For some reason, good cryptography is just *much* harder than
it looks. This field seems to have a continuous flow of experts from
other fields who offer cryptographic variations of ideas which are
common in their other field. Now, there is nothing wrong with new
ideas. But there are in fact *many* extremely intelligent and
extremely well-educated people with wide-ranging scientific interests
who are active in this field. It is *very common* to find that
so-called "new" ideas have been previously addressed under another
name or as a general concept. Try to get some background before
you get in too deep.

You may wish to help support this work by patronizing Ritter's Crypto Bookshop.

- The Fundamental Idea of Cryptography
- A Concrete Example
- Naive Ciphers
- Naive Challenges
- What Cryptography Can Do
- What Cryptography Can
*Not*Do - Cryptography with Keys
- Problems with Keys
- Cryptography without Keys
- Keyspace
- Strength
- Cipher Trust
- System Design And Strength
- Cryptanalysis versus Subversion
- Secret Ciphers
- Hardware vs. Software Ciphers
- Block Ciphers
- Stream Ciphers
- Public Key Ciphers
- The Most Important Book
- Classical Cryptanalysis
- Other Books
- Coding Theory
- For Designers

It is possible to transform or
encipher a
message or
*plaintext*
into "an intermediate form" or
*ciphertext*
in which the original information is *present* but
*hidden.*
Then we can release the transformed message (the ciphertext)
without exposing the information it represents.

By using different transformations, we can create many different ciphertexts for the exact same message. So if we select a particular transformation "at random," we can hope that anyone wishing to expose the message ("break" the cipher) can do no better than simply trying all available transformations (on average, half) one-by-one. This is a brute force attack.

The difference between intermediate forms is the
*interpretation* of the ciphertext data. Different
ciphers and different
keys will produce different
interpretations (different plaintexts) for the exact same
ciphertext. The uncertainty of how to interpret any particular
ciphertext is how information is "hidden."

Naturally, the intended recipient needs to know how to transform or decipher the intermediate form back into the original message, and this is the key distribution problem.

By itself, ciphertext is literally *meaningless*, in the
sense of having no one clear interpretation. In so-called
perfect ciphers,
*any* ciphertext (of appropriate size) can be interpreted as
*any* message, just by selecting an appropriate key.
In fact, any number of *different* messages can produce
*exactly the same ciphertext,* by using the appropriate keys.
In other ciphers, this may not always be possible, but it must
always be considered. To
attack and break a cipher, it
is necessary to somehow confirm that the message we generate from
ciphertext is the exact particular message which was sent.

Most of us have encountered a simple form of ciphering in grade school, and it usually goes something like this:

On a piece of lined paper, write the alphabet in order, one character per line:

A B C ...Then, on each line, we write another character to the right. In this second column, we also want to use each alphabetic character exactly once, but we want to place them in some different order.

A F B W C A ...

When we have done this, we can take any message and encipher it letter-by-letter.

To encipher a letter, we find that letter in the left column, then use the associated letter from the right column and write that down. Each letter in the right column thus becomes a substitute for the associated letter in the left column.

Deciphering
is similar, except
that we find the ciphertext letter in the right column, then use the
associated plaintext letter from the left column. This is a little
harder, because the letters in the right column are not in order.
But if we wanted to, we could make a list where the ciphertext
letters were in order; this would be the *inverse* of the
enciphering transformation. And if we have both lists, enciphering
and deciphering are both easy.

The grade school cipher is a
simple substitution
cipher, a
streaming or repeated
letter-by-letter application of the same transformation. That
"transformation" is the particular arrangement of letters in the
second column, a
permutation of the alphabet.
There can be *many* such arrangements. But in this case the
key *is* that particular
arrangement. We can copy it and give it to someone and then send
secret messages to them. But if that sheet is acquired -- or even
copied -- by someone else, the enciphered messages would be exposed.
This means that we have to keep the transformation secret.

Now suppose we have a full notebook of lined pages, each of which
contains a *different* arrangement in the second column.
Suppose each page is numbered. Now we just pick a number and
encipher our message using that particular page. That number thus
becomes our
key, which is now a sort of numeric
shorthand for the full transformation. So even if the notebook is
exposed, someone who wishes to expose our message must try about
half of the transformations in the book before finding the right
one. Since exposing the notebook does not immediately expose our
messages, maybe we can leave the notebook unprotected. We also can
use the same notebook for messages to different people, and each of
them can use the exact same notebook for their own messages to each
other. Different people can use the same notebook and yet still
cipher messages which are difficult to expose without knowing the
right key.

Note that there is some potential for confusion in first calling
the transformation a
key, and then calling the number
which selects that transformation *also* a key. But both of
these act to select a particular ciphertext construction from among
many, and they are only two of the various kinds of "key" in
cryptography.

The
simple substitution
used in our grade school cipher is very weak, because it "leaks"
information: The more often a particular plaintext letter is used,
the more often the associated ciphertext letter appears. And since
language uses some letters more than others, simply by counting the
number of times each ciphertext letter occurs we can make a good
guess about which plaintext letter it represents. Then we can try
our guess and see if it produces something we can understand. It
usually does not take too long before we can
break the cipher, even
*without* having the key. In fact, we *develop* the
ultimate key (the enciphering transformation) to break the cipher.
This is a
codebook attack.

