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hash generator and difficulty content

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Andreas M. Antonopoulos 2013-08-18 15:35:38 -07:00
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2 changed files with 67 additions and 31 deletions
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@ -52,7 +52,7 @@ With SHA-256, the output is always 256 bits long, regardless of the size of the
[[sha256_example1]] [[sha256_example1]]
.SHA256 Example .SHA256 Example
==== ====
[source, python] [source, shell]
---- ----
$ python <1> $ python <1>
Python 2.7.1 (r271:86832, Jul 31 2011, 19:30:53) Python 2.7.1 (r271:86832, Jul 31 2011, 19:30:53)
@ -72,39 +72,47 @@ Type "help", "copyright", "credits" or "license" for more information.
The example shows that if we calculate the hash of the phrase +"I am Satoshi Nakamoto"+, it will produce +5d7c7ba21cbbcd75d14800b100252d5b428e5b1213d27c385bc141ca6b47989e+. This 256-bit number is the _hash_ or _digest_ of the phrase and depends on every part of the phrase. Adding a single letter, punctuation mark or any character will produce a different hash. The example shows that if we calculate the hash of the phrase +"I am Satoshi Nakamoto"+, it will produce +5d7c7ba21cbbcd75d14800b100252d5b428e5b1213d27c385bc141ca6b47989e+. This 256-bit number is the _hash_ or _digest_ of the phrase and depends on every part of the phrase. Adding a single letter, punctuation mark or any character will produce a different hash.
Now, if we vary the phrase, we will expect to see completely different hashes. Let's try that by adding a number to the end of our phrase: Now, if we vary the phrase, we will expect to see completely different hashes. Let's try that by adding a number to the end of our phrase, using this simple Python script
[[sha256_example2]] [[sha256_example_generator]]
.SHA256 Iterating on a Nonce .SHA256 A script for generating many hashes by iterating on a nonce
==== ====
[source, python] [source, python]
---- ----
>>> print hashlib.sha256("I am Satoshi Nakamoto1").hexdigest() include::code/hash_example.py[]
f7bc9a6304a4647bb41241a677b5345fe3cd30db882c8281cf24fbb7645b6240 ----
>>> print hashlib.sha256("I am Satoshi Nakamoto2").hexdigest() ====
ea758a8134b115298a1583ffb80ae62939a2d086273ef5a7b14fbfe7fb8a799e
>>> print hashlib.sha256("I am Satoshi Nakamoto3").hexdigest() Running this will produce the hashes of several phrases, made different by adding a unique number, called a _nonce_ at the end of the text. By incrementing the nonce, we can get different hadhes.
bfa9779618ff072c903d773de30c99bd6e2fd70bb8f2cbb929400e0976a5c6f4
>>> print hashlib.sha256("I am Satoshi Nakamoto4").hexdigest() [[sha256_example_generator_output]]
bce8564de9a83c18c31944a66bde992ff1a77513f888e91c185bd08ab9c831d5 .SHA256 Output of a script for generating many hashes by iterating on a nonce
>>> print hashlib.sha256("I am Satoshi Nakamoto5").hexdigest() ====
eb362c3cf3479be0a97a20163589038e4dbead49f915e96e8f983f99efa3ef0a [source, shell]
>>> print hashlib.sha256("I am Satoshi Nakamoto6").hexdigest() ----
4a2fd48e3be420d0d28e202360cfbaba410beddeebb8ec07a669cd8928a8ba0e $ python hash_example.py
>>> print hashlib.sha256("I am Satoshi Nakamoto7").hexdigest() I am Satoshi Nakamoto0 => a80a81401765c8eddee25df36728d732acb6d135bcdee6c2f87a3784279cfaed
790b5a1349a5f2b909bf74d0d166b17a333c7fd80c0f0eeabf29c4564ada8351 I am Satoshi Nakamoto1 => f7bc9a6304a4647bb41241a677b5345fe3cd30db882c8281cf24fbb7645b6240
>>> print hashlib.sha256("I am Satoshi Nakamoto8").hexdigest() I am Satoshi Nakamoto2 => ea758a8134b115298a1583ffb80ae62939a2d086273ef5a7b14fbfe7fb8a799e
702c45e5b15aa54b625d68dd947f1597b1fa571d00ac6c3dedfa499f425e7369 I am Satoshi Nakamoto3 => bfa9779618ff072c903d773de30c99bd6e2fd70bb8f2cbb929400e0976a5c6f4
>>> print hashlib.sha256("I am Satoshi Nakamoto9").hexdigest() I am Satoshi Nakamoto4 => bce8564de9a83c18c31944a66bde992ff1a77513f888e91c185bd08ab9c831d5
7007cf7dd40f5e933cd89fff5b791ff0614d9c6017fbe831d63d392583564f74 I am Satoshi Nakamoto5 => eb362c3cf3479be0a97a20163589038e4dbead49f915e96e8f983f99efa3ef0a
>>> print hashlib.sha256("I am Satoshi Nakamoto10").hexdigest() I am Satoshi Nakamoto6 => 4a2fd48e3be420d0d28e202360cfbaba410beddeebb8ec07a669cd8928a8ba0e
c2f38c81992f4614206a21537bd634af717896430ff1de6fc1ee44a949737705 I am Satoshi Nakamoto7 => 790b5a1349a5f2b909bf74d0d166b17a333c7fd80c0f0eeabf29c4564ada8351
>>> print hashlib.sha256("I am Satoshi Nakamoto11").hexdigest() I am Satoshi Nakamoto8 => 702c45e5b15aa54b625d68dd947f1597b1fa571d00ac6c3dedfa499f425e7369
7045da6ed8a914690f087690e1e8d662cf9e56f76b445d9dc99c68354c83c102 I am Satoshi Nakamoto9 => 7007cf7dd40f5e933cd89fff5b791ff0614d9c6017fbe831d63d392583564f74
