Consider the steps involved in sending messages from a sender, S, to a recipient, R. If S entrusts the message to T, who then delivers it to R, T then becomes the transmission medium. If an outsider, O, wants to access the message (to read, change, or even destroy it), we call O an interceptor or intruder.

**Terminology and Background**

Consider
the steps involved in sending messages from a **sender**, S, to a **recipient**,
R. If S entrusts the message to T, who then delivers it to R, T then becomes
the **transmission medium**. If an
outsider, O, wants to access the message (to read, change, or even destroy it),
we call O an **interceptor** or **intruder**. Any time after S transmits it
via T, the message is vulnerable to exploitation, and O might try to access the
message in any of the following ways:

Block it, by preventing its reaching R, thereby affecting the
availability of the message.

Intercept it, by reading or listening to the message, thereby
affecting the confidentiality of the message.

Modify it, by seizing the message and changing it in some way,
affecting the message's integrity.

Fabricate an authentic-looking message, arranging for it to be
delivered as if it came from S, thereby also affecting the integrity of the
message.

As you
can see, a message's vulnerabilities reflect the four possible security
failures we identified in __Chapter 1__. Fortunately,
encryption is a technique that can address all these problems. Encryption,
probably the most fundamental building block of secure computing, is a means of
maintaining secure data in an insecure environment. (It is not the only
building block, however.) In this book, we study encryption as a security
technique, and we see how it is used in protecting programs, databases,
networks, and electronic communications.

**Terminology**

**Encryption **is the process of encoding a message so that
its meaning is not obvious;** decryption **is
the reverse process, transforming an** **encrypted
message back into its normal, original form. Alternatively, the terms **encode** and **decode** or **encipher** and **decipher** are used

instead
of encrypt and decrypt.That is, we say that we encode, encrypt, or
encipher the original message to hide its meaning. Then, we decode, decrypt, or
decipher it to reveal the original message. A system for encryption and
decryption is called a **cryptosystem**.

The
original form of a message is known as **plaintext**,
and the encrypted form is called **ciphertext**.
This relationship is shown in __Figure 2-1__. For convenience, we denote a plaintext message P as a
sequence of individual characters P = <p_{1}, p_{2}, …, p_{n}>. Similarly,
ciphertext is

written as C = <c_{1}, c_{2}, …, c_{m}>. For instance, the plaintext message
"I want cookies" can be denoted as the message string <I,
,w,a,n,t, , c,o,o,k,i,e,s>. It can be transformed into ciphertext <c_{1}, c_{2}, …, c_{14}>, and the encryption
algorithm tells us how the transformation is done.

We use
this formal notation to describe the transformations between plaintext and
ciphertext. For example, we write C = E(P) and P = D (C), where C represents
the ciphertext, E is the encryption rule, P is the plaintext, and D is the
decryption rule. What we seek is a cryptosystem for which P = D(E(P)). In other
words, we want to be able to convert the message to protect it from an
intruder, but we also want to be able to get the original message back so that
the receiver can read it properly.

**Encryption Algorithms**

The
cryptosystem involves a set of rules for how to encrypt the plaintext and how
to decrypt the ciphertext. The encryption and decryption rules, called **algorithms** , often use a device called
a **key**, denoted by K, so that the
resulting ciphertext depends on the original plaintext message, the algorithm,
and the key value. We write this dependence as C = E(K, P). Essentially, E is a
set of encryption algorithms, and the key K selects one specific algorithm from
the set. We see later in this chapter that a cryptosystem, such as the Caesar
cipher, is keyless but that keyed encryptions are more difficult to break.

This
process is similar to using mass-produced locks in houses. As a homeowner, it
would be very expensive for you to contract with someone to invent and make a
lock just for your house. In addition, you would not know whether a particular
inventor's lock was really solid or how it compared with those of other
inventors. A better solution is to have a few well -known, well-respected
companies producing standard locks that differ according to the (physical) key.
Then, you and your neighbor might have the same model of lock, but your key
will open only your lock. In the same way, it is useful to have a few
well-examined encryption algorithms that everyone could use, but the differing
keys would prevent someone from breaking into what you are trying to protect.