Obviously, when we have few transformations from plaintext to ciphertext, each transformation will be used many times. And if the transformation is known or suspected on even one of those uses, every other use also will be exposed.

One way to reduce this problem is to increase the size of
the cipher
alphabet.
Rather than considering our cipher alphabet to be just the 26
letters, each with a single keyable transformation to ciphertext,
we could instead use *pairs* of those same letters, and have
at least 26 x 26 = 676 transformations.
This vast increase in keyable transformations makes the code harder
to create and store, but also decreases the number of times each
individual transformation might be used.
We can continue expanding the alphabet by having triplets and
quadruplets and so on.
Rather quickly we will need a machine to do the operations for us.

A "real" conventional block cipher will have a far larger
alphabet. For example, the usual 64-bit
block cipher
will encipher 8 plaintext characters at the same time, and a change
in even one
bit
in one of those characters will affect all 64 bits of the resulting
ciphertext, typically changing about half the values.
This is still simple substitution, but with a huge alphabet.
Instead of using 26 letters, a 64-bit block cipher views each of
2^{64} different block values as a separate letter, which
is something like 18,000,000,000,000,000,000 "letters."

There are various opportunities for increasing cipher strength:

- One strength opportunity is to change the key frequently. That generally requires additional processing overhead and also requires that a larger amount of key material be transported in some way.
- Another strength opportunity is to randomize the plaintext, so that each letter occurs with the same probability. Letter frequency randomization can be done statistically in a block cipher operating mode, or by multiple encryption. Or some form of dynamic letter frequency compensation system could be constructed.
- Yet another strength opportunity is to construct a homophonic cipher, in which any particular plaintext can be represented by many different unrelated ciphertexts. Then, when plaintext reuse does occur, hopefully the ciphertext will be different. This will expand the ciphertext.
- An uncommon strength opportunity is to add nulls to plaintext or ciphertext. Some sort of keyed cryptographic random number generator computes positions for the characters. For encryption the desired characters are placed at the computed positions. For decryption the characters at those locations are retrieved. Adding huge numbers of nulls could expand the ciphertext by huge amounts.
- Yet another strength opportunity is to come up with some form
of conventional block cipher that can key-select and realize
*every possible*substitution table. Unfortunately, that goal typically is well beyond being merely infeasible for blocks of reasonable size.

No matter what we do, what we *think* is a
strong
cipher may not actually *be* a strong cipher.
We are unlikely to know the practical strength of our cipher.
In practice, strength is
contextual
and depends not only upon some unknown "absolute" strength, but also
upon the knowledge and abilities of the attacker or
opponent.

Unfortunately, we do not expect to know who the attackers may be,
nor their capabilities, nor will they tell us of their successes.
So, absent some sort of
"proof
of strength in practice" (which is
generally *not* possible), there is no way to know whether a
cipher is actually protecting the information we entrust to it.

Suppose we have 256 pages of transformations in the notebook;
this means there are exactly 256 different
keys we can select from.
If we write the number 256 in
binary we get "100000000"; here
the leftmost "1" represents 1 count of 2^{8}, and we call
this an "8 bit" number.
Or we can compute the base 2 logarithm by first taking the natural
log of 256 (about 5.545) and dividing that by the natural log of 2
(about 0.693); this result is also 8. So we say that having 256
key possibilities is an "8 bit"
keyspace. If we choose one
of the 256 key values at random, and use that transformation to
encipher a message, someone wishing to
break our cipher should have to
try about 128 decipherings before happening upon the correct one.
The effort involved in trying, on average, 128 decipherings (a
brute force attack)
before finding the right one, is the design
strength of the cipher.

If our notebook had 65,536 pages or keys (instead of just 256),
we would have a "16 bit" keyspace. Notice that this number of key
possibilities is 256 *times* that of an "8 bit" keyspace, while
the key itself has only 8 bits *more* than the "8 bit" cipher.
The strength of the "16 bit" cipher is the effort involved in trying,
on average, 32,768 decipherings before finding the right one.

The *idea* is the same as a modern cipher: We have a machine
which can produce a huge number of different transformations between
plaintext and ciphertext, and we select one of those transformations
with a key value. Since there are many, many possible keys, it is
difficult to expose a message, even though the machine itself is not
secret. And many people can use the exact same machine for their own
secrets, *without* revealing those secrets to everyone who has
such a machine.

One of the consequences of having a digital electronic machine
for ciphering, is that it operates very, very fast. This means that
someone can try a lot more possibilities than they could with a
notebook of paper pages. For example, a "40 bit" keyspace represents
about 10^{12} keys, which sounds like a lot. Unfortunately,
special-purpose hardware could try this many decipherings in under 5
seconds, which is not much strength.
A "56 bit" keyspace represents about ^{16}*also* not much strength.
The current strength recommendation is 112 to 128 bits, and 256 is
not out of the question. 128 bits is just 16 bytes, which is the
amount of storage usually consumed by 16 text characters, a very
minimal amount. A 128 bit key is "strong enough" to defeat even
unimaginably extensive brute force attacks.

Under the theory that if a little is good, a lot is better, some
people suggest using huge keys of 56,000 bits, or 1,000,000 bits,
or even more. We *can* build such devices, and they can operate
quickly. We can even afford the storage for big keys. What we do
*not* have is a *reason* for such keys: a 128 bit key is
"strong enough" to defeat even unimaginably extensive brute force
attacks. While a designer might use a larger key for convenience,
even immense keys cannot provide more strength than "strong enough."
And while different attacks may show that the cipher actually has
less strength, a huge keyspace is not going to solve those problems.

