2 cissp ® Official Study Guide Eighth Edition

Sender
Receiver
Encryption
Algorithm
P
C
Receiver’s
Public Key
Decryption
Algorithm
C
P
Receiver’s
Private Key
Key requirements
In a class one of the authors of this book taught recently, a student wanted to see an illustra-
tion of the scalability issue associated with symmetric encryption algorithms. The fact that 
symmetric cryptosystems require each pair of potential communicators to have a shared 
private key makes the algorithm nonscalable. The total number of keys required to com-
pletely connect 
n
parties using symmetric cryptography is given by the following formula:
Number of Keys
=
−
n n
(
)
1
2
Now, this might not sound so bad (and it’s not for small systems), but consider the follow-
ing figures. Obviously, the larger the population, the less likely a symmetric cryptosystem 
will be suitable to meet its needs.
Number of participants
Number of symmetric
keys required
Number of asymmetric
keys required
2
1
4
3
3
6
4
6
8
5
10
10
10
45
20

---

218
Chapter 6 
■
Cryptography and Symmetric Key Algorithms
Number of participants
Number of symmetric
keys required
Number of asymmetric
keys required
100
4,950
200
1,000
499,500
2,000
10,000
49,995,000
20,000
Asymmetric key algorithms also provide support for digital signature technology. 
Basically, if Bob wants to assure other users that a message with his name on it was actu-
ally sent by him, he first creates a message digest by using a hashing algorithm (you’ll find 
more on hashing algorithms in the next section). Bob then encrypts that digest using his 
private key. Any user who wants to verify the signature simply decrypts the message digest 
using Bob’s public key and then verifies that the decrypted message digest is accurate. 
Chapter 7 explains this process in greater detail.
The following is a list of the major strengths of asymmetric key cryptography: