Tag Archives: Bitcoin

In this post, we will learn to build a very simple miner in Python. Of course this miner will be comparatively slow and limited and only be useful in our test network, but it will hopefully help to explain the principles behind mining.

When we want to mine a block, we first need some information on the current state of the blockchain, like the hash of the current last block, the current value of the difficulty or the coin base value, i.e. the number of BTC that we earn when mining the block. When we are done building the block, we need to find a way to submit it into the bitcoin network so that it is accepted by all nodes and permanently added to the chain.

If we were member of a mining pool, there would be a mining server that would provide us the required information. As we want to build a solo mining script, we need to communicate with bitcoin core to get that information and to submit our final block. Fortunately, the RPC interface of bitcoin core offers methods to facilitate that communication that were introduced with BIP22.

First, there is the method getblocktemplate. It will deliver all the required information that we need to build a valid block and even propose transactions that we should include in the block. These transactions will be taken from the so called mempool which is a collection of transactions that the bitcoin server knows which have not been added to a block yet (see miner.cpp/BlockAssembler::addPackageTxs in the bitcoin core source code for details on how the selection process works).

If the client is done building the block, it can submit the final block using the method submitblock. This method will run a couple of checks on the block, for instance that it can be correctly decoded, that the first transaction – and only the first – is a coinbase transaction, that it is not a duplicate and that the proof-of-work is valid. If all the checks pass, it will add the block to the local copy of the blockchain. If a check fails, it will return a corresponding error code to the caller.

With that understanding, let us now write down the processing logic for our simple miner, assuming that we only want to mine one additional block. First, we will use getblocktemplate to get the basic parameters that we need and transaction that we can include. Then we will create a new block and a new coinbase transaction. We then add the coinbase transaction followed by all the other transactions to the block.

Once we have that block, we enter a loop. Within the loop, we calculate the hash of the block and compare this against the target. If we can meet the target, we are done and submit the newly created block using submitblock. Otherwise, we increment the nonce and try again.

We have discussed most of these steps in some details in the previous posts, with one exception – coinbase transactions. A coinbase transaction is, by definition, a transaction which generates bitcoin because it has valid outputs, but does not spend any UTXOs. Technically, a coinbase transaction is a transaction which (see CTransaction::IsCoinBase())

• has exactly one transaction input
• the previous transaction ID in this input is zero (i.e. a hexadecimal string consisting of 32 zeros “00”)
• the index of the previous output is -1 (encoded as  0xFFFFFFFF)

As it does not refer to any output, the signature script of a coinbase transaction will never be executed. It can therefore essentially contain an arbitrary value. The only restriction defined by the protocol is described in BIP34, which defines that the first bytes of the signature script should be a valid script that consists of the height of the new block as pushed data. The remainder of the coinbase signature script (which is limited to 100 bytes in total) can be used by the miner at will.

Many miners use this freedom to solve a problem with the length of the nonce in the block header. Here, the nonce is a 32 bit value, which implies that a miner can try 2³², i.e. roughly 4 billion different combinations. Modern mining hardware based on ASICs can search that range within fractions of seconds, and the current difficulty is so high that it is rather likely that no solution can be found by just changing the nonce. So we have to change other fields in the block header to try out more hashes.

What are good candidates for this? We could of course use the block creation time, but the bitcoin server validates this field and will reject the block if it deviates significantly from the current time. Instead miners typically use the coinbase signature script as an extra nonce that they modify to increase the range of possible hashes. Therefore the fields after the height are often combinations of an extra nonce and additional data, like the name of the mining pool (increasing the extra nonce is a bit less effective than increasing the nonce in the block header, as it changes the hash of the coinbase transactions and therefore forces us to recalculate the Merkle root, therefore this is most often implemented as an outer loop, with the inner loop being the increments of the nonce in the block header).

To illustrate this, let us look at an example. The coinbase signature script of the coinbase transaction in block #400020 is:

03941a060004c75ccf5604a070c007089dcd1424000202660a636b706f6f6c102f426974667572792f4249503130302f

If we decode this, we find that the first part is in fact a valid script and corresponds to the following sequence of instructions (keep in mind that all integers are encoded as little endian within the script):

OP_PUSH 400020
OP_0
OP_PUSH 1456430279
OP_PUSH 130052256
OP_PUSH 7350439741450669469

As specified by BIP34, the first pushed data is the height of that block as expected. After the OP_0, we see another push instruction, pushing the Unix system time corresponding to Thu Feb 25 20:57:59 2016, which is the creation time of the block.

The next pushed data is a bit less obvious. After looking at the source code of the used mining software, I assume that this is the nanoseconds within the second returned by the Unix system call clock_gettime. This is then followed by an eight byte integer (7350439741450669469) which is the extra nonce.

The next part of the signature script is not actually a valid script, but a string – a newline character (0xa), followed by the string “ckpool”. This is a fixed sequence of bytes that indicates the mining software used.

Finally, there is one last push operation which pushes the string “/Bitfury/BIP100/”, which tells us that the block has been mined by the Bitfury pool and that this pool supports BIP100.

Enough theory – let us put this to work! Using the utility functions in my btc Python package, it is now not difficult to write a short program that performs the actual mining.

However, we need some preparations to set up our test environment that are related to our plan to use the getblocktemplate RPC call. This call performs a few validations that can be a bit tricky in a test environment. First, it will verify that the server is connected, i.e. we need at least one peer. So we need to start two docker container, let us call them alice and bob again, and find out the IP address of the container bob in the Docker bridget network. The three following statements should do this for you.

$ docker run --rm -d -p 18332:18332 --name="alice" alice
$ docker run --rm -d  --name="bob" bitcoin-alpine
$ docker network inspect bridge | grep  -A 4  "bob" - | grep "IPv4" -

Assuming that this gives you 172.17.0.3 (replace this with whatever the result is in your case), we can now again use the addnode RPC call to connect the two nodes.

$ bitcoin-cli --rpcuser=user --rpcpassword=password -regtest addnode "172.17.0.3" add

The next validation that the bitcoin server will perform when we ask for a block template is that the local copy of the blockchain is up to date. It does by verifying that the time stamp of the last block in the chain is less than 24 hours in the past. As it is likely that a bit more time has passed since you have created the Alice container, we therefore need to use the mining functionality built into bitcoin core to create at least one new block.

$ bitcoin-cli --rpcuser=user --rpcpassword=password -regtest generate 1

Now we are ready to run our test. The next few lines will download the code from GitHub, create one transaction that will then be included in the block. We will create this transaction using the script SendMoney.py that we have already used in an earlier post.

$ git clone https://github.com/christianb93/bitcoin.git
$ cd bitcoin
$ python SendMoney.py
$ python Miner.py

You should then see an output telling you that a block with two transactions (one coinbase transaction and the transaction that we have generated) was mined, along with the previous height of the blockchain and the new height which should be higher by one.

Let us now verify that everything works. First, let us get the hash of the current last block.

$ bitcoin-cli --rpcuser=user --rpcpassword=password -regtest getchaintips
[
  {
    "height": 109,
    "hash": "07849d5c8ddcdc609d7acc3090bc48bbe4403c36008d46b5a291185334efe1bf",
    "branchlen": 0,
    "status": "active"
  }
]

Take the value from the hash field in the output and feed it into a call to getblock:

$ bitcoin-cli --rpcuser=user --rpcpassword=password -regtest getblock "07849d5c8ddcdc609d7acc3090bc48bbe4403c36008d46b5a291185334efe1bf"
{
  "hash": "07849d5c8ddcdc609d7acc3090bc48bbe4403c36008d46b5a291185334efe1bf",
  "confirmations": 1,
  "strippedsize": 367,
  "size": 367,
  "weight": 1468,
  "height": 109,
  "version": 536870912,
  "versionHex": "20000000",
  "merkleroot": "8769987458af75adc80d6792848e5cd5cb8178a9584157bb4be79b77cda95909",
  "tx": [
    "7ba3186ca8e5aae750614a3211422423a0a217f5999d0de6dfeb8968aeb01900", 
    "1094360149626a421b4ddbc7eb58a815762700316c36407770b96ffc36a7735b"
  ],
  "time": 1522952768,
  "mediantime": 1521904060,
  "nonce": 1,
  "bits": "207fffff",
  "difficulty": 4.656542373906925e-10,
  "chainwork": "00000000000000000000000000000000000000000000000000000000000000dc",
  "previousblockhash": "2277e40bf4c0ebde3fb5f38fcbd384e39df3471ad192cc46f66ea8d8d96327e7"
}

The second entry in the list tx should now match the ID of the newly created transaction which was displayed when executing the SendMoney.py script. This proves that our new transaction has been included in the block.

