Update ch04.asciidoc

Suspected typos.

ch04.asciidoc

@@ -131,7 +131,7 @@ or
 \end{equation}
 ++++
 
-The +mod p+ (module prime number p) indicates that this curve is over a finite field of prime order +p+, also written as latexmath:[\(\mathbb{F}_p\)], where p = 2^256^ - 2^32^ - 2^9^ - 2^8^ - 2^7^ - 2^6^ - 2^4^ - 1\)], a very large prime number. 
+The +mod p+ (modulo prime number p) indicates that this curve is over a finite field of prime order +p+, also written as latexmath:[\(\mathbb{F}_p\)], where p = 2^256^ - 2^32^ - 2^9^ - 2^8^ - 2^7^ - 2^6^ - 2^4^ - 1\)], a very large prime number. 
 
 Because this curve is defined over a finite field of prime order instead of over the real numbers it looks like a pattern of dots scattered in two dimensions, which makes it difficult to visualize. However, the math is identical as that of an elliptic curve over the real numbers shown above. As an example, below is the same elliptic curve over a much smaller finite field of prime order 17, showing a pattern of dots on a grid. The +secp256k1+ bitcoin elliptic curve can be thought of as a much more complex pattern of dots on a unfathomably large grid. 
 
@@ -583,7 +583,7 @@ Another way to find a vanity address is to outsource the work to a pool of vanit
 
 Vanity addresses can be used to enhance _and_ to defeat security measures, they are truly a double-edged sword. Used to improve security, a distinctive address makes it harder for adversaries to substitute their own address and fool your customers into paying them instead of you. Unfortunately, vanity addresses also make it possible for anyone to create an address that _resembles_ any random address, or even another vanity address, thereby fooling your customers. 
 
-He could advertise a randomly generated address (e.g. 1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy) to which people to send their donations. Or, Eugenio could generate a vanity address that starts with 1Kids, to make it more distinctive. 
+He could advertise a randomly generated address (e.g. 1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy) to which people can send their donations. Or, Eugenio could generate a vanity address that starts with 1Kids, to make it more distinctive. 
 
 In both cases, one of the risks of using a single fixed address (rather than a separate dynamic address per donor) is that a thief might be able to infiltrate your website and replace it with their own address, thereby diverting donations to themselves. If you have advertised your donation address in a number of different places, your users may visually inspect the address before making a payment to ensure it is the same one they saw on your website, on your email, and on your flyer. In the case of a random address like "1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy", the average user will inspect the first few characters "1J7mdg" perhaps and be satisfied that the address matches. Using a vanity address generator, someone with the intent to steal by substituting a similar-looking address can quickly generate addresses that match the first few characters:
 
@@ -615,7 +615,7 @@ Paper wallets can be generated easily using a tool such as the client-side Javas
 .An example of a simple paper wallet from bitaddress.org
 image::images/paper_wallet_simple.png["paper_wallet_simple"]
 
-The disadvantage of the simple paper wallet system is that the printed keys are vulnerable to theft. A thief who is able to gain access to the paper can either steal it or photograph the keys and take control of the bitcoins locked with those keys. A more sophisticate paper wallet storage system uses BIP0038 encrypted private keys. The keys printed on the paper wallet are protected by a passphrase that the owner has memorized. Without the passphrase, the encrypted keys are useless. Yet, they still are superior to a passphrase protected wallet because the keys have never been online and must be physically retrieved from a safe or other physically secured storage. 
+The disadvantage of the simple paper wallet system is that the printed keys are vulnerable to theft. A thief who is able to gain access to the paper can either steal it or photograph the keys and take control of the bitcoins locked with those keys. A more sophisticated paper wallet storage system uses BIP0038 encrypted private keys. The keys printed on the paper wallet are protected by a passphrase that the owner has memorized. Without the passphrase, the encrypted keys are useless. Yet, they still are superior to a passphrase protected wallet because the keys have never been online and must be physically retrieved from a safe or other physically secured storage. 
 
 .An example of an encrypted paper wallet from bitaddress.org. The passphrase is "test"
 image::images/paper_wallet_encrypted.png["paper_wallet_encrypted"]