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drusselloctal@gmail.com 2014-10-31 04:15:15 -07:00
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@ -453,7 +453,7 @@ Running this will produce the hashes of several phrases, made different by addin
((("nonce"))) ((("nonce")))
[[sha256_example_generator_output]] [[sha256_example_generator_output]]
.SHA256 Output of a script for generating many hashes by iterating on a nonce .SHA256 output of a script for generating many hashes by iterating on a nonce
==== ====
[source,bash] [source,bash]
---- ----
@ -484,11 +484,11 @@ I am Satoshi Nakamoto19 => cda56022ecb5b67b2bc93a2d764e75f...
---- ----
==== ====
Each phrase produces a completely different hash result. They seem completely random, but you can re-produce the exact results in this example on any computer with Python and see the same exact hashes. Each phrase produces a completely different hash result. They seem completely random, but you can reproduce the exact results in this example on any computer with Python and see the same exact hashes.
The number used as a variable in such a scenario is called a _nonce_. The nonce is used to vary the output of a cryptographic function, in this case to vary the SHA-256 fingerprint of the phrase. The number used as a variable in such a scenario is called a _nonce_. The nonce is used to vary the output of a cryptographic function, in this case to vary the SHA256 fingerprint of the phrase.
To make a challenge out of this algorithm, let's set an arbitrary target: find a phrase that produces a hexadecimal hash that starts with a zero. Fortunately, this isn't so difficult! If you notice above, we can see that the phrase "I am Satoshi Nakamoto13" produces the hash 0ebc56d59a34f5082aaef3d66b37a661696c2b618e62432727216ba9531041a5, which fits our criteria. It took 13 attempts to find it. In terms of 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 every 16 hashes (one out of 16 hexadecimal digits 0 through F). In numerical terms, that means finding a hash value that is less than +0x1000000000000000000000000000000000000000000000000000000000000000+. We call this threshold the _target_ and the goal is to find a hash that is numerically _less than the target_. If we decrease the target, the task of finding a hash that is less than the target becomes more and more difficult. To make a challenge out of this algorithm, let's set an arbitrary target: find a phrase that produces a hexadecimal hash that starts with a zero. Fortunately, this isn't so difficult! If you notice in <<sha256_example_generator_output>>, we can see that the phrase "I am Satoshi Nakamoto13" produces the hash +0ebc56d59a34f5082aaef3d66b37a661696c2b618e62432727216ba9531041a5+, which fits our criteria. It took 13 attempts to find it. In terms of 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 every 16 hashes (one out of 16 hexadecimal digits 0 through F). In numerical terms, that means finding a hash value that is less than +0x1000000000000000000000000000000000000000000000000000000000000000+. We call this threshold the _target_ and the goal is to find a hash that is numerically _less than the target_. If we decrease the target, the task of finding a hash that is less than the target becomes more and more difficult.
To give a simple analogy, imagine a game where players throw a pair of dice repeatedly, trying to throw less than a specified target. In the first round, the target is 12. Unless you throw double-six, you win. In the next round the target is 11. Players must throw 10 or less to win, again an easy task. Let's say a few rounds later the target is down to 5. Now, more than half the dice throws will add up to more than 5 and therefore be invalid. It takes exponentially more dice throws to win, the lower the target gets. Eventually, when the target is 2 (the minimum possible), only one throw out of every 36, or 2% of them will produce a winning result. To give a simple analogy, imagine a game where players throw a pair of dice repeatedly, trying to throw less than a specified target. In the first round, the target is 12. Unless you throw double-six, you win. In the next round the target is 11. Players must throw 10 or less to win, again an easy task. Let's say a few rounds later the target is down to 5. Now, more than half the dice throws will add up to more than 5 and therefore be invalid. It takes exponentially more dice throws to win, the lower the target gets. Eventually, when the target is 2 (the minimum possible), only one throw out of every 36, or 2% of them will produce a winning result.