2 cissp ® Official Study Guide Eighth Edition

Public and Private Keys
Recall from Chapter 6 that 
public key cryptosystems
rely on pairs of keys assigned to each 
user of the cryptosystem. Every user maintains both a public key and a private key. As 
the names imply, public key cryptosystem users make their public keys freely available to 

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Asymmetric Cryptography 
239
anyone with whom they want to communicate. The mere possession of the public key by 
third parties does not introduce any weaknesses into the cryptosystem. The private key, on 
the other hand, is reserved for the sole use of the individual who owns the keys. It is never 
shared with any other cryptosystem user.
Normal communication between public key cryptosystem users is quite straightforward. 
Figure 7.1 shows the general process.
F I g u r e 7.1
Asymmetric key cryptography
Sender
Receiver
Encryption
Algorithm
P
C
Receiver’s
Public Key
Decryption
Algorithm
C
P
Receiver’s
Private Key
Notice that the process does not require the sharing of private keys. The sender encrypts 
the plaintext message (
P
) with the recipient’s public key to create the ciphertext message 
(
C
). When the recipient opens the ciphertext message, they decrypt it using their private key 
to re-create the original plaintext message.
Once the sender encrypts the message with the recipient’s public key, no user (includ-
ing the sender) can decrypt that message without knowing the recipient’s private key (the 
second half of the public-private key pair used to generate the message). This is the beauty 
of public key cryptography—public keys can be freely shared using unsecured communica-
tions and then used to create secure communications channels between users previously 
unknown to each other.
You also learned in the previous chapter that public key cryptography entails a higher 
degree of computational complexity. Keys used within public key systems must be longer 
than those used in private key systems to produce cryptosystems of equivalent strengths.
RSA
The most famous public key cryptosystem is named after its creators. In 1977, Ronald 
Rivest, Adi Shamir, and Leonard Adleman proposed the 
RSA public key algorithm
that 
remains a worldwide standard today. They patented their algorithm and formed a commer-
cial venture known as RSA Security to develop mainstream implementations of their secu-
rity technology. Today, the RSA algorithm has been released into the public domain and is 
widely used for secure communication.

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240
Chapter 7 
■
PKI and Cryptographic Applications
The RSA algorithm depends on the computational difficulty inherent in factoring large 
prime numbers. Each user of the cryptosystem generates a pair of public and private keys 
using the algorithm described in the following steps: