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How Blockchains Work

Chances are, you know what Bitcoin is. After all, it’s valued at over $47,000
per Bitcoin right now. This post isn’t about the business side of things,
though, or the BTC speculative bubble. I want to explain how it works.^[3]1

Foundations: Hashes and Ledgers

First, a hash algorithm is a way to convert a given string into an
unpredictable string of a fixed length, called a digest.

A diagram illustrating that a hash algorithm produces a digest from a string.

Here’s a small Python program to demonstrate:

#!/usr/bin/env python3
from argparse import ArgumentParser
from hashlib import md5


def hash_string(string):
    hash = md5()
    hash.update(string.encode("utf-8"))
    return hash.hexdigest()


if __name__ == "__main__":
    parser = ArgumentParser()
    parser.add_argument("STRING", help="The string to be hashed")
    args = parser.parse_args()
    print(hash_string(args.STRING))

Running this with different string arguments will give you digests of the
arguments:

$ ./hash ninja
3899dcbab79f92af727c2190bbd8abc5

$ ./hash samurai
99b1983cf3ee09bbaf6f43ac7b4c8748

Hashes of this type are used to check passwords—you can check whether a
password matches without storing the password itself.^[4]2

Blockchains are a kind of ledger: they have entries added to them over time.
Hashes can help with that by protecting the ordering and contents of messages.

A diagram illustrating that blockchains capture the previous digest and the
current message to produce a digest.

Here’s a brief implementation:

def hash_ledger_entry(string, previous_digest=None):
    """Hashes a string with the hash of previous entries in the ledger, if any."""
    hash = md5(string.encode("utf-8"))

    if previous_digest:
        hash.update(previous_digest.encode("utf-8"))

    return hash.hexdigest()


def generate_ledger(*strings):
    """Generates the entries in a ledger consisting of a set of strings."""
    digest = None

    for string in strings:
        digest = hash_ledger_entry(string, digest)
        yield digest, string


if __name__ == "__main__":
    parser = ArgumentParser()
    parser.add_argument("STRINGS", help="The ledger entries", nargs="+")
    args = parser.parse_args()

    for digest, string in generate_ledger(*args.STRINGS):
        print(f"{digest}\t{string}")

With this script, providing a set of strings will generate a unique and ordered
ledger:

$ ./hash ninja samurai
3899dcbab79f92af727c2190bbd8abc5        ninja
6bf8d2cadde40af53d7f0fef95d4ec2c        samurai

These hash ledgers are tamper-resistant because the digests of later entries
depend on the earlier entries. Modifying or adding entries will change the
digest of later entries.

$ ./hash ninja pirate samurai
3899dcbab79f92af727c2190bbd8abc5        ninja
7ec21dcf528e12036b04774754ecc4e0        pirate
636730d86709d03fed9ba64f84fc9be6        samurai

We can also add a known ending entry to the ledger to protect the last entry
from tampering:

$ ./hash ninja pirate samurai
3899dcbab79f92af727c2190bbd8abc5        ninja
7ec21dcf528e12036b04774754ecc4e0        pirate
636730d86709d03fed9ba64f84fc9be6        samurai
b233d566fe677d394aafb5eaf149e453        END

Validation

To validate a ledger, you can replay the transactions and make sure that you
get the same hashes at each step:

our_digest = None

for line in fileinput.input():
    file_digest, word = line.strip().split("\t")
    our_digest = hash_ledger_entry(word, our_digest)

    if our_digest != file_digest:
        sys.exit(f"The digest for {word} does not match.")

print("All entries match.")

With a tamper-resistant ledger where each entry depends on the previous
entries, we’ve effectively implemented a very simple blockchain. This is not
the same as the blockchain, though; for that we need…

Proofs without Authority

The novelty of Bitcoin is that it is a distributed system with no owner. This
is what enthusiasts mean when they say that the blockchain is trustless:
instead of central authority, like a bank, many “miners” compete to
successfully write a new message to the blockchain. They do this by means of a
proof-of-work algorithm, which we can implement in our ledger as well.

# Add this to your imports.
from secrets import token_bytes


def hash_ledger_entry_with_salt(salt, string, previous_digest=None):
    """Hashes a string with the hash of previous entries in the ledger, if any."""
    hash = md5(string.encode("utf-8"))
    hash.update(salt)

    if previous_digest:
        hash.update(previous_digest.encode("utf-8"))

    return hash.hexdigest()


def generate_ledger(difficulty, *strings):
    # Difficulty determines how many zeroes we require at the beginning of a digest.
    prefix = "0" * difficulty

    digest = None
    previous_digest = None

    for string in strings:
        # We re-hash a string over and over, with random salts, until it matches the
        # prefix determined by our difficulty.
        while digest is None or not digest.startswith(prefix):
            salt = token_bytes(16)
            digest = hash_ledger_entry_with_salt(salt, string, previous_digest)

        # We yield back the digest and entry, as before, but we need the salt, too.
        # Without that, we can't replay the entries and verify them.
        yield digest, salt.hex(), string
        previous_digest = digest
        digest = None

    yield hash_ledger_entry_with_salt(salt, "END", previous_digest), salt, "END"


if __name__ == "__main__":
    parser = ArgumentParser()
    parser.add_argument(
        "DIFFICULTY", help="The difficulty of confirming a ledger entry.", type=int
    )
    parser.add_argument("STRINGS", help="The ledger entries", nargs="+")
    args = parser.parse_args()

    for digest, salt, string in generate_ledger(args.DIFFICULTY, *args.STRINGS):
        print(f"{digest}\t{salt}\t{string}")

The new utility accepts an additional argument, difficulty, and tries to
generate a salt value that generates a hash which matches the expected number
of zeroes:

$ ./hash 5 ninja pirate samurai
00000ad72553509e6c197e45ab7fa436        af0dce7ac4c87c2b9d9eafb6561c09f4        ninja
000000f556426cfa894ba2ce57383b1d        b9d51e0e8ea977ba004e7c30be757144        pirate
000006373b2b336d6dac403a5fa90a73        dd9c6ad89f5014a0901bcb142e04e28b        samurai
fa35b5a39bc0318015620684d60a27f0        dd9c6ad89f5014a0901bcb142e04e28b        END

The “mining” process can require a lot of calculations. The example required,
on average, around 2.5 million attempts. That’s why Bitcoin mining consumes [5]
more electricity than many countries: on the “real” blockchain, miners are
calculating and recalculating quadrillions of hashes per bitcoin mined.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

 1. If you want to read about the bubble, I recommend [6]David Gerard. [7]↩︎

 2. Note that md5 should not be used for this purpose in real applications. I
    chose it here for the brevity of its digests, but it isn’t secure. [8]↩︎


References:

[1] https://asthasr.github.io/
[2] https://asthasr.github.io/index.xml
[3] https://asthasr.github.io/posts/how-blockchains-work/#fn:1
[4] https://asthasr.github.io/posts/how-blockchains-work/#fn:2
[5] https://www.bbc.com/news/technology-56012952
[6] https://davidgerard.co.uk/blockchain/
[7] https://asthasr.github.io/posts/how-blockchains-work/#fnref:1
[8] https://asthasr.github.io/posts/how-blockchains-work/#fnref:2