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<body class="article">
<div id="header">
</div>
<div id="content">
<div class="sect1">
<h2 id="mining">Mining and Consensus</h2>
<div class="sectionbody">
<div class="paragraph">
<p>The word "mining" is somewhat
misleading. By evoking the extraction of precious metals, it focuses our
attention on the reward for mining, the new bitcoins created in each
block. Although mining is incentivized by this reward, the primary
purpose of mining is not the reward or the generation of new bitcoins. If
you view mining only as the process by which bitcoins are created, you are
mistaking the means (incentives) as the goal of the process. Mining is
the mechanism that underpins the decentralized clearinghouse, by which
transactions are validated and cleared. Mining is one of the inventions that
makes Bitcoin special, a decentralized consensus mechanism that is the
basis for P2P digital cash.</p>
</div>
<div class="paragraph">
<p>Mining <em>secures the Bitcoin system</em> and enables the
emergence of network-wide <em>consensus without a central authority</em>.
The reward of newly minted bitcoins and
transaction fees is an incentive scheme that aligns the actions of
miners with the security of the network, while simultaneously
implementing the monetary supply.</p>
</div>
<div class="admonitionblock tip">
<table>
<tr>
<td class="icon">
<div class="title">Tip</div>
</td>
<td class="content">
<div class="paragraph">
<p>Mining
is one of the mechanisms by which Bitcoin’s <em>consensus security</em> is <em>decentralized</em>.</p>
</div>
</td>
</tr>
</table>
</div>
<div class="paragraph">
<p>Miners record new transactions on the global blockchain. A
new block, containing transactions that occurred since the last block,
is <em>mined</em> every 10 minutes on average, thereby adding those
transactions to the blockchain. Transactions that become part of a block
and added to the blockchain are considered <em>confirmed</em>, which allows the
new owners of the bitcoins to know that irrevocable effort was expended
securing the bitcoins they received in those
transactions.</p>
</div>
<div class="paragraph">
<p>Additionally, transactions in the blockchain have a <em>topological order</em>
defined by their position in the blockchain. One transaction is
earlier than another if it appears in an earlier block or if it appears
earlier in the same block. In the Bitcoin protocol, a transaction is
only valid if it spends the outputs of transactions that appeared
earlier in the blockchain (whether they are earlier in the same block or
in an earlier block), and only if no previous transaction spent any of
those same outputs. Within a single chain of blocks, the enforcement of
topological ordering ensures no two valid transactions can spend the same
output, eliminating the problem of <em>double spending</em>.</p>
</div>
<div class="paragraph">
<p>In some protocols built on top of Bitcoin, the topological order of
Bitcoin transactions is also used to establish a sequence of events;
we’ll discuss that idea further in <a href="#single_use_seals">[single_use_seals]</a>.</p>
</div>
<div class="paragraph">
<p>Miners receive two types of rewards in
return for the security provided by mining: new bitcoins created with each
new block (called the <em>subsidy</em>), and transaction fees from all the transactions included in
the block. To earn this reward, miners compete to satisfy a challenge
based on a cryptographic hash algorithm. The
solution to the problem, called the proof of work, is included in the
new block and acts as proof that the miner expended significant
computing effort. The competition to solve the proof-of-work algorithm
to earn the reward and the right to record transactions on the
blockchain is the basis for Bitcoin’s security model.</p>
</div>
<div class="paragraph">
<p>Bitcoin’s money supply is created in a process that’s similar to how
a central bank issues new money by printing bank notes. The maximum
amount of newly created bitcoin a miner can add to a block decreases
approximately every four years (or precisely every 210,000 blocks). It
started at 50 bitcoins per block in January 2009 and halved to 25
bitcoins per block in November 2012. It halved again to 12.5 bitcoins
in July 2016, and again to 6.25 in May 2020. Based on this formula, mining rewards decrease
exponentially until approximately the year 2140, when all bitcoins
will have been issued. After 2140, no new bitcoin
will be issued.</p>
</div>
<div class="paragraph">
<p>Bitcoin miners also earn fees from transactions. Every transaction may
include a transaction fee in the form of a surplus of bitcoins between
the transaction’s inputs and outputs. The winning bitcoin miner gets to
"keep the change" on the transactions included in the winning block.
Today, the fees usually represent only a small percentage of a
miner’s income, with the
vast majority coming from the newly minted bitcoins. However, as the
reward decreases over time and the number of transactions per block
increases, a greater proportion of mining earnings will come
from fees. Gradually, the mining reward will be dominated by transaction
fees, which will form the primary incentive for miners. After 2140, the
amount of new bitcoins in each block drops to zero and mining
will be incentivized only by transaction fees.</p>
</div>
<div class="paragraph">
<p>In this chapter, we will first examine mining as a monetary supply
mechanism and then look at the most important function of mining: the
decentralized consensus mechanism that underpins Bitcoin’s security.</p>
</div>
<div class="paragraph">
<p>To understand mining and consensus, we will track Alice’s transaction
as it is received and added to a block by Jing’s mining equipment. Then
we will follow the block as it is mined, added to the blockchain, and
accepted by the Bitcoin network through the process of emergent
consensus.</p>
</div>
<div class="sect2">
<h3 id="_bitcoin_economics_and_currency_creation">Bitcoin Economics and Currency Creation</h3>
<div class="paragraph">
<p>Bitcoin are minted during the creation of each block at a
fixed and diminishing rate. Each block, generated on average every 10
minutes, contains entirely new bitcoins, created from nothing. Every
210,000 blocks, or approximately every four years, the currency issuance
rate is decreased by 50%. For the first four years of operation of the
network, each block contained 50 new bitcoins.</p>
</div>
<div class="paragraph">
<p>The first halving occurred at block 210,000. The next expected halving
after publication of this book will occur at block 840,000, which will
probably be produced in April or May of 2024.
The rate of new bitcoins decreases
exponentially over 32 of these <em>halvings</em> until block 6,720,000 (mined
approximately in year 2137), when it reaches the minimum currency unit
of 1 satoshi. Finally, after 6.93 million blocks, in approximately 2140,
almost 2,099,999,997,690,000 satoshis, or almost 21 million bitcoin,
will have been issued. Thereafter, blocks will contain no new bitcoins, and
miners will be rewarded solely through the transaction fees.
<a href="#bitcoin_money_supply">Supply of bitcoin currency over time based on a geometrically decreasing issuance rate.</a> shows the total bitcoins in circulation over
time, as the issuance of currency decreases.</p>
</div>
<div id="bitcoin_money_supply" class="imageblock">
<div class="content">
<img src="images/mbc3_1201.png" alt="BitcoinMoneySupply">
</div>
<div class="title">Figure 1. Supply of bitcoin currency over time based on a geometrically decreasing issuance rate.</div>
</div>
<div class="admonitionblock note">
<table>
<tr>
<td class="icon">
<div class="title">Note</div>
</td>
<td class="content">
<div class="paragraph">
<p>The maximum number of bitcoins mined is the <em>upper limit</em> of possible
mining rewards for Bitcoin. In practice, a miner may intentionally mine
a block taking less than the full reward. Such blocks have already been
mined and more may be mined in the future, resulting in a lower total
issuance of the currency.</p>
</div>
</td>
</tr>
</table>
</div>
<div class="paragraph">
<p>In the code in <a href="#max_money">A script for calculating how much total bitcoin will be issued</a>, we calculate the total amount of
bitcoin that will be issued.</p>
</div>
<div id="max_money" class="exampleblock">
<div class="title">Example 1. A script for calculating how much total bitcoin will be issued</div>
<div class="content">
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-python" data-lang="python"># Original block reward for miners was 50 BTC
start_block_reward = 50
# 210000 is around every 4 years with a 10 minute block interval
reward_interval = 210000
def max_money():
# 50 BTC = 50 0000 0000 Satoshis
current_reward = 50 * 10**8
total = 0
while current_reward > 0:
total += reward_interval * current_reward
current_reward /= 2
return total
print("Total BTC to ever be created:", max_money(), "Satoshis")</code></pre>
</div>
</div>
</div>
</div>
<div class="paragraph">
<p><a href="#max_money_run">Running the max_money.py script</a> shows the output produced by running this script.</p>
</div>
<div id="max_money_run" class="exampleblock">
<div class="title">Example 2. Running the max_money.py script</div>
<div class="content">
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-bash" data-lang="bash">$ python max_money.py
Total BTC to ever be created: 2099999997690000 Satoshis</code></pre>
</div>
</div>
</div>
</div>
<div class="paragraph">
<p>The finite and diminishing issuance creates a fixed monetary supply that
resists inflation. Unlike a fiat currency, which can be printed in
infinite numbers by a central bank, no individual party has the ability
to inflate the supply of bitcoin.</p>
</div>
<div class="sidebarblock">
<div class="content">
<div class="title">Deflationary Money</div>
<div class="paragraph">
<p>The most important and debated consequence of
fixed and diminishing monetary issuance is that the currency tends to be
inherently <em>deflationary</em>. Deflation is the phenomenon of appreciation
of value due to a mismatch in supply and demand that drives up the value
(and exchange rate) of a currency. Price deflation is the opposite of inflation; it means that the money has more purchasing power over time.</p>
</div>
<div class="paragraph">
<p>Many economists argue that a deflationary economy is a disaster that
should be avoided at all costs. That is because in a period of rapid
deflation, people tend to hoard money instead of spending it, hoping
that prices will fall. Such a phenomenon unfolded during Japan’s "Lost
Decade," when a complete collapse of demand pushed the currency into a
deflationary spiral.</p>
</div>
<div class="paragraph">
