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Re-applying fix from Issue #28, which seems to have been accidentally ovewritten by a recent merge

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Minh T. Nguyen 2014-05-26 23:16:04 -07:00 committed by Andreas M. Antonopoulos
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@ -47,7 +47,7 @@ The bitcoin private key is just a number. A public key can be generated from any
The first and most important step in generating keys is to find a secure source of entropy, or randomness. Creating a bitcoin key is essentially the same as "Pick a number between 1 and 2^256^". The exact method you use to pick that number does not matter as long as it is not predictable or repeatable. Bitcoin software uses the underlying operating system's random number generators to produce 256 bits of entropy (randomness). Usually, the OS random number generator is initialized by a human source of randomness, which is why you may be asked to wiggle your mouse around for a few seconds. For the truly paranoid, nothing beats dice, pencil and paper.
More accurately, the private key can be any number between +1+ and +n - 1+, where n is a constant (n = 1.158 * 10^77^ or slightly less than 2^256^) defined as the order of the elliptic curve used in bitcoin (see <<elliptic_curve>>). To create such a key, we randomly pick a 256-bit number and check that it is less than +n - 1+. In programming terms, this is usually achieved by feeding a larger string of random bits, collected from a cryptographically-secure source of randomness, into the SHA-256 hash algorithm which will conveniently produce a 256-bit number. If the result is less than +n - 1+, we have a suitable private key. If it is greater than +n - 1+, we simply try again with another random number.
More accurately, the private key can be any number between +1+ and +n - 1+, where n is a constant (n = 1.158 * 10^77^ or slightly less than 2^256^) defined as the order of the elliptic curve used in bitcoin (see <<elliptic_curve>>). To create such a key, we randomly pick a 256-bit number and check that it is less than +n - 1+. In programming terms, this is usually achieved by feeding a larger string of random bits, collected from a cryptographically-secure source of randomness, into the SHA-256 hash algorithm which will conveniently produce a 256-bit number. If the result is less than +n - 1+, we have a suitable private key. Otherwise, we simply try again with another random number.
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