Sometimes
the encryption and decryption keys are the same, so P = D(K, E(K,P)). This form
is called **symmetric** encryption
because D and E are mirror-image processes. At other times, encryption and
decryption keys come in pairs. Then, a decryption key, K_{D}, inverts the

encryption
of key K_{E} so that P = D(K_{D}, E(K_{E},P)). Encryption algorithms of this form are
called **asymmetric** because converting
C back to

P involves a series of steps and a key that are different from the
steps and key of E. The difference between symmetric and asymmetric encryption
is shown in __Figure 2-2__.

A key
gives us flexibility in using an encryption scheme. We can create different
encryptions of one plaintext message just by changing the key. Moreover, using
a key provides additional security. If the encryption algorithm should fall
into the interceptor's hands, future messages can still be kept secret because
the interceptor will not know the key value. __Sidebar
2 -1__ describes how the British dealt with written keys and codes in
World War II. An encryption scheme that does not require the use of a key is
called a **keyless cipher**.

The
history of encryption is fascinating; it is well documented in Kahn's book __[KAH96]__. Encryption has been used for centuries
to protect diplomatic and military communications, sometimes without full
success. The word **cryptography** means
hidden writing, and it refers to the practice of using encryption to conceal
text. A **cryptanalyst** studies
encryption and encrypted messages, hoping to find the hidden meanings.

Both a cryptographer and a cryptanalyst attempt to translate coded
material back to its original form. Normally, a cryptographer works on behalf
of a legitimate sender or receiver, whereas a cryptanalyst works on behalf of
an unauthorized interceptor. Finally, **cryptology**
is the research into and study of encryption and decryption; it includes both
cryptography and cryptanalysis.

**Sidebar 2-1:
Silken Codes**

Marks __[MAR98]__ describes the life of
a code-maker in Britain during World War II. That is, the British hired Marks
and others to devise codes that could be used by spies and soldiers in the
field. In the early days, the encryption scheme depended on poems that were
written for each spy and relied on the spy's ability to memorize and recall
them correctly.

Marks reduced the risk of error
by introducing a coding scheme that was printed on pieces of silk. Silk hidden
under clothing could not be felt when the spy was patted down and searched.
And, unlike paper, silk burns quickly and completely, so the spy could destroy
the incriminating evidence, also ensuring that the enemy could not get even
fragments of the valuable code. When pressed by superiors as to why the British
should use valuable silk (which was already needed for war-time necessities
like parachutes) for codes, Marks said that it was a choice "between silk
and cyanide."

**Cryptanalysis**

A
cryptanalyst's chore is to **break** an
encryption. That is, the cryptanalyst attempts to deduce the original meaning
of a ciphertext message. Better yet, he or she hopes to determine which
decrypting algorithm matches the encrypting algorithm so that other messages
encoded in the same way can be broken. For instance, suppose two countries are
at war and the first country has intercepted encrypted messages of the second.
Cryptanalysts of the first country want to decipher a particular message so
that the first country can anticipate the movements and resources of the second. But
it is even better to discover the actual decryption algorithm; then the first
country can easily break the encryption of all messages sent by the second
country.

Thus, a
cryptanalyst can attempt to do any or all of six different things:

break a single message

recognize patterns in encrypted messages, to be able to break
subsequent ones by applying a straightforward decryption algorithm

infer some meaning without even breaking the encryption, such as
noticing an unusual frequency of communication or determining something by
whether the communication was short or long

deduce the key, to break subsequent messages easily

find weaknesses in the implementation or environment of use of
encryption

find general weaknesses in an encryption algorithm, without
necessarily having intercepted any messages

In this
book, we see examples of each type of activity.

An
analyst works with a variety of pieces of information: encrypted messages,
known encryption algorithms, intercepted plaintext, data items known or
suspected to be in a ciphertext message, mathematical or statistical tools and
techniques, properties of languages, computers, and plenty of ingenuity and
luck. Each piece of evidence can provide a clue, and the analyst puts the clues
together to try to form a larger picture of a message's meaning in the context
of how the encryption is done. Remember that there are no rules. An interceptor
can use any means available to tease out the meaning of the message.

