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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 * 1077, slightly less than 2256) defined as the order of the elliptic curve used in bitcoin (see “Elliptic Curve Cryptography Explained” on page 65). 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. Do not write your own code to create a random number or use a “simple” random number generator offered by your programming language. Use a cryptographically-secure pseudo-random number generator (CSPRNG) with a seed from a source of sufficient entro‐ py. Study the documentation of the random number generator li‐ brary you choose to make sure it is cryptographically secure. Cor‐ rect implementation of the CSPRNG is critical to the security of the keys. Below is a randomly generated private key shown in hexadecimal format (256 binary digits shown as 64 hexadecimal digits, each 4 bits): Randomly generated private key (k). 1E99423A4ED27608A15A2616A2B0E9E52CED330AC530EDCC32C8FFC6A526AEDD The size of bitcoin’s private key space, 2256 is an unfathomably large number. It is approximately 1077 in decimal. The visible universe is estimated to contain 1080 atoms. To generate a new key with the Bitcoin Core Client (see Chapter 3), use the getnewad dress command. For security reasons it displays the public key only, not the private key. To ask bitcoind to expose the private key, use the dumpprivkey command. The dumpprivkey shows the private key in a base-58 checksum encoded format called the Wallet Import Format (WIF), which we will examine in more detail in “Private Key 64 | Chapter 4: Keys, Addresses, WalletsPDF Image | Mastering Bitcoin
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