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CH12: simplify PoW example

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Previous example used python to describe how PoW works.  Replace
the first example with a bash one-liner and remove the unnecessary
details.

Inspired by review comments from Jorge Lesmes
This commit is contained in:
David A. Harding 2023-08-09 15:51:20 -10:00
parent 114d7bf25a
commit 43ae026233
2 changed files with 31 additions and 179 deletions
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146
ch10.asciidoc
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@ -683,27 +683,16 @@ way as to produce a desired digest, other than trying random
inputs. inputs.
With SHA256, the output is always 256 bits long, regardless of the size With SHA256, the output is always 256 bits long, regardless of the size
of the input. In <<sha256_example1>>, we will use the Python interpreter of the input. For example, we will to calculate the SHA256 hash of the
to calculate the SHA256 hash of the phrase, "I am Satoshi Nakamoto." phrase, "Hello, World!"
[[sha256_example1]]
.SHA256 example
====
[source,bash]
---- ----
$ python $ echo "Hello, world!" | sha256sum
d9014c4624844aa5bac314773d6b689ad467fa4e1d1a50a1b8a99d5a95f72ff5 -
---- ----
[source,pycon]
----
Python 2.7.1
>>> import hashlib
>>> print hashlib.sha256("I am Satoshi Nakamoto").hexdigest()
5d7c7ba21cbbcd75d14800b100252d5b428e5b1213d27c385bc141ca6b47989e
----
====
This This
256-bit number is the _hash_ or _digest_ of the phrase and depends on 256-bit number (represented in hex) is the _hash_ or _digest_ of the phrase and depends on
every part of the phrase. Adding a single letter, punctuation mark, or every part of the phrase. Adding a single letter, punctuation mark, or
any other character will produce a different hash. any other character will produce a different hash.
@ -713,10 +702,21 @@ this case to vary the SHA256 fingerprint of the phrase.
To make a challenge out of this algorithm, let's set a target: find a To make a challenge out of this algorithm, let's set a target: find a
phrase that produces a hexadecimal hash that starts with a zero. phrase that produces a hexadecimal hash that starts with a zero.
Fortunately, this isn't difficult! <<sha256_example_generator_output>> Fortunately, this isn't difficult:
shows that the phrase "I am Satoshi Nakamoto13" produces the hash
+0ebc56d59a34f5082aaef3d66b37a661696c2b618e62432727216ba9531041a5+, [[sha256_example_generator_output]]
which fits our criteria. It took 13 attempts to find it. In terms of ----
$ for nonce in $( seq 100 ) ; do echo "Hello, world! $nonce" | sha256sum ; done
3194835d60e85bf7f728f3e3f4e4e1f5c752398cbcc5c45e048e4dbcae6be782 -
bfa474bbe2d9626f578d7d8c3acc1b604ec4a7052b188453565a3c77df41b79e -
[...]
f75a100821c34c84395403afd1a8135f685ca69ccf4168e61a90e50f47552f61 -
09cb91f8250df04a3db8bd98f47c7cecb712c99835f4123e8ea51460ccbec314 -
----
The phrase "Hello, World! 32" produces the hash
+09cb91f8250df04a3db8bd98f47c7cecb712c99835f4123e8ea51460ccbec314+,
which fits our criteria. It took 32 attempts to find it. In terms of
probabilities, if the output of the hash function is evenly distributed probabilities, if the output of the hash function is evenly distributed
we would expect to find a result with a 0 as the hexadecimal prefix once we would expect to find a result with a 0 as the hexadecimal prefix once
every 16 hashes (one out of 16 hexadecimal digits 0 through F). In every 16 hashes (one out of 16 hexadecimal digits 0 through F). In
@ -754,13 +754,18 @@ any possible outcome can be calculated in advance. Therefore, an outcome
of specified difficulty constitutes proof of a specific amount of work. of specified difficulty constitutes proof of a specific amount of work.
==== ====
In <<sha256_example_generator_output>>, the winning "nonce" is 13 and In <<sha256_example_generator_output>>, the winning "nonce" is 32 and
this result can be confirmed by anyone independently. Anyone can add the this result can be confirmed by anyone independently. Anyone can add the
number 13 as a suffix to the phrase "I am Satoshi Nakamoto" and compute number 32 as a suffix to the phrase "Hello, world!" and compute
the hash, verifying that it is less than the target. The successful the hash, verifying that it is less than the target.
result is also Proof-of-Work, because it proves we did the work to find
that nonce. While it only takes one hash computation to verify, it took ----
us 13 hash computations to find a nonce that worked. If we had a lower $ echo "Hello, world! 32" | sha256sum
09cb91f8250df04a3db8bd98f47c7cecb712c99835f4123e8ea51460ccbec314 -
----
Although it only takes one hash computation to verify, it took
us 32 hash computations to find a nonce that worked. If we had a lower
target (higher difficulty) it would take many more hash computations to target (higher difficulty) it would take many more hash computations to
find a suitable nonce, but only one hash computation for anyone to find a suitable nonce, but only one hash computation for anyone to
verify. Furthermore, by knowing the target, anyone can estimate the verify. Furthermore, by knowing the target, anyone can estimate the
@ -785,95 +790,6 @@ current difficulty in the Bitcoin network, miners have to try
a huge number of times before finding a nonce that results in a low a huge number of times before finding a nonce that results in a low
enough block header hash. enough block header hash.
A very simplified Proof-of-Work algorithm is implemented in Python in
<<pow_example1>>.
[[pow_example1]]
.Simplified Proof-of-Work implementation
====
[source, python]
----
include::code/proof-of-work-example.py[]
----
====
Running this code, you can set the desired difficulty (in bits, how many
of the leading bits must be zero) and see how long it takes for your
computer to find a solution. In <<pow_example_outputs>>, you can see how
it works on an average laptop.
[[pow_example_outputs]]
.Running the Proof-of-Work example for various difficulties
====
[source, bash]
----
$ python proof-of-work-example.py*
----
----
Difficulty: 1 (0 bits)
[...]
Difficulty: 8 (3 bits)
Starting search...
Success with nonce 9
Hash is 1c1c105e65b47142f028a8f93ddf3dabb9260491bc64474738133ce5256cb3c1
Elapsed Time: 0.0004 seconds
Hashing Power: 25065 hashes per second
Difficulty: 16 (4 bits)
Starting search...
Success with nonce 25
Hash is 0f7becfd3bcd1a82e06663c97176add89e7cae0268de46f94e7e11bc3863e148
Elapsed Time: 0.0005 seconds
Hashing Power: 52507 hashes per second
Difficulty: 32 (5 bits)
Starting search...
Success with nonce 36
Hash is 029ae6e5004302a120630adcbb808452346ab1cf0b94c5189ba8bac1d47e7903
Elapsed Time: 0.0006 seconds
Hashing Power: 58164 hashes per second
[...]
Difficulty: 4194304 (22 bits)
Starting search...
Success with nonce 1759164
Hash is 0000008bb8f0e731f0496b8e530da984e85fb3cd2bd81882fe8ba3610b6cefc3
Elapsed Time: 13.3201 seconds
Hashing Power: 132068 hashes per second
Difficulty: 8388608 (23 bits)
Starting search...
Success with nonce 14214729
Hash is 000001408cf12dbd20fcba6372a223e098d58786c6ff93488a9f74f5df4df0a3
Elapsed Time: 110.1507 seconds
Hashing Power: 129048 hashes per second
Difficulty: 16777216 (24 bits)
Starting search...
Success with nonce 24586379
Hash is 0000002c3d6b370fccd699708d1b7cb4a94388595171366b944d68b2acce8b95
Elapsed Time: 195.2991 seconds
Hashing Power: 125890 hashes per second
[...]
Difficulty: 67108864 (26 bits)
Starting search...
Success with nonce 84561291
Hash is 0000001f0ea21e676b6dde5ad429b9d131a9f2b000802ab2f169cbca22b1e21a
Elapsed Time: 665.0949 seconds
Hashing Power: 127141 hashes per second
----
====
As you can see, increasing the difficulty by 1 bit causes a doubling in
the time it takes to find a solution. If you think of the entire 256-bit
number space, each time you constrain one more bit to zero, you decrease
the search space by half. In <<pow_example_outputs>>, it takes 84
million hash attempts to find a nonce that produces a hash with 26
leading bits as zero. Even at a speed of more than 120,000 hashes per
second, it still requires 10 minutes on a laptop to find this solution.
[[target_bits]] [[target_bits]]
==== Target Representation ==== Target Representation