Congratulations, you have just mined 50 BTC – unfortunately only in your local installation, not in the production network. Of course, real miners work differently, using mining pools to split the work between many different nodes and modern ASICS to achieve the hash rates that you need to be successful in the production network. But at least we have built a simple miner more or less from scratch, relying only on the content of this and the previous posts in this series and without using any of the many Python bitcoin libraries that are out there.

This concludes my current series on the bitcoin blockchain –  I hope you enjoyed the posts and had a bit of fun. If you want to learn more, here are a few excellent sources of information that I recommend.

1. Of course the ultimative source of information is always the bitcoin core source code itself that we have already consulted several times
2. The Bitcoin wiki contains many excellent pages on most of what we have discussed
3. There is of course the original bitcoin paper which you should now be able to read and understand
4. and of course there are tons of good books out there, I personally liked Mastering Bitcoin by A. Antonopoulos which is also available online

Mining is a challenge – a miner has to solve a mathematical puzzle to create a valid block and is rewarded with a certain bitcoin amount (12.5 at the time of writing) for investing electricity and computing power. But technology evolves, and the whole mining process would be pointless if the challenge could not be adapted dynamically to make sure that mining power and the difficulty of the challenge stay in balance. In this post, we will look in a bit more detail into this mechanism.

We have already seen that a block header contains – at character 144 – a four byte long number that is called bits in the source code and which seems to be related to the difficulty. As an example, let us take the block with the hash

0000000000000000000595a828f927ec02763d9d24220e9767fe723b4876b91e

You can get a human readable description of the block at this URL and will see the following output.

This output has a field bits that has the value 391129783. If you convert this into a hexadecimal string, you obtain 0x17502ab7, using for instance Pythons hex function. Now this function will give you the big-endian representation of the integer value. To convert to little endian as it can be found in the serialized format of a bitcoin block, you have to reverse the order byte wise and get b72a5017. If you now display the raw format of the block using this link and search for that string, you will actually find it at character 144 at expected.

Now on the screenshot above, you also see the difficulty displayed, which is a floating point number and is 3511060552899.72 in this case. How is that difficulty related to the bits?

As so often, we can find the answer in the bitcoin core source code, starting at the JSON RPC interface. So let us look at the function blockheaderToJSON in rpc/blockchain.cpp that is responsible for transforming a block in the internal representation into a human readable JSON format. Here we find the line

result.push_back(Pair("difficulty", GetDifficulty(blockindex)));

So let us visit the function GetDifficulty that we find in the same file, actually just a few lines up. Here we see that the bits are actually split into two parts. The first part, let me call this the size is just the value of the top 8 bits. The second part, the value of remaining 24 bits, is called the coefficient. Then the difficulty is calculated by dividing the constant 0xFFFF by the coefficient and shifting by 29 – size bits, i.e. according to the formula

In Python, we can therefore use the following two lines to extract the difficulty from a block header in raw format.

nBits = int.from_bytes(bytes.fromhex(raw[144:152]), "little")
difficulty = 256**(29 - (nBits >> 24))*(65535.0 / ((float)(nBits & 0xFFFFFF)))

If you try this out for the transaction above, you will get 3511060552899.7197. Up to rounding after the second digit after the decimal point, this is exactly what we also see on the screenshot of blockchain.info. So far this is quite nice…

However, we are not yet done – this is not the only way to represent the difficulty. The second quantity we need to understand is the target. Recall that the mathematical puzzle that a miner needs to solve is to produce a block with a hash that does not exceed a given number. This number is the target. The lower the target, the smaller the range of 256 bit numbers that do not exceed the target, and the more difficult to solve that puzzle. So a low target implies high difficulty and vice versa.