Some forms of cipher *need* relatively large key values
simply to have a sufficiently large keyspace. Most number-theory
based
public key ciphers
are in this class. Basically, these systems require key values in
a very special form, so that most key values are unacceptable and
unused. This means that the actual keyspace is much smaller than
the size of the key would indicate. For this reason, public key
systems need keys in the 1,000 bit range, while delivering strength
perhaps comparable to 128 bit
secret key ciphers.

Suppose we want to hide a name: We might think to innovate a different rule for each letter. We might say: "First we have 'T', but 't' is the 3rd letter in 'bottle' so we write '3.'" We can continue this way, and such a cipher could be very difficult to break. So why is this sort of thing not done? There are several reasons:

- First, any cipher construction must be
decipherable, and it is all
too easy, when choosing rules at random, to make a rule that
depends upon
plaintext, which will
of course not be present until
*after*the ciphertext is deciphered. - The next problem is remembering the rules, since the rules constitute the key. If we choose from among many rules, in no pattern at all, we may have a strong cipher, but be unable to remember the key. And if we write the key down, all someone has to do is read that and properly interpret it (which may be another encryption issue). So we might choose among few rules, in some pattern, which will make a weaker cipher.
- Another problem is the question of what we do for longer messages.
This sort of scheme seems to want a different key, or perhaps just
more key, for a longer message, which is certainly inconvenient.
What often happens in practice is that the key is re-used repeatedly,
and
*that*will be very, very weak. - Yet another problem is the observation that describing the
rule selection may take more information than the message itself.
To send the message to someone else, we must somehow transport the
key securely to the other end. But if we
*can*transfer this amount of data securely in the first place, we wonder why we cannot securely transfer the smaller message itself.

Modern ciphering is about constructions which attempt to solve these problems. A modern cipher has a large keyspace, which might well be controlled by a hashing computation on a language phrase we can remember. A modern cipher system can handle a wide range of message sizes, with exactly the same key, and normally provides a way to securely re-use keys. And the key can be much, much smaller than a long message.

Moreover, in a modern cipher, we expect the key to not be
exposed, *even if* the
opponent has *both*
the plaintext *and* the associated ciphertext for many
messages (a
known-plaintext attack).
In fact, we normally assume that the opponent knows the full
construction of the cipher, and has lots of
known plaintext, and
*still* cannot find the key. Such designs are not trivial.

Sometimes a novice gives us 40 or 50 random-looking characters and says, "Bet you can't break this!" But that is not very realistic.

In actual use, we normally assume that a
cipher will be widely distributed,
and thus somewhat available. So we assume the
opponent will somehow acquire
either the cipher machine or its complete design.
We also assume a cipher will be widely used, so a lot of ciphered
material will be around somewhere. We assume the opponent will somehow
acquire some amount of
plaintext and the associated
ciphertext
(that is,
known plaintext).
And even in this situation, we *still* expect the cipher
to hide the key and other messages.

A cipher designer should expect everything to be exposed -- the complete cipher design, ciphertext, unlimited associated plaintext, etc. -- except the actual message and key. All of the exposed information should be provided to anyone working on the problem.

Potentially, cryptography can hide information while it is in transit or storage. In general, cryptography can:

- Provide secrecy.
- Authenticate that a message has not changed in transit.
- Implicitly authenticate the sender.

Cryptography hides *words*: At most, it can only hide
*talking about* contraband or illegal actions. But in a country
with "freedom of speech," we normally expect crimes to be more
than just "talk."

Cryptography can kill in the sense that boots can kill; that is,
as a part of some other process, but that does not make cryptography
like a rifle or a tank. Cryptography is defensive, and can
*protect* ordinary commerce and ordinary people.
Cryptography may be to our private information as our home is to
our private property, and our home is our "castle."

Potentially, cryptography can hide *secrets,* either from
others, or during communication. There are many good and non-criminal
reasons to have secrets: Certainly, those engaged in commercial
research and development (R&D) have "secrets" they must keep.
Business often needs secrecy from competitors while plans and laid
and executed, and the need for secrecy often continues as long as
there are business operations.
Professors and writers may want to keep their work private, until
an appropriate time. Negotiations for new jobs are generally
secret, and romance often is as well, or at least we might prefer
that detailed discussions not be exposed. And health information
is often kept secret for good reason.

One possible application for cryptography is to secure on-line
communications between work and home, perhaps leading to a
society-wide reduction in driving, something we could *all*
appreciate.

Cryptography can only hide information *after* it is
encrypted and *while*
it remains encrypted. But secret information generally does not
*start out* encrypted, so there is normally an original period
during which the secret is not protected. And secret information
generally is not *used* in encrypted form, so it is again
outside the cryptographic envelope every time the secret is used.

Secrets are often related to public information, and subsequent activities based on the secret can indicate what that secret is.

And while cryptography can hide *words,* it cannot hide:

- Physical contraband,
- Cash,
- Physical meetings and training,
- Movement to and from a central location,
- An extravagant lifestyle with no visible means of support, or
- Actions.

And cryptography simply cannot protect against:

- Informants,
- Undercover spying,
- Bugs,
- Photographic evidence, or
- Testimony.