<p>Bitcoin experts argue that deflation is not bad per se. Rather,
deflation is associated with a collapse in demand because that is the
most obvious example of deflation we have to study. In a fiat currency with the
possibility of unlimited printing, it is very difficult to enter a
deflationary spiral unless there is a complete collapse in demand and an
unwillingness to print money. Deflation in Bitcoin is not caused by a
collapse in demand, but by a predictably constrained supply.</p>
</div>
<div class="paragraph">
<p>The positive aspect of deflation, of course, is that it is the opposite
of inflation. Inflation causes a slow but inevitable debasement of
currency, resulting in a form of hidden taxation that punishes savers in
order to bail out debtors (including the biggest debtors, governments
themselves). Currencies under government control suffer from the moral
hazard of easy debt issuance that can later be erased through debasement
at the expense of savers.</p>
</div>
<div class="paragraph">
<p>It remains to be seen whether the deflationary aspect of the currency is
a problem when it is not driven by rapid economic retraction, or an
advantage because the protection from inflation and debasement
outweighs the risks of deflation.</p>
</div>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_decentralized_consensus">Decentralized Consensus</h3>
<div class="paragraph">
<p>In the previous chapter we looked at the
blockchain, the global list of all transactions, which
everyone in the Bitcoin network accepts as the authoritative record of
ownership transfers.</p>
</div>
<div class="paragraph">
<p>But how can everyone in the network agree on a single universal "truth"
about who owns what, without having to trust anyone? All traditional
payment systems depend on a trust model that has a central authority
providing a clearinghouse service, basically verifying and clearing all
transactions. Bitcoin has no central authority, yet somehow every full
node has a complete copy of a public blockchain that it can trust as the
authoritative record. The blockchain is not created by a central
authority but is assembled independently by every node in the network.
Somehow, every node in the network, acting on information transmitted
across insecure network connections, can arrive at the same conclusion
and assemble a copy of the same blockchain as everyone else. This
chapter examines the process by which the Bitcoin network achieves
global consensus without central authority.</p>
</div>
<div class="paragraph">
<p>One of Satoshi Nakamoto’s inventions is the decentralized
mechanism for <em>emergent consensus</em>. Emergent because consensus is not
achieved explicitly—there is no election or fixed moment when consensus
occurs. Instead, consensus is an emergent artifact of the asynchronous
interaction of thousands of independent nodes, all following simple
rules. All the properties of Bitcoin, including currency, transactions,
payments, and the security model that does not depend on central
authority or trust, derive from this invention.</p>
</div>
<div class="paragraph">
<p>Bitcoin’s decentralized consensus emerges from the interplay of four
processes that occur independently on nodes across the network:</p>
</div>
<div class="ulist">
<ul>
<li>
<p>Independent verification of each transaction, by every full node,
based on a comprehensive list of criteria</p>
</li>
<li>
<p>Independent aggregation of those transactions into new blocks by
mining nodes, coupled with demonstrated computation through a
proof-of-work algorithm</p>
</li>
<li>
<p>Independent verification of the new blocks by every node and assembly
into a chain</p>
</li>
<li>
<p>Independent selection, by every node, of the chain with the most
cumulative computation demonstrated through proof of work</p>
</li>
</ul>
</div>
<div class="paragraph">
<p>In the next few sections, we will examine these processes and how they
interact to create the emergent property of network-wide consensus that
allows any Bitcoin node to assemble its own copy of the authoritative,
trusted, public, global blockchain.</p>
</div>
</div>
<div class="sect2">
<h3 id="tx_verification">Independent Verification of Transactions</h3>
<div class="paragraph">
<p>In
<a href="#c_transactions">[c_transactions]</a>, we saw how wallet software creates transactions by
collecting UTXOs, providing the appropriate authentication data, and then
constructing new outputs assigned to a new owner. The resulting
transaction is then sent to the neighboring nodes in the Bitcoin network
so that it can be propagated across the entire Bitcoin network.</p>
</div>
<div class="paragraph">
<p>However, before forwarding transactions to its neighbors, every Bitcoin
node that receives a transaction will first verify the transaction. This
ensures that only valid transactions are propagated across the network,
while invalid transactions are discarded at the first node that
encounters them.</p>
</div>
<div class="paragraph">
<p>Each node verifies every transaction against a long checklist of
criteria:</p>
</div>
<div class="ulist">
<ul>
<li>
<p>The transaction’s syntax and data structure must be correct.</p>
</li>
<li>
<p>Neither lists of inputs nor outputs are empty.</p>
</li>
<li>
<p>The transaction weight is low enough to allow it to fit in a block.</p>
</li>
<li>
<p>Each output value, as well as the total, must be within the allowed
range of values (zero or more, but not exceeding 21 million bitcoins).</p>
</li>
<li>
<p>Lock time is equal to INT_MAX, or lock time and sequence
values are satisfied according to the lock time and BIP68 rules.</p>
</li>
<li>
<p>The number of signature operations (SIGOPS) contained in the
transaction is less than the signature operation limit.</p>
</li>
<li>
<p>The outputs being spent match outputs in the mempool or unspent
outputs in a block in the main branch.</p>
</li>
<li>
<p>For each input, if the referenced output transaction is a coinbase
output, it must have at least COINBASE_MATURITY (100) confirmations.
