Made changes to ch04.asciidoc

ch04.asciidoc

@@ -51,16 +51,15 @@ The bitcoin private key is just a number. You can pick your private keys randoml
 
 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^, 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. 
+More accurately, the private key can be any number between +1+ and +n - 1+, where n is a constant (n = 1.158 * 10^77^, 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 SHA256 hash algorithm that 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. 
 	
 [TIP]
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-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 entropy. Study the documentation of the random number generator library you choose to make sure it is cryptographically secure. Correct implementation of the CSPRNG is critical to the security of the keys.
+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 entropy. Study the documentation of the random number generator library you choose to make sure it is cryptographically secure. Correct implementation of the CSPRNG is critical to the security of the keys.
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-Below is a randomly generated private key shown in hexadecimal format (256 binary digits shown as 64 hexadecimal digits, each 4 bits):
+The following is a randomly generated private key (k) shown in hexadecimal format (256 binary digits shown as 64 hexadecimal digits, each 4 bits):
 
-.Randomly generated private key (k)
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 1E99423A4ED27608A15A2616A2B0E9E52CED330AC530EDCC32C8FFC6A526AEDD
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@@ -71,7 +70,7 @@ Below is a randomly generated private key shown in hexadecimal format (256 binar
 The size of bitcoin's private key space, 2^256^ is an unfathomably large number. It is approximately 10^77^ in decimal. The visible universe is estimated to contain 10^80^ atoms.
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-To generate a new key with the Bitcoin Core Client (see <<ch03_bitcoin_client>>), use the +getnewaddress+ 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 <<priv_formats>>. Here's an example of generating and displaying a private key using these two commands:
+To generate a new key with the Bitcoin Core client (see <<ch03_bitcoin_client>>), use the +getnewaddress+ 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+ command shows the private key in a Base58 checksum-encoded format called the _Wallet Import Format_ (WIF), which we will examine in more detail in <<priv_formats>>. Here's an example of generating and displaying a private key using these two commands:
 
 ----
 $ bitcoind getnewaddress
@@ -82,9 +81,8 @@ KxFC1jmwwCoACiCAWZ3eXa96mBM6tb3TYzGmf6YwgdGWZgawvrtJ
 
 The +dumpprivkey+ command opens the wallet and extracts the private key that was generated by the +getnewaddress+ command. It is not otherwise possible for bitcoind to know the private key from the public key, unless they are both stored in the wallet. 
 
-You can also use the command-line +sx tools+ (see <<sx_tools>>) to generate and display private keys:
+You can also use the command-line sx tools (see <<sx_tools>>) to generate and display private keys with the sx command +newkey+:
 
-===== New key with sx tools
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 $ sx newkey
 5J3mBbAH58CpQ3Y5RNJpUKPE62SQ5tfcvU2JpbnkeyhfsYB1Jcn