It is a joke to imagine that cryptography alone could protect most information against Government investigation. Cryptography is only a small part of the protection needed for "absolute" secrecy.

Usually, we arrange to select among a huge number of possible intermediate forms by using some sort of "pass phrase" or key. Normally, this is some moderately-long language phrase which we can remember, instead of something we have to write down (which someone else could then find).

Those who have one of the original keys can expose the information hidden in the message. This reduces the problem of protecting information to:

- Performing transformations, and
- Protecting the keys.

This is similar to locking our possessions in our house and keeping the keys in our pocket.

The physical key model reminds us of various things that can go wrong with keys:

- We can lose our keys.
- We can forget which key is which.
- We can give a key to the wrong person.
- Somebody can steal a key.
- Somebody can pick the lock.
- Somebody can go through a window.
- Somebody can break down the door.
- Somebody can ask for entry, and unwisely be let in.
- Somebody can get a warrant, then legally do whatever is required.
- Somebody can burn down the house, thus making everything irrelevant.

Even absolutely perfect keys cannot solve all problems, nor can they guarantee privacy. Indeed, when cryptography is used for communications, generally at least two people know what is being communicated. So either party could reveal a secret:

- By accident.
- To someone else.
- Through third-party eavesdropping.
- As revenge, for actions real or imagined.
- For payment.
- Under duress.
- In testimony.

When it is substantially less costly to acquire the secret by means other then a technical attack on the cipher, cryptography has pretty much succeeded in doing what it can do.

It is fairly easy to design a complex cipher program to produce a single complex, intermediate form. In this case, the program itself becomes the "key."

But this means that the deciphering program must be kept available to access protected information. So if someone steals your laptop, they probably will also get the deciphering program, which -- if it does not use keys -- will immediately expose all of your carefully protected data. This is why cryptography generally depends upon at least one remembered key, and why we need ciphers which can produce a multitude of different ciphertexts.

Cryptography
deliberately creates the situation of "a needle in
a haystack." That is, of all possible
keys,
only one should recover the correct message, and that one key is
hidden among all possible keys. Of course, the
opponent
*might* get lucky, but *probably* will have to perform
about half of the possible
decipherings to find the
message.

To keep messages secret, it is important that a
cipher
be able to produce a multitude of different intermediate forms or
ciphertexts.
Clearly, no cipher can possibly be stronger than requiring The
opponent to check
*every possible* deciphering. If such a
brute force
search is practical, the cipher is weak. The number of possible
ciphertexts is the "design strength" of a cipher.

[ Actually, there is at least one other possibility for
delivering strength, and that is the Shannon idea of
Perfect Secrecy:
If a cipher can be constructed such that *every* possible
plaintext can be deciphered from any given ciphertext, a full
brute-force attack just produces every possible plaintext.
Unfortunately, this requires as much keying information
as plaintext, which then becomes a
key distribution problem
as in the
one time pad.
However, the basic idea might be used to strengthen *parts*
of an overall imperfect cipher. ]

Each different ciphertext requires a different key. So the number of different ciphertexts which we can produce is limited to the number of different keys we can use. We describe the keyspace by the length in bits of the binary value required to represent the number of possible ciphertexts or keys.

It is not particularly difficult to design ciphers which may have a design strength of hundreds or thousands of bits, and these can operate just as fast as our current ciphers. However, the U.S. Government generally does not allow the export of data ciphers with a keyspace larger than about 40 bits, which is a very searchable value.

Recently, a 56-bit keyspace was searched (with special hardware)
and the correct key found in about 56 hours. Note that a 56-bit
key represents 2^{16} times as many transformations as a
40-bit key. So, all things being equal, similar equipment might
find a 40-bit key in about 3 seconds. But at the same rate, an
80-bit key (which is presumably 2^{24} times as strong as
a 56-bit key) would take over 100,000 years.

Keyspace
alone only sets an *upper limit* to
cipher strength;
a cipher can be *much weaker* than it appears. An in-depth
understanding or
analysis
of the design may lead to
"shortcuts" in the solution. Perhaps a few tests can be designed,
each of which eliminates vast numbers of keys, thus in the end
leaving a searchable keyspace; this is one form of
cryptanalysis.

Given the large and developed field of
cryptography,
one might think that surely there must be tests which can report the
strength
of an arbitrary
cipher.
Alas, there can be no such test. Every keyed cipher is weak if the
key
can be found, so what we normally mean by "strength" is the inability
of unknown
opponents
to develop the correct key based on whatever information they can
acquire. (Normally, we assume the opponent has a large amount of
both the plaintext and the associated ciphertext, because it is
difficult in practice to eliminate all
known-plaintext
exposure.)
Thus, strength in practice depends upon the abilities of opponents
we cannot know. Those opponents will have all the knowledge of the
"open scientific literature," *plus* whatever additional
knowledge they may have developed in their own groups.

Every user of cryptography should understand that, in practice,
**all** known ciphers (*including* the
one time pad, when used in practice)
are at least potentially vulnerable to some unknown technical
attack. And if such a
break *does* occur, our
private information could be exploited for years and there
is no reason to expect that we would find out about it.

With respect to
trust,
cryptography is *not* like most areas
of technology: Normally, we can *see* or *hear* or
otherwise directly sense when our devices perform as designed.
For example, when we build a car, we can see how fast and far it
goes, how easily it starts, and so on; the goal of moving people
inside a machine is observable and measurable in many ways.
Whenever we use a car and *see* that it works, that builds
trust.
When thousands of cars cross a bridge successfully, we learn to
trust that bridge, at least for cars.
When we turn on a radio and listen to a station we know the radio
"works."