64
code/proof-of-work-example.py
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@ -1,64 +0,0 @@
#!/usr/bin/env python
# example of proof-of-work algorithm
import hashlib
import time
try:
long # Python 2
xrange
except NameError:
long = int # Python 3
xrange = range
max_nonce = 2 ** 32 # 4 billion
def proof_of_work(header, difficulty_bits):
# calculate the difficulty target
target = 2 ** (256 - difficulty_bits)
for nonce in xrange(max_nonce):
hash_result = hashlib.sha256(str(header) + str(nonce)).hexdigest()
# check if this is a valid result, below the target
if long(hash_result, 16) < target:
print("Success with nonce %d" % nonce)
print("Hash is %s" % hash_result)
return (hash_result, nonce)
print("Failed after %d (max_nonce) tries" % nonce)
return nonce
if __name__ == '__main__':
nonce = 0
hash_result = ''
# difficulty from 0 to 31 bits
for difficulty_bits in xrange(32):
difficulty = 2 ** difficulty_bits
print("Difficulty: %ld (%d bits)" % (difficulty, difficulty_bits))
print("Starting search...")
# checkpoint the current time
start_time = time.time()
# make a new block which includes the hash from the previous block
# we fake a block of transactions - just a string
new_block = 'test block with transactions' + hash_result
# find a valid nonce for the new block
(hash_result, nonce) = proof_of_work(new_block, difficulty_bits)
# checkpoint how long it took to find a result
end_time = time.time()
elapsed_time = end_time - start_time
print("Elapsed Time: %.4f seconds" % elapsed_time)
if elapsed_time > 0:
# estimate the hashes per second
hash_power = float(long(nonce) / elapsed_time)
print("Hashing Power: %ld hashes per second" % hash_power)