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Wireless Networks

Notes
Example: If a sender wants to encrypt a message using this method, the sender knows
that every instance of the letter A in plaintext would be changed by the key to the letter D in
ciphertext; every instance of the letter B in plaintext would be changed to the letter E in the
ciphertext, and so on. Using this key, which has an algorithm of "shift the letters forward by
three," the word "help" in plaintext would be encrypted to be "khos" as ciphertext.
When the recipient receives the ciphertext message, the recipient would transform it back into
plaintext by using the key to decrypt the information, in this case by shifting the letters backward
by three, reversing the change.

In this example, both the sender and the recipient must keep the key secret because anyone who
knows the key can use it to decrypt and read the message. A lost key renders the encryption
useless. In addition, the strength of the algorithm is important. An unauthorized party can take
encrypted ciphertext and attempt to break the encryption by determining the key based on the
ciphertext.

Note that both the sender and the recipient use the same key. This type of encryption is referred
to as "symmetric key" encryption, because both parties use the same key.
Although this is a simple example, it illustrates the core concepts and functionality of
cryptography. Recent improvements and advancements in cryptography are ones of degree.

14.4.1 How Public-key Cryptography Works

In 1976, Whitfield Diffe and Martin Hellman created public key cryptography. Public key
cryptography represents a major innovation because it fundamentally alters the process of
encryption and decryption.
Instead of a single shared, secret key, Diffe and Hellman proposed the use of two keys. One key,
called the "private key" remains a secret. Instead of being shared between parties, it is held by
only one party. The second key, called the "public key," is not a secret and can be shared widely.
These two keys, or "key pair" as they are called, are used together in encryption and decryption
operations. The key pair has a special, reciprocal relationship so that each key can only be used in
conjunction with the other key in the pair. This relationship ties the keys in the pair exclusively
to one another: a public key and its corresponding private key are paired together and are related
to no other keys.
This pairing is possible because of a special mathematical relationship between the algorithms
for the public keys and private keys. The key pairs are mathematically related to one another
such that using the key pair together achieves the same result as using a symmetrical key twice.
The keys must be used together: each individual key cannot be used to undo its own operation.
This means that the operation of each individual key is a one-way operation: a key cannot be
used to reverse its operation. In addition, the algorithms used by both keys are designed so that
a key cannot be used to determine the opposite key in the pair. Thus, the private key cannot
be determined from the public key. The mathematics that makes key pairs possible, however,
contributes to one disadvantage of key pairs as opposed to symmetric keys. The algorithms used
must be strong enough to make it impossible for people to use the known public key to decrypt
information that has been encrypted with it through brute force. A public key uses mathematical
complexity and its one-way nature to compensate for the fact that it is publicly known to help
prevent people from successfully breaking information encoded with it.
Applying this concept to the preceding example, the sender would use the public key to encrypt
the plaintext into ciphertext. The recipient would then use the private key to decrypt the
ciphertext back into plaintext.
Because of the special relationship between the private key and public key in the key pair, it is
possible for one person to use the same key pair with many people rather than having to use a

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