Any absolute or relative lock time must also be satisfied. Nodes may
relay transactions a block before they mature since they will be
mature if included in the next block.</p>
</li>
<li>
<p>Reject if the sum of input values is less than sum of output values.</p>
</li>
<li>
<p>The scripts for each input must validate against the
corresponding output scripts.</p>
</li>
</ul>
</div>
<div class="paragraph">
<p>Note that the conditions change over time, to add new features or
address new types of denial-of-service attacks.</p>
</div>
<div class="paragraph">
<p>By independently verifying each transaction as it is received and before
propagating it, every node builds a pool of valid (but unconfirmed)
transactions known as the <em>memory pool</em> or
<em>mempool</em>.</p>
</div>
</div>
<div class="sect2">
<h3 id="_mining_nodes">Mining Nodes</h3>
<div class="paragraph">
<p>Some of the nodes on the Bitcoin network are specialized nodes
called <em>miners</em>. Jing is a
Bitcoin miner; he
earns bitcoin by running a "mining rig," which is a specialized
computer-hardware system designed to mine bitcoin. Jing’s specialized
mining hardware is connected to a server running a full node.
Like every other full node, Jing’s node receives and
propagates unconfirmed transactions on the Bitcoin network. Jing’s node,
however, also aggregates these transactions into new blocks.</p>
</div>
<div class="paragraph">
<p>Let’s follow the blocks that were created during the time Alice made a
purchase from Bob (see <a href="#spending_bitcoin">[spending_bitcoin]</a>). For the purpose of
demonstrating the concepts in this chapter, let’s assume the block
containing Alice’s transaction was mined by Jing’s mining system and
follow Alice’s transaction as it becomes part of this new block.</p>
</div>
<div class="paragraph">
<p>Jing’s mining node maintains a local copy of the blockchain. By the time
Alice buys something, Jing’s
node is caught up with the chain of blocks with the most proof of work.
Jing’s node is listening
for transactions, trying to mine a new block and also listening for
blocks discovered by other nodes. As Jing’s node is mining, it receives
a new block through the Bitcoin network. The arrival of this block
signifies the end of the search for that block and the beginning
of the search to create the next block.</p>
</div>
<div class="paragraph">
<p>During the previous several minutes, while Jing’s node was searching for a
solution to the previous block, it was also collecting transactions in
preparation for the next block. By now it has collected a few thousand
transactions in its memory pool. Upon receiving the new block and
validating it, Jing’s node will also compare it against all the
transactions in the memory pool and remove any that were included in
that block. Whatever transactions remain in the memory pool are
unconfirmed and are waiting to be recorded in a new block.</p>
</div>
<div class="paragraph">
<p>Jing’s node immediately constructs a new partial block, a
candidate for the next block. This block is called a <em>candidate block</em>
because it is not yet a valid block, as it does not contain a valid
proof-of-work. The block becomes valid only if the miner succeeds in
finding a solution according to the proof-of-work algorithm.</p>
</div>
<div class="paragraph">
<p>When Jing’s node aggregates all the transactions from the memory pool,
the new candidate block has several thousand transactions that each pay
transaction fees he’ll attempt to claim.</p>
</div>
<div class="sect3">
<h4 id="_the_coinbase_transaction">The Coinbase Transaction</h4>
<div class="paragraph">
<p>The first transaction in any
block is a special transaction, called a <em>coinbase transaction</em>. This
transaction is constructed by Jing’s node and pays out his <em>reward</em> for
the mining effort.</p>
</div>
<div class="paragraph">
<p>Jing’s node creates the coinbase transaction as a payment to his own
wallet. The total amount of
reward that Jing collects for mining a block is the sum of the block
subsidy (6.25 new bitcoins in 2023) and the transaction fees from all
the transactions included in the block.</p>
</div>
<div class="paragraph">
<p>Unlike regular transactions, the coinbase transaction does not consume
(spend) UTXOs as inputs. Instead, it has only one input, called the
<em>coinbase input</em>, which implicitly contains the block reward. The coinbase transaction
must have at least one output and may have as many outputs as will fit
in the block. It’s common for coinbase transactions in 2023 to have two
outputs: one of these is a zero-value output that uses OP_RETURN to
commit to all of the witnesses for segregated witness (segwit)
transactions in the block. The other output pays the miner their
reward.</p>
</div>
</div>
<div class="sect3">
<h4 id="_coinbase_reward_and_fees">Coinbase Reward and Fees</h4>
<div class="paragraph">
<p>To construct the
coinbase transaction, Jing’s node first calculates the total amount of
transaction fees:</p>
</div>
<div class="stemblock">
<div class="content">
\[\begin{equation}
Total\:Fees = Sum(Inputs) - Sum(Outputs)
\end{equation}\]
</div>
</div>
<div class="paragraph">
<p>Next, Jing’s node calculates the correct reward for the new block. The
reward is calculated based on the block height, starting at 50 bitcoin
per block and reduced by half every 210,000 blocks.</p>
</div>
<div class="paragraph">
<p>The calculation can be seen in function GetBlockSubsidy in the Bitcoin
Core client, as shown in <a href="#getblocksubsidy_source">Calculating the block reward—Function <span class="plain">GetBlockSubsidy,</span> Bitcoin Core Client, <span class="plain">main.cpp</span></a>.</p>
</div>
<div id="getblocksubsidy_source" class="exampleblock">
<div class="title">Example 3. Calculating the block reward—Function <span class="plain">GetBlockSubsidy,</span> Bitcoin Core Client, <span class="plain">main.cpp</span></div>
<div class="content">
<div class="listingblock c_less_space">
<div class="content">
<pre class="highlight"><code class="language-cpp" data-lang="cpp">CAmount GetBlockSubsidy(int nHeight, const Consensus::Params& consensusParams)
{
int halvings = nHeight / consensusParams.nSubsidyHalvingInterval;
// Force block reward to zero when right shift is undefined.
if (halvings >= 64)
return 0;
CAmount nSubsidy = 50 * COIN;
// Subsidy is cut in half every 210,000 blocks.
nSubsidy >>= halvings;
return nSubsidy;
}</code></pre>
</div>
</div>
</div>
</div>
<div class="paragraph">
<p>The initial subsidy is calculated in satoshis by multiplying 50 with the
COIN constant (100,000,000 satoshis). This sets the initial reward
(nSubsidy) at 5 billion satoshis.</p>
</div>
<div class="paragraph">
<p>Next, the function calculates the number of halvings
that have occurred by dividing the current block height by the halving
interval (SubsidyHalvingInterval).</p>
</div>
<div class="paragraph">
<p>Next, the function uses the binary-right-shift operator to divide the
reward <span class="keep-together">(nSubsidy)</span> by two for each round of halving. In the case of
block 277,316, this would binary-right-shift the reward of 5 billion
satoshis once (one halving) and result in 2.5 billion satoshis, or 25
bitcoins. After the 33rd halving, the subsidy will be rounded down to
zero. The binary-right-shift operator is used because it is more
efficient than multiple repeated divisions. To avoid a potential bug,
the shift operation is skipped after 63 halvings, and the subsidy is set
to 0.</p>
</div>
<div class="paragraph">
<p>Finally, the coinbase reward (nSubsidy) is added to the transaction
fees (nFees), and the sum is returned.</p>
</div>
<div class="admonitionblock tip">
<table>
<tr>
<td class="icon">
<div class="title">Tip</div>
</td>
<td class="content">
<div class="paragraph">
<p>If Jing’s mining node writes the coinbase transaction, what stops Jing
from "rewarding" himself 100 or 1,000 bitcoin? The answer is that an
inflated reward would result in the block being deemed invalid by
everyone else, wasting Jing’s electricity used for PoW. Jing