Small corrections (JWBurgers#5)

* Small text revisions

Chapter 3 - Symmetric Cryptography.md

@@ -42,7 +42,7 @@ You can see a depiction of situation (1) in *Figure 1* below. Bob wants to send
 
 Bob first encrypts the message M with the key K. He, then, sends the ciphertext C to Alice. Once Alice has received the ciphertext, she can decrypt it using the key K and read the plaintext. With a good encryption scheme, any attacker that intercepts the ciphertext C should not be able to learn anything of real significance about the message M.  
 
-You can see a depiction of situation (2) in *Figure 2* below. Bob wants prevent others from viewing certain information. A typical situation might be that Bob is an employee storing sensitive data on his computer, which neither outsiders nor his colleagues are supposed to read.  
+You can see a depiction of situation (2) in *Figure 2* below. Bob wants to prevent others from viewing certain information. A typical situation might be that Bob is an employee storing sensitive data on his computer, which neither outsiders nor his colleagues are supposed to read.  
 
 Bob encrypts the message M at time T0 with the key K to produce the ciphertext C. At time T1 he needs the message again, and decrypts the ciphertext C with the key K. Any attacker that might have come across the ciphertext C in a meantime should not have been able to deduce anything significant about M from it. 
 
@@ -280,7 +280,7 @@ While I have drawn a distinction between message authenticity and integrity in m
 
 Typically, you would want to guarantee both secrecy and authenticity in communication and, hence, encryption schemes and MAC schemes are typically used together. 
 
-An **authenticated encryption scheme** is scheme that combines encryption with a MAC in a highly secure manner. Specifically, it has to meet the standards for existential unforgeability as well as a very strong notion of secrecy, namely one that is resistant to **chosen-ciphertext attacks**.<sup>[4](#footnote4)</sup> 
+An **authenticated encryption scheme** is a scheme that combines encryption with a MAC in a highly secure manner. Specifically, it has to meet the standards for existential unforgeability as well as a very strong notion of secrecy, namely one that is resistant to **chosen-ciphertext attacks**.<sup>[4](#footnote4)</sup> 
 
 In order for an encryption scheme to be resistant to chosen-ciphertext attacks, it must meet the standards for **non-malleability**: that is, any modification of a ciphertext by an attacker should yield either an invalid ciphertext or one that decrypts to a plaintext having no relation to the original one.<sup>[5](#footnote5)</sup> 
 
@@ -340,4 +340,4 @@ The communication session starts by Bob sending a ciphertext C<sub>0,B</sub> to
 
 <a name="footnote4">4</a>. The specific results discussed in this section are from Katz and Lindell, pp. 131–47.
 
-<a name="footnote5">5</a>. Technically, the definition of chosen cipher text attacks is different than the notion of non-malleability. But you can show that those two notions of security are equivalent. 
+<a name="footnote5">5</a>. Technically, the definition of chosen cipher text attacks is different than the notion of non-malleability. But you can show that those two notions of security are equivalent. 

Chapter 4 - Asymmetric Cryptography.md

@@ -37,7 +37,7 @@ So, Jim’s Sporting Goods would have to store a pair of keys for each customer,
 
 - Jim’s Sporting Goods would have to store thousands of pairs of keys, one set for each customer.
 - These keys would have to be properly secured, as they would be a sure fire target for hackers. Any breaches of security would require the repetition of costly key exchanges, either at special key exchange locations or by courier. 
-- Any customer of Jim’s Sporting Goods would have to safely store a pair of keys. Losses and thefts will occur, requiring a repetition of key exchanges. Customers would also have to also have to go through this process for any other online stores or other types of entities they wish to communicate with over the Internet.  
+- Any customer of Jim’s Sporting Goods would have to safely store a pair of keys. Losses and thefts will occur, requiring a repetition of key exchanges. Customers would also have to go through this process for any other online stores or other types of entities they wish to communicate with over the Internet.  
 
 These two main challenges just described were very fundamental concerns until the late 1970s. They were known as the **key distribution problem** and the **key management problem**, respectively. 
 
@@ -107,7 +107,7 @@ An overview of asymmetric encryption with the help of Bob and Alice is provided
 
 Alice first creates a pair of keys, consisting of one public key (K<sub>P</sub>) and one private key (K<sub>S</sub>), where the “P” in K<sub>P</sub> stands for “public” and the “S” in K<sub>S</sub> for “secret”. She, then, distributes this public key freely to others. We will return to the details of this distribution process a little later. But for now assume that anyone, including Bob, can securely obtain Alice’s public key K<sub>P</sub>.
 
-At some later point, Bob wants to write a message M to Alice. As it includes sensitive information, however, he wants the contents to remain secret for everyone but Alice. So, Bob first encrypts his message M using P<sub>K</sub>. He then sends the resulting ciphertext C to Alice, who decrypts C with K<sub>S</sub> to produce the original message M.
+At some later point, Bob wants to write a message M to Alice. As it includes sensitive information, however, he wants the contents to remain secret for everyone but Alice. So, Bob first encrypts his message M using K<sub>P</sub>. He then sends the resulting ciphertext C to Alice, who decrypts C with K<sub>S</sub> to produce the original message M.
 
 *Figure 1: Asymmetric encryption*
 
@@ -513,4 +513,4 @@ Nevertheless, with adding a bit of clever complexity, the RSA problem can be use
 
 <a name="footnote9">9</a>. The same is true for discrete logarithm problems. Hence, why asymmetric constructions work with much larger keys than symmetric cryptographic constructions. 
 
-<a name="footnote10">10</a>. See, for example, Jonathan Katz and Yehuda Lindell, *Introduction to Modern Cryptography*, CRC Press (Boca Raton, FL: 2015), pp. 410–32 on RSA encryption and pp. 444–41 for RSA digital signatures. 
+<a name="footnote10">10</a>. See, for example, Jonathan Katz and Yehuda Lindell, *Introduction to Modern Cryptography*, CRC Press (Boca Raton, FL: 2015), pp. 410–32 on RSA encryption and pp. 444–41 for RSA digital signatures.