>>> print hashlib.sha256("I am Satoshi Nakamoto12").hexdigest() I am Satoshi Nakamoto10 => c2f38c81992f4614206a21537bd634af717896430ff1de6fc1ee44a949737705
60f01db30c1a0d4cbce2b4b22e88b9b93f58f10555a8f0f4f5da97c3926981c0 I am Satoshi Nakamoto11 => 7045da6ed8a914690f087690e1e8d662cf9e56f76b445d9dc99c68354c83c102
>>> print hashlib.sha256("I am Satoshi Nakamoto13").hexdigest() I am Satoshi Nakamoto12 => 60f01db30c1a0d4cbce2b4b22e88b9b93f58f10555a8f0f4f5da97c3926981c0
0ebc56d59a34f5082aaef3d66b37a661696c2b618e62432727216ba9531041a5 I am Satoshi Nakamoto13 => 0ebc56d59a34f5082aaef3d66b37a661696c2b618e62432727216ba9531041a5
I am Satoshi Nakamoto14 => 27ead1ca85da66981fd9da01a8c6816f54cfa0d4834e68a3e2a5477e865164c4
I am Satoshi Nakamoto15 => 394809fb809c5f83ce97ab554a2812cd901d3b164ae93492d5718e15006b1db2
I am Satoshi Nakamoto16 => 8fa4992219df33f50834465d30474298a7d5ec7c7418e642ba6eae6a7b3785b7
I am Satoshi Nakamoto17 => dca9b8b4f8d8e1521fa4eaa46f4f0cdf9ae0e6939477e1c6d89442b121b8a58e
I am Satoshi Nakamoto18 => 9989a401b2a3a318b01e9ca9a22b0f39d82e48bb51e0d324aaa44ecaba836252
I am Satoshi Nakamoto19 => cda56022ecb5b67b2bc93a2d764e75fc6ec6e6e79ff6c39e21d03b45aa5b303a
$
---- ----
==== ====
@ -182,12 +190,29 @@ Hash is 000005a5312680389e451a65fed9c3885bfe35afb446a0971d5c13ce471c3712
Elapsed Time: 4.69 seconds Elapsed Time: 4.69 seconds
Hashing Power: 179120 hashes per second Hashing Power: 179120 hashes per second
Difficulty: 24
Starting search...
Success with nonce 18779387
Hash is 000000a7e616c6968f22435687aae9e071cd5a8cb5b704ef2bff67bd258e4aab
Elapsed Time: 106.63 seconds
Hashing Power: 176122 hashes per second
---- ----
==== ====
As you can see, increasing the difficulty by 4 bits causes an exponential increase 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 the example above, it takes 18 million hash attempts to find a nonce that produces a hash with 24 leading bits as zero. Even at a speed of more than 170 thousand hashes per second, it almost two minutes to find this solution.
At the time of writing this, the network is attempting to find a block whose header hash is less than +000000000000004c296e6376db3a241271f43fd3f5de7ba18986e517a243baa7+. As you can see, there are a lot of zeroes at the beginning of that hash, meaning that the acceptable range of hashes is much smaller, hence more difficult to find a valid hash. It will take on average more than 10 minutes of searching at more than 500 trillion hash calculations per second for the network to discover the next block. At the time of writing this, the network is attempting to find a block whose header hash is less than +000000000000004c296e6376db3a241271f43fd3f5de7ba18986e517a243baa7+. As you can see, there are a lot of zeroes at the beginning of that hash, meaning that the acceptable range of hashes is much smaller, hence more difficult to find a valid hash. It will take on average more 150 quadrillion hash calculations per second for the network to discover the next block. That seems like an impossible task, but fortunately the network is bringing 500 TH/sec of processing power to bear, which will be able to find a block in about 10 minutes on average.
==== Diificulty Adjustment
Bitcoin is tuned to generate blocks approximately every 10 minutes. This is achieved by automatically adjusting the target difficulty to account for increases and decreases in the available computing power on the network. This process occurs automatically and on every node independently. Each node recalculates the expected difficulty every 2106 blocks, based on the time it took to hash the previous 2106 blocks. In simple terms: If the network is finding blocks faster than every 10 minutes, the difficulty increases. If block discovery is slower than expected, the difficulty will decrease.
[TIP]
====
The difficulty of finding a bitcoin block is approximately '10 minutes of processing' for the entire network, based on the time it took to find the previous 2106 blocks, adjusted every 2106 blocks. If you know the processing power of the network in hashes per second, you can calculate how many hashes per 10 minutes, which is how many on avergae to find a block, ie. the current difficulty.
====
===
=== Transaction Fees === Transaction Fees

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code/hash_example.py Normal file
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@ -0,0 +1,11 @@
# example of iterating a nonce in a hashing algorithm's input
import hashlib
text = "I am Satoshi Nakamoto"
for nonce in xrange(20): # iterate nonce from 0 to 19
input = text + str(nonce) # add the nonce to the end of the text
hash = hashlib.sha256(input).hexdigest() # calculate the SHA-256 hash of the input (text+nonce)
print input, '=>', hash # show the input and hash result