@DannyHamilton: Thank you for your answer.
No, according to @achow101 this is not right.
Please have a look at the following thread:
https://bitcointalksearch.org/topic/entropy-length-53-vs-99-1871338 (post #6)
In otherwords, we ALWAYS use the random number directly as a private key. We just represent that random number in a way that makes the most sense for it's use.
No, according to @achow101 this is not right.
Please have a look at the following thread:
https://bitcointalksearch.org/topic/entropy-length-53-vs-99-1871338 (post #6)
According to achow101, that IS right.
Please have a look at your thread:
https://bitcointalksearch.org/topic/m.18602354 (post #4)
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private keys are not actually strings with randomly generated characters. They are actually 256 bit integers
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private keys are not actually strings with randomly generated characters. They are actually 256 bit integers
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I am now confused.
That much is certain.
Entropy (more accurately known as Shannon entropy) in information theory is a measure of randomness.
A private key (in the bitcoin protocol) is a number between 1 and 115792089237316195423570985008687907852837564279074904382605163141518161494336.
Since numbers can be represented in many forms, you can also say that a private key is a number between 0x01 and 0xFFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4140
When choosing which number you want to use as your private key, it is important (in the interest of security) to have enough entropy (randomness) in your selection. While any number in that range IS a valid private key, your method of choosing a private key might not have an equal probability of generating any of the numbers in the range. This is where "entropy" becomes important. You need enough entropy to make any number in the valid range nearly equal in probability of being selected.
If you roll a cube die 3 times and use the resulting digits as your private key, you will only be capable of generating one of 216 possible private keys. There isn't enough randomness in this. Another person could roll a cube die a few thousand times and they would almost certainly get the same private key as you at least once. Since there are 216 possible results, and all of them are equally likely to occur, the entropy can be described as approximately 7.7 bits of entropy.
If you roll a cube die 100 times and use the resulting digits as a base 6 representation of your private key, you will generate one of:
6.53 X 1077 possible private keys. This has enough randomness. Another person could roll a cube die continuously for the rest of the time that the earth will exist and they still won't have even a 0.000000000000001% chance of generating the same private key as you. Since there are 6.53 X 1077 possible results, and all of them are equally likely to occur, the entropy can be described as a bit more than 256 bits of entropy.
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