We even know when software "works": In general, we use software to produce some sort of result we want. We can then examine the results and decide whether or not they are indeed what we want. Even if bugs do occur, they are generally secondary to the results we manage to produce. So as we use software, we can build trust that it will do what we expect, because we can see what it does.

In contrast, the purpose of cryptography is to protect our secret
information, and that is a result we *cannot* see: The loss of
information is something we simply can neither see nor measure.
We do not know whether or not a cipher "works."
And since we cannot tell whether a cipher is "working," simply using
a cipher *should not* build trust, even if many people use
that cipher over many years.
Unfortunately, this is such an unusual situation that most people
do not recognize the distinction.

The inability to measure whether or not a cipher "works" lends an ironic aspect to the concept of cryptography as a science.

It is sometimes argued that not knowing whether or not a cipher
"works" is not too far from the situation of pharmaceutical drugs,
in the sense that we simply cannot know the long-term implications
of any medication.
But we certainly *do* expect that a drug actually *will*
improve matters in some observable way, or it will not be used.
And in cryptography, we cannot even say that using a cipher will
improve matters. In a real sense, any cipher could be a "placebo,"
presenting only the *appearance* of medication, and we may be
the sad unmedicated patient. The belief that we are being helped
when that is not the truth is precisely the situation our opponents
wish to achieve!

But what about cipher "contests," and all the *pro-bono*
analysis contributed by crypto experts? Surely all that must tell us
*something* we can believe in!
Well, that does tell us *something*, but perhaps not what
we hope for.

What academic
cryptanalysis
tells us is that those who participate and who know the open
scientific literature are unaware of any obvious successful attacks.
Unfortunately, that says nothing at all about strength with respect
to non-academic opponents, who know both the open academic
literature *and* their own in-house development, and may
spend far more time on cryptanalysis.

If our opponents are successful at breaking our cipher they
will not tell us.
For if we know for sure that our cipher is broken, we will
eventually change the cipher, and the new one may be more
difficult to break than the old one.
So our opponents will seek to avoid providing even *hints*
that our cipher is weak.
In fact, opponents who are successful in breaking our cipher may
actively seek to discount any hints of cipher weakness, and also
disparage anyone carrying that message.
Propaganda is a natural,
expected consequence of the situation.
In the end, there is no reason to expect that we will know when
our cipher becomes weak, or if it has been weak all along.

Cryptographic design may seem as easy as selecting a
cipher from a book of ciphers.
But ciphers, *per se,* are only *part* of a secure
encryption system. It is *common* for a cipher system to
require cryptographic design beyond simply selecting a cipher, and
such design is much trickier than it looks.

The use of an
unbreakable cipher does
*not* mean that the encryption system will be similarly
unbreakable. A prime example of this is the
man-in-the-middle attack
on
public-key ciphers.
Public-key ciphers *require* that one use the correct
key for the desired person. The
correct key must be known *to cryptographic levels of assurance*,
or this becomes the weak link in the system: Suppose an
opponent can get us to use
his key instead of the right one (perhaps by sending a faked message
saying "Here is my new key"). If he can do this to both ends, and
also intercept all messages between them (which is conceivable, since
Internet routing is *not* secure), the opponent can sit "in the
middle." He can decipher each message (now in one of his keys), then
re-encipher that message in the correct user key, and send it along.
So the users communicate, and no cipher has been broken, yet the
opponent is still reading the conversation.
Such are the consequences of system design error.

Cryptanalysis is hard; it is often tedious, repetitive, and very, very expensive. Success is never assured, and resources are always limited. Consequently, other approaches for obtaining the hidden information (or the key!) can be more effective.

Approaches other than a direct technical attack on ciphertext include getting the information by cunning, outright theft, bribery, or intimidation. The room or computer could be bugged, secretaries subverted, files burglarized, etc. Most information can be obtained in some way other than "breaking" ciphertext.

When the strength of a cipher greatly exceeds the effort required to obtain the same information in another way, the cipher is probably strong enough. And the mere fact that information has escaped does not necessarily mean that a cipher has been broken.

Although, in some cases,
cryptanalysis
might succeed even if the
ciphering
process was unknown, we would certainly expect that this would
make The
opponents' job much harder.
It thus can be argued that the ciphering process *should*
remain secret. Certainly, military cipher systems are not actually
*published* (although it may be assumed internally that the
equipment is known to the other side). But in commercial
cryptography we normally assume (see
Kerckhoff's
Requirements)
that the opponents *will* know every detail of the cipher
(although not the
key,
of course). There are several reasons for this:

- First, it is common for a cipher to have unexpected weaknesses which are not found by its designers. But if the cipher design is kept secret, it cannot be examined by various interested parties, and so the weakness will not be publicly exposed. And this means that the weakness might be exploited in practice, while the cipher continues to be used.
- Next, if a cipher itself is a secret, that secret is increasingly
compromised by making it available for use: For a cipher to be used,
it must be present at various locations, and the more widely it is
used, the greater the risk the secret will be exposed.
So whatever advantage there may be in cipher secrecy cannot be
maintained, and the opponents eventually will have the same
advantage they would have had from public disclosure. Only now
the cipher designers can comfort themselves with the dangerous
delusion that their opponents do
*not*have an advantage they actually*will*have.

