Archive-name: cryptography-faq/part03
This is the third of ten parts of the sci.crypt FAQ. The parts are
mostly independent, but you should read the first part before the rest.
We don't have the time to send out missing parts by mail, so don't ask.
Notes such as ``[KAH67]'' refer to the reference list in the last part.
Contents:
3.1. What is cryptology? Cryptography? Plaintext? Ciphertext? Encryption? Key?
3.2. What references can I start with to learn cryptology?
3.3. How does one go about cryptanalysis?
3.4. What is a brute-force search and what is its cryptographic relevance?
3.5. What are some properties satisfied by every strong cryptosystem?
3.6. If a cryptosystem is theoretically unbreakable, then is it
guaranteed analysis-proof in practice?
3.7. Why are many people still using cryptosystems that are
relatively easy to break?
3.1. What is cryptology? Cryptography? Plaintext? Ciphertext? Encryption? Key?
The story begins: When Julius Caesar sent messages to his trusted
acquaintances, he didn't trust the messengers. So he replaced every A
by a D, every B by a E, and so on through the alphabet. Only someone
who knew the ``shift by 3'' rule could decipher his messages.
A cryptosystem or cipher system is a method of disguising messages so
that only certain people can see through the disguise. Cryptography is
the art of creating and using cryptosystems. Cryptanalysis is the art
of breaking cryptosystems---seeing through the disguise even when
you're not supposed to be able to. Cryptology is the study of both
cryptography and cryptanalysis.
The original message is called a plaintext. The disguised message is
called a ciphertext. Encryption means any procedure to convert
plaintext into ciphertext. Decryption means any procedure to convert
ciphertext into plaintext.
A cryptosystem is usually a whole collection of algorithms. The
algorithms are labelled; the labels are called keys. For instance,
Caesar probably used ``shift by n'' encryption for several different
values of n. It's natural to say that n is the key here.
The people who are supposed to be able to see through the disguise are
called recipients. Other people are enemies, opponents, interlopers,
eavesdroppers, or third parties.
3.2. What references can I start with to learn cryptology?
For an introduction to technical matter, the survey articles given
in part 10 are the best place to begin as they are, in general,
concise, authored by competent people, and well written. However,
these articles are mostly concerned with cryptology as it has
developed in the last 50 years or so, and are more abstract and
mathematical than historical. The Codebreakers by Kahn [KAH67] is
encyclopedic in its history and technical detail of cryptology up
to the mid-60's.
Introductory cryptanalysis can be learned from Gaines [GAI44] or
Sinkov [SIN66]. This is recommended especially for people who want
to devise their own encryption algorithms since it is a common
mistake to try to make a system before knowing how to break one.
The selection of an algorithm for the DES drew the attention of
many public researchers to problems in cryptology. Consequently
several textbooks and books to serve as texts have appeared. The
book of Denning [DEN82] gives a good introduction to a broad range
of security including encryption algorithms, database security,
access control, and formal models of security. Similar comments
apply to the books of Price & Davies [PRI84] and Pfleeger [PFL89].
The books of Konheim [KON81] and Meyer & Matyas [MEY82] are quite
technical books. Both Konheim and Meyer were directly involved in
the development of DES, and both books give a thorough analysis of
DES. Konheim's book is quite mathematical, with detailed analyses
of many classical cryptosystems. Meyer and Matyas concentrate on
modern cryptographic methods, especially pertaining to key management
and the integration of security facilities into computer systems and
networks.
The books of Rueppel [RUE86] and Koblitz [KOB89] concentrate on
the application of number theory and algebra to cryptography.
3.3. How does one go about cryptanalysis?
Classical cryptanalysis involves an interesting combination of
analytical reasoning, application of mathematical tools, pattern
finding, patience, determination, and luck. The best available
textbooks on the subject are the Military Cryptanalytics series
[FRIE1]. It is clear that proficiency in cryptanalysis is, for
the most part, gained through the attempted solution of given
systems. Such experience is considered so valuable that some of the
cryptanalyses performed during WWII by the Allies are still
classified.
Modern public-key cryptanalysis may consist of factoring an integer,
or taking a discrete logarithm. These are not the traditional fare
of the cryptanalyst. Computational number theorists are some of the
most successful cryptanalysts against public key systems.
3.4. What is a brute-force search and what is its cryptographic relevance?
In a nutshell: If f(x) = y and you know y and can compute f, you can
find x by trying every possible x. That's brute-force search.
Example: Say a cryptanalyst has found a plaintext and a corresponding
ciphertext, but doesn't know the key. He can simply try encrypting the
plaintext using each possible key, until the ciphertext matches---or
decrypting the ciphertext to match the plaintext, whichever is faster.
Every well-designed cryptosystem has such a large key space that this
brute-force search is impractical.
Advances in technology sometimes change what is considered
practical. For example, DES, which has been in use for over 10 years
now, has 2^56, or about 10^17, possible keys. A computation with
this many operations was certainly unlikely for most users in the
mid-70's. The situation is very different today given the dramatic
decrease in cost per processor operation. Massively parallel
machines threaten the security of DES against brute force search.
Some scenarios are described by Garron and Outerbridge [GAR91].
One phase of a more sophisticated cryptanalysis may involve a
brute-force search of some manageably small space of possibilities.
3.5. What are some properties satisfied by every strong cryptosystem?
The security of a strong system resides with the secrecy of the key
rather than with the supposed secrecy of the algorithm.
A strong cryptosystem has a large keyspace, as mentioned above. It
has a reasonably large unicity distance; see question 8.8.
A strong cryptosystem will certainly produce ciphertext which appears
random to all standard statistical tests (see, for example, [CAE90]).
A strong cryptosystem will resist all known previous attacks. A
system which has never been subjected to scrutiny is suspect.
If a system passes all the tests mentioned above, is it necessarily
strong? Certainly not. Many weak cryptosystems looked good at first.
However, sometimes it is possible to show that a cryptosystem is
strong by mathematical proof. ``If Joe can break this system, then
he can also solve the well-known difficult problem of factoring
integers.'' See part 6. Failing that, it's a crap shoot.
3.6. If a cryptosystem is theoretically unbreakable, then is it
guaranteed analysis-proof in practice?
Cryptanalytic methods include what is known as ``practical
cryptanalysis'': the enemy doesn't have to just stare at your
ciphertext until he figures out the plaintext. For instance, he might
assume ``cribs''---stretches of probable plaintext. If the crib is
correct then he might be able to deduce the key and then decipher the
rest of the message. Or he might exploit ``isologs''---the same
plaintext enciphered in several cryptosystems or several keys. Thus
he might obtain solutions even when cryptanalytic theory says he
doesn't have a chance.
Sometimes, cryptosystems malfunction or are misused. The one-time pad,
for example, loses all security if it is used more than once! Even
chosen-plaintext attacks, where the enemy somehow feeds plaintext into
the encryptor until he can deduce the key, have been employed. See
[KAH67].
3.7. Why are many people still using cryptosystems that are
relatively easy to break?
Some don't know any better. Often amateurs think they can design
secure systems, and are not aware of what an expert cryptanalyst
could do. And sometimes there is insufficient motivation for anybody
to invest the work needed to crack a system.