In fact, there are two target values. One target is part of every block and stored in the bits field – we will see in a minute how this works. The second target is a global target that all nodes in the bitcoin network share – this value is updated independently by each node, but based on the same data (the blockchain) and the same rules so that they arrive at the same conclusion. A block considered valid if solves the mathematical puzzle according to the target which is stored in itself and if, in addition, this target matches the global target.

To understand how this works and the exact relation between target and difficulty, it is again useful to take a look at the source code. The relevant function is the function CheckProofOfWork in pow.cpp which is surprisingly short.

bool CheckProofOfWork(uint256 hash, unsigned int nBits, const Consensus::Params& params)
{
    bool fNegative;
    bool fOverflow;
    arith_uint256 bnTarget;

    bnTarget.SetCompact(nBits, &fNegative, &fOverflow);

    // Check range
    if (fNegative || bnTarget == 0 || fOverflow || bnTarget > UintToArith256(params.powLimit))
        return false;

    // Check proof of work matches claimed amount
    if (UintToArith256(hash) > bnTarget)
        return false;

    return true;
}

Let us try to understand what is going on here. First, a new 256 bit integer bnTarget is instantiated and populated from the bits (that are taken from the block) using the method SetCompact. In addition to a range check, it is then checked that the hash of the block does not exceed the target – this the mathematical puzzle that we need to solve.

The second check – verifying that the target in the block matches the global target – happens in validation.cpp in the function ContextualCheckBlockHeader. At this point, the function GetNextWorkRequired required is called which determines the correct value for the global target. Then this is compared to the bits field in the block and the validation fails if they do not match. So for a block to be accepted as valid, the miner needs to:

• Actually solve the puzzle, i.e. provide a block with a hash value equal to or smaller than the current global target
• Include this target as bits in the generated block

This leaves a couple of questions open. First, we still have to understand how the second step – encoding the target in the bits field – works. And then we have to understand how the global target is determined.

Let us start with the first question. We have seen that the target is determined from the bits using the SetCompact method of the class uint256. This function is in fact quite similar to GetDifficulty studied before. Ignoring overflows and signs for a moment, we find that the target is determined from the bits as

If we compare this to the formula for the difficulty that we have obtained earlier, we find that there a simple relation between them:

where std_target is the target corresponding to difficulty 1.0 and given by 0xFFFF shifted by 208 bits to the left, i.e. by 0xFFFF with 52 trailing zeros. So up to a constant, target and difficulty are simply inverse to each other.

Now let us turn to the second question – how can the nodes agree on the correct global target? To see this, we need to look at the function GetNextWorkRequired. In most cases, this function will simply return the bits field of the current last block in the blockchain. However, every 2016 blocks, it will adjust the difficulty according to the following rule.

First, it will use the time stamps in the block to calculate how much time has passed since the block which is 2016 blocks back in the chain has been created – this value is called the actual time span. Then, this is compared with the target time span which is two weeks. The new target is then obtained by the formula (ignoring some range checks that are done to avoid too massive jumps)

Thus if the actual time span is smaller than the target time span, indicating that the mining power is too high and therefore the rate of block creation is too high, the target decreases and consequently the difficulty increases. This should make it more difficult for the miners to create new blocks and the block creation rate should go down again. Similarly, if the difficulty is too high, this mechanism will make sure that it is adjusted downwards. Thus the target rate is 2016 blocks being created in two weeks, i.e. 336 hours, which is a rate of six blocks per hours, i.e. 10 minutes for one block.

Finally, it is worth mentioning that there is lower limit for the difficulty, corresponding to a higher limit for the target. This limit is (as most of the other parameters that we have discussed) contained in chainparams.cpp and specific for the three networks main, net and regtest. For instance, for the main network, this is

consensus.powLimit = uint256S("00000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffff");

whereas the same parameter for the regression testing network is

consensus.powLimit = uint256S("7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff");

This, together with the target of the genesis block (which determines the target for the first 2016 blocks) (bits = 0x207fffff ) determines the initial difficulty in a regression test network. Let us verify this (I knew I would somehow find a reason to add a notebook to this post…)

We are now well equipped to move towards our final project in this series – building a Python based miner. The last thing that we need to understand is how the miner operates and communicates with the bitcoin server, and this will be the topic of the next post.