There is another level of secrecy here, and that is the trade secrecy involved with particular software designs. Very few large companies are willing to release source code for their products without some serious controls, and those companies may have a point. While the crypto routines themselves presumably might be patented, releasing that code alone probably would not support a thorough security evaluation. Source code might reasonably be made available to customers under a nondisclosure agreement, but this will not satisfy everyone. And while it might seem nice to have all source code available free, this will certainly not support an industry of continued cipher design and development. Unfortunately, there appears to be no good solution to this problem.

Currently, most ciphers are implemented in software; that is, by a program of instructions executed by a general-purpose computer. Normally, software is cheaper, but hardware can run faster, and nobody can change it. Of course, there are levels to hardware, from chips (which thus require significant interface software) to external boxes with communications lines running in and out. But there are several possible problems:

- Software, especially in a multi-user system, is almost completely insecure. Anyone with access to the machine could insert modified software which would then be repeatedly used under the false assumption that effective security was still in place. This may not be an issue for home users, and real solution here may depend upon a secure operating system.
- Hardware represents a capital expense, and is extremely inflexible. So if problems begin to be suspected in a hardware cipher, the expense of replacement argues against an update. Indeed, a society-wide system might well take years to update anyway.

One logical possibility is the development of ciphering processors -- little ciphering computers -- in secure packaging. Limited control over the processor might allow a public-key authenticated software update, while otherwise looking like hardware. But probably most users will not care until some hidden software system is exposed on some computers.

There are a whole range of things which can distinguish one cipher from another. But perhaps the easiest and most useful distinction is that between stream ciphers and block ciphers. A block cipher requires that a full block of data be collected before ciphering can begin; a stream cipher can cipher individual units (perhaps bits or bytes) as they occur. As a consequence, if it ever becomes necessary to cipher individual bits or bytes in a block cipher, it will be necessary to fill the rest of the block with padding before ciphering.

Logically, a conventional block cipher (other than a
transposition cipher) is just
simple substitution: A
block of
plaintext
data is collected and then
substituted into an arbitrary
ciphertext value.
So a toy version of a block cipher is just a
table look-up, much
like the amusement ciphers in newspapers.
Of course, a realistic block cipher has a block width which is far
too large to hold the transformation in any physical table. Because
of the large block size, the invertible transformation must be
*simulated,* in some way dynamically *constructed* for each
block
enciphered.

In a conventional block cipher, any possible
permutation of "table"
values is a potential
key. So if we have a
64-bit block, there would
theoretically be 2^{64}
factorial possible keys,
which is a huge, huge value. But the well-known 64-bit block cipher
DES has "only" 2^{56} keys,
which is as nothing in comparison. In part, this is because any
real mechanism can only *emulate* the theoretical ideal of a
huge simple substitution. But mostly, 56-bit keys have in the past
been thought to be "large enough." Now we expect at least 128 bits,
or perhaps somewhat more.

If a block cipher is a *huge*
simple substitution,
a stream cipher can be a *small* substitution which is in some
way *altered* for each
bit or
byte enciphered. Clearly,
repeatedly using a small unchanging substitution (or even a
linear transformation) is not
going to be secure in a situation where the
opponent will have a
substantial quantity of
known plaintext.
One way to use a small transformation securely is to use a simple
additive combiner to
mix data with a
really random
confusion sequence;
done properly, this is the supposedly "unbreakable"
one time pad.

[ In practice, a one time pad is in fact at least potentially
breakable.
All that is necessary to break a one time pad is to
predict the random sequence.
Predicting future values in a sequence *can* be tough, but the
issue is whether we really *know* that prediction *must*
be tough, or just choose to have that
belief.
It is easy to wave hands and say: "That's unpredictable," but
actually *producing* a
provably unpredictable
sequence requires far more than mere handwaves. ]

Logically, a stream cipher can be seen as the general concept of repeatedly using a block transformation to handle more than one block of data. I would say that even the simple repeated use of a block cipher in ECB mode would be "streaming" the cipher. And use in more complex chaining modes like CBC are even more clearly stream meta-ciphers which use block transformations.

One common idea that comes up again and again with novice
cryptographers
is to take a textual key phrase, and then add (or
exclusive-OR) the key
with the data, byte-by-byte, starting the key over each time it
is exhausted. This is a very simple and weak stream cipher,
with a short and repeatedly-used
running key and an
additive combiner.
I suppose that part of the problem in seeing this weakness is in
distinguishing between different types of stream cipher "key":
In a real stream cipher, even a single bit change in a key phrase
would be expected to produce a *different* running key
sequence, a sequence which would not repeat across a message of
any practical size. In the weak version, a single bit change in
the short running key would affect only one bit each time it was
used, and would do so repeatedly, as the keying sequence was
re-used over and over again. In any additive stream cipher, the
re-use of a keying sequence is absolutely deadly. And a real
stream cipher would almost certainly use a random
message key as the key
which actually protects data.

Public key ciphers are generally block ciphers, with the unusual property that one key is used to encipher, and a different, apparently unrelated key is used to decipher a message. So if we keep one of the keys private, we can release the other key (the "public" key), and anyone can use that to encipher a message to us. Then we use our private key to decipher any such messages. It is interesting that someone who enciphers a message to us cannot decipher their own message even if they want to.

