or simply a new block that took a long time to mine.

Indirect control of timestamps accuracy:
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If we assume that miners have no motive to increase difficulty artificially, then the PoW adjusting algorithm yields a second mechanism of accuracy control.

The adjustment rules are given in pow.cpp (bitcoin-core source, version 0.15.1), in the function 'CalculateNextWorkRequired', by the formula (with some additional adjustments which I omit):

    (old_target* (time_of_last_block_in_2016_blocks_interval - time_of_first_block_in_2016_blocks_interval) )/time_of_two_weeks

It uses a simple average of block time in the last 2016 blocks. But such averages ignore any values besides the first and last one in the interval. Hence, if the difficulty is constant, the following sequence is valid from both the protocol and the miners incentives point of views:

    1, 2, 3,…., 2015, 1209600 (time of two weeks), 2017, 2018, 2019,…., 4031, 1209600*2, 4033, 4044, …

If we want to be pedantic, the best lower bound for a block timestamp is the timestamp of the block that closes the adjustment interval in which it resides.

Possible improvement:
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We may consider exchanging average with standard deviation in the difficulty adjustment formula. It both better mirrors changes in the hash power along the interval, and disables the option to manipulate timestamps without affecting the difficulty.

I'm aware that this change requires a hardfork, and won't happen any time soon. But does it make sense to add it to a potential future hard fork?

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