**Breakable Encryption**

An
encryption algorithm is called breakable when, given enough time and data, an
analyst can determine the algorithm. However, an algorithm that is
theoretically breakable may in fact be impractical to try to break. To see why,
consider a 25-character message that is

expressed
in just uppercase letters. A given cipher scheme may have 26^{25} (approximately 10^{35}) possible decipherments, so
the task is to select the right one out of the 26^{25}. If your computer could
perform on the order of 10^{10} operations per second, finding this decipherment

would
require on the order of 10^{16} seconds, or roughly 10^{11} years. In this case, although we know that
theoretically we could generate the solution, determining the deciphering
algorithm by examining all possibilities can be ignored as infeasible with
current technology.

Two
other important issues must be addressed when considering the breakability of
encryption algorithms. First, the cryptanalyst cannot be expected to try only
the hard, long way. In the example just presented, the obvious decryption might
require 26^{25} machine operations, but a

more ingenious approach might require only 10^{15} operations. At the speed of
10 ^{10} operations per second, 10^{15} operations take slightly more than one day.
The ingenious approach is certainly feasible. As we see later in this chapter,
some of the algorithms we study in this book are based on known
"hard" problems that take an unreasonably long time to solve. But the
cryptanalyst does not necessarily have to solve the underlying problem to break
the encryption of a single message. As we note in __Sidebar
2-2__, sloppy use of controls can reveal likely words or phrases, and
an analyst can use educated guesses combined with careful analysis to generate
all or most of an important message.

**Sidebar 2-2:
Hidden Meanings Change the Course of World War II**

In the spring of 1942, the United States
was fighting Japan in the Pacific. American cryptanalysts had cracked some of
the Japanese naval codes, but they didn't understand the extra encoding the
Japanese used to describe particular sites. A message intercepted by the United
States told the Allies' officers that "AF" was to be the target of a
major assault. The U.S. Navy suspected that the assault would be on Midway
island, but it needed to be sure.

Commander Joseph Rochefort, head
of the U.S. Navy's cryptography center at Pearl Harbor, devised a clever plan
to unearth the meaning of "AF." He directed the naval group at Midway
to send a message, requesting fresh water because the water distillery had been
damaged. Soon, the United States intercepted a Japanese message indicating that
"AF" was short of waterverifying that "AF" indeed meant
Midway! __[SEI01]__

Second, estimates of breakability are based on current technology.
An enormous advance in computing technology has occurred since 1950. Things
that were infeasible in 1940 became possible by the 1950s, and every succeeding
decade has brought greater improvements.

A
conjecture known as "Moore's Law" asserts that the speed of
processors doubles every 1.5 years, and this conjecture has been true for over
two decades. It is risky to pronounce an algorithm secure just because it
cannot be broken with current technology, or worse, that it has not been broken
yet.

**Representing Characters**

We want
to study ways of encrypting any computer material, whether it is written as
ASCII characters, binary data, object code, or a control stream. However, to
simplify the explanations, we begin with the encryption of messages written in
the standard 26-letter English alphabet, A through Z.

Because
this book is written in English, the explanations refer to English. However,
with slight variations, the techniques are applicable to most other written
languages as well.

Throughout the book, we use the convention that plaintext is
written in UPPERCASE letters, and ciphertext is in lowercase letters. Because
most encryption algorithms are based on mathematical transformations, they can
be explained or studied more easily in mathematical form. Therefore, in this
book, we switch back and forth between letters and the numeric encoding of each
letter as shown here.

Thus, the letter A is represented by a zero, B by a one, and so on. This representation allows us to consider performing arithmetic on the "letters" of a message. That is, we can perform addition and subtraction on letters by adding and subtracting the corresponding code numbers. Expressions such as A + 3 = D or K - 1 = J have their natural interpretation. Arithmetic is performed as if the alphabetic table were circular. In other words, addition wraps around from one end of the table to the other so that Y + 3 = B. Thus, every result of an arithmetic operation is between 0 and 25.

There are many types of encryption. In the next two sections we
look at two simple forms of encryption: substitutions, in which one letter is
exchanged for another, and transpositions, in which the order of the letters is
rearranged. The goals of studying these two forms are to become familiar with
the concept of encryption and decryption, to learn some of the terminology and
methods of cryptanalysis, and to study some of the weaknesses to which
encryption is prone. Once we have mastered the simple encryption algorithms, we
explore "commercial grade" algorithms used in modern computer
applications.

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