The prototypical public key cipher is RSA, which uses the arithmetic of huge numeric values. These values may contain 1,000 bits or more (over 400 decimal digits), in which each and every bit is significant. The keyspace is much smaller, however, because there are very severe constraints on the keys; not just any random value will do. So a 1,000-bit public key may have a brute-force strength similar to a 128-bit secret key cipher.

Because public key ciphers operate on huge values, they are very slow, and so are normally used just to encipher a random message key. The message key is then used by a conventional secret key cipher which actually enciphers the data.

At first glance, public key ciphers apparently solve the
key distribution
problem. But in fact they also open up the new possibility of a
man-in-the-middle
attack. To avoid this, it is necessary to assure that one is
using exactly the correct key for the desired user. This requires
authentication
(validation or certification) via some sort of secure channel,
and that can take as much effort as a secure secret key exchange.
A man-in-the-middle attack is extremely worrisome, because it
does *not* involve
breaking any cipher, which
means that all the effort spent in cipher design and analysis and
mathematical proofs and public review would be completely
irrelevant.

The most important book in cryptography is:

by David Kahn (Macmillan, 1967).**The Codebreakers**,

*The Codebreakers* is the detailed *history* of
cryptography, a book of style and adventure. It is non-mathematical
and generally non-technical. But the author does explain why simple
ciphers fail to hide information; these are the same problems
addressed by increasingly capable cryptosystems. Various accounts
show how real cryptography is far more than just schemes for
enciphering data. A very good read.

Other important books include

by Friedrich Bauer (Springer-Verlag, 1997).**Decrypted Secrets**,-
In some ways

*Decrypted Secrets*continues in the style of*The Codebreakers,*but is far more technical. Almost half the book concerns cryptanalysis or ways to attack WWII ciphers.by Menezes, van Oorschot and Vanstone (CRC Press, 1997).**Handbook of Applied Cryptography**,-
The

*Handbook of Applied Cryptography*seems to be the best technical reference so far. While some sections do raise the hackles of your reviewer, this happens far less than with other comprehensive references.by William Stallings (2nd ed., Prentice Hall, 1998).**Cryptography and Network Security: Principles and Practice**,*Cryptography and Network Security*is an introductory text and a reference for actual implementations. It covers both conventional and public-key cryptography (including authentication). It also covers web security, as in Kerberos, PGP, S/MIME, and SSL. It covers real ciphers*and*real systems using ciphers.edited by Gustavus Simmons (IEEE Press, 1992).**Contemporary Cryptology**,*Contemporary Cryptology,*is a substantial survey of mostly mathematical cryptology, although the US encryption standard DES is also covered. It describes the state of the art at that time.by Peter Wright (Viking Penguin, 1987).**Spy Catcher**,*Spy Catcher*places the technology in the context of reality. While having little on cryptography*per se,*it has a lot on*security,*on which cryptography is necessarily based. Also a good read.by James Bamford (Houghton Mifflin, 1982).**The Puzzle Palace**,*The Puzzle Palace*is the best description we have of the National Security Agency (NSA), which has been the dominant force in cryptography in the US since WWII.

Good books on "The Vietnam War" (and which have nothing to do with cryptography) include:

by Neil Sheehan (Random House, 1988),**A Bright Shining Lie**,by Colonel David H. Hackworth (Simon & Schuster, 1989), and**About Face**,by Sam Adams (Steerforth Press, South Royalton, Vermont, 1994).**War of Numbers**,

Normally,
cryptanalysis
is thought of as the way
ciphers are
broken. But cryptanalysis
is really *analysis* -- the ways we come to understand a cipher
in detail. Since most ciphers have weaknesses, a deep understanding
can expose the best attacks for a particular cipher.

Two books often mentioned as introductions to classical cryptanalysis are:

by Helen Gaines (1939, but still available from Dover Publications), and**Cryptanalysis**by Abraham Sinkov (1966, but still available from The Mathematical Association of America).**Elementary Cryptanalysis**

**The Caesar Cipher**replaces each plaintext letter with the letter*n*(originally 3) places farther along in the normal alphabet. Classically, the only possible key is the value for*n,*but in a computer environment, it is easy to be general: We can select*n*for each position in the message by using a random number generator (this could be a stream cipher), and also key the alphabet by shuffling it into a unique ordering (which is Monoalphabetic Substitution).**Monoalphabetic Substitution**replaces each plaintext letter with an associated letter from a (keyed)*random alphabet.*Classically, it was tough to specify an arbitrary order for the alphabet, so this was often based on understandable keywords (skipping repeated letters), which helped make the cipher easier to crack. But in the modern computer version, it is easy to select among the set of*all possible*permutations by shuffling the alphabet with a keyed random number generator.Another problem with monoalphabetic substitution is that the most frequently used letters in the plaintext become the most frequently used letters in the ciphertext, and statistical techniques can be used to help identify which letters are which. Classically, multiple different alphabets (Polyalphabetic Substitution) or multiple ciphertext letters for a single plaintext letter (Homophonic Substitution) were introduced to avoid this. But in a modern computer version, we can continue to permute the single alphabet, as in Dynamic Substitution (see my article). Moreover, if the original "plaintext" is evenly distributed (which can be assured by a previous combining), then statistical techniques are little help.

**Polyalphabetic Substitution**replaces each plaintext letter with an associated letter from one of multiple "random" alphabets. But, classically, it was tough to produce arbitrary alphabets, so the "multiple alphabets" tended to be different offset values as in Caesar ciphers. Moreover, it was tough even to choose alphabets at random, so they tended to be used in rotating sequence, which gave the cryptanalyst enormous encouragement. On the other hand, a modern improved version of polyalphabetic substitution, with a special keyed Latin square combiner, with each "alphabet" selected character-by-character by a keyed random number generator, can be part of a very serious cipher.**Transposition Ciphers**re-arrange the plaintext letters to form ciphertext. But, classically, it was tough to form an arbitrary re-arrangement (or*permutation*), so the re-ordering tended to occur in particular graphic patterns (along columns instead of rows, across diagonals, etc.). Normally, two messages of the same size would be transposed similarly, leading to a "multiple anagramming" attack: Two equal-size messages were permuted in the same way until they both "made sense." But, in the modern general form, a keyed random number generator can shuffle blocks of arbitrary size in a general way, almost never permute two blocks similarly, and work on a randomized content which may not make sense, making the classical attack useless (see my article).

Thus, it was often the restrictions on the general
design -- necessary for "pen and paper" practicality -- which
made these classical ciphers easy to attack. And the attacks
which work well on specific classical versions may have very
little chance on a modern very-general version of *the same
cipher.*

Other books on cryptanalysis:

by Solomon Kullback (Laguna Hills, CA: Aegean Park Press, 1976 ; original publication 1938),**Statistical Methods in Cryptanalysis**,-
Basically a statistics text oriented toward statistics
useful in cryptanalysis.

by William Bennett, Jr. (Prentice-Hall, 1976), Chapter 4, Language, and**Scientific and Engineering Problem-Solving with the Computer**,-
Basically an introduction to programming in Basic, the
text encounters a number of real world problems, one of
which is language and cryptanalysis.

by T. W. Korner (Cambridge, 1996).**The Pleasures of Counting**,-
An introduction to real mathematics for high-school (!)
potential prodigies, the text contains two or three chapters
on Enigma and solving Enigma.

A perhaps overly famous book for someone programming existing ciphers or selecting protocols is:

by Bruce Schneier (John Wiley & Sons, 1996).**Applied Cryptography**

Some other books I like include:

by Deavours, Kahn, Kruh, Mellen and Winkel (Artech House, 1987),**Cryptology Yesterday, Today, and Tomorrow**,by Beker and Piper (Wiley, 1982),**Cipher Systems**,by Meyer and Matyas (Wiley, 1982),**Cryptography**,by Beker and Piper (Academic Press, 1985),**Secure Speech Communications**,by Davies and Price (Wiley, 1984),**Security for Computer Networks**,**Network Security,****by Kaufman, Perlman and Speciner**(Prentice-Hall, 1995),by Pfleeger (Prentice-Hall, 1989), and**Security in Computing**,by Peter Wayner (Academic Press, 1996).**Disappearing Cryptography**,

Although most authors recommend a background in Number Theory, I recommend some background in Coding Theory:

by Golomb (Aegean Park Press, 1982),**Shift Register Sequences**,by Arazi (MIT Press, 1988),**A Commonsense Approach to the Theory of Error Correcting Codes**,by Hamming (Prentice-Hall, 1980),**Coding and Information Theory**,by Peterson and Weldon (MIT Press, 1972),**Error-Correcting Codes**,by Clark and Cain (Plenum Press, 1981),**Error-Correction Coding for Digital Communications**,by Blahut (Addison-Wesley, 1983),**Theory and Practice of Error Control Codes**,by Lin and Costello (Prentice-Hall, 1983), and**Error Control Coding**,by Aho, Hopcroft and Ullman (Addison-Wesley, 1974).**The Design and Analysis of Computer Algorithms**,

Those who would *design* ciphers would do well to follow
the few systems whose rise and fall are documented in the open
literature.
Ciarcia [1] and Pearson [5] are an excellent example of how
tricky the field is; first study Ciarcia (a real circuit design),
and only then read Pearson (how the design is broken). Geffe [2]
and Siegenthaler [8] provide a more technical lesson.
Retter [6,7] shows that the MacLaren-Marsaglia randomizer is not
cryptographically secure, and Kochanski [3,4] cracks some common
PC cipher programs.

- Ciarcia, S. 1986. Build a Hardware Data Encryptor.
*Byte.*September. 97-111. - Geffe, P. 1973. How to protect data with ciphers that are
really hard to break.
*Electronics.*January 4. 99-101. - Kochanski, M. 1987. A Survey of Data Insecurity Packages.
*Cryptologia.*11(1): 1-15. - Kochanski, M. 1988. Another Data Insecurity Package.
*Cryptologia.*12(3): 165-173. - Pearson, P. 1988. Cryptanalysis of the Ciarcia Circuit Cellar
Data Encryptor.
*Cryptologia.*12(1): 1-9. - Retter, C. 1984. Cryptanalysis of a MacLaren-Marsaglia System.
*Cryptologia.*8: 97-108. (Also see letters and responses:*Cryptologia.*8: 374-378). - Retter, C. 1985. A Key Search Attack on MacLaren-Marsaglia
Systems.
*Cryptologia.*9: 114-130. - Siegenthaler, T. 1985. Decrypting a Class of Stream Ciphers
Using Ciphertext Only.
*IEEE Transactions on Computers.*C-34: 81-85.