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Subject: Cryptography FAQ (08/10: Technical Miscellany)
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Date: 13 Dec 1995 16:29:58 GMT
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Archive-name: cryptography-faq/part08
Last-modified: 94/01/25
This is the eighth 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.
The sections of this FAQ are available via anonymous FTP to rtfm.mit.edu
as /pub/usenet/news.answers/cryptography-faq/part[xx]. The Cryptography
FAQ is posted to the newsgroups sci.crypt, talk.politics.crypto,
sci.answers, and news.answers every 21 days.
Contents
8.1. How do I recover from lost passwords in WordPerfect?
8.2. How do I break a Vigenere (repeated-key) cipher?
8.3. How do I send encrypted mail under UNIX? [PGP, RIPEM, PEM, ...]
8.4. Is the UNIX crypt command secure?
8.5. How do I use compression with encryption?
8.6. Is there an unbreakable cipher?
8.7. What does ``random'' mean in cryptography?
8.8. What is the unicity point (a.k.a. unicity distance)?
8.9. What is key management and why is it important?
8.10. Can I use pseudo-random or chaotic numbers as a key stream?
8.11. What is the correct frequency list for English letters?
8.12. What is the Enigma?
8.13. How do I shuffle cards?
8.14. Can I foil S/W pirates by encrypting my CD-ROM?
8.15. Can you do automatic cryptanalysis of simple ciphers?
8.16. What is the coding system used by VCR+?
8.1. How do I recover from lost passwords in WordPerfect?
WordPerfect encryption has been shown to be very easy to break.
The method uses XOR with two repeating key streams: a typed password
and a byte-wide counter initialized to 1+. Full
descriptions are given in Bennett [BEN87] and Bergen and Caelli
[BER91].
Chris Galas writes: ``Someone awhile back was looking for a way to
decrypt WordPerfect document files and I think I have a solution.
There is a software company named: Accessdata (87 East 600 South,
Orem, UT 84058), 1-800-658-5199 that has a software package that will
decrypt any WordPerfect, Lotus 1-2-3, Quatro-Pro, MS Excel and Paradox
files. The cost of the package is $185. Steep prices, but if you
think your pw key is less than 10 characters, (or 10 char) give them a
call and ask for the free demo disk. The demo disk will decrypt files
that have a 10 char or less pw key.'' Bruce Schneier says the phone
number for AccessData is 801-224-6970.
8.2. How do I break a Vigenere (repeated-key) cipher?
A repeated-key cipher, where the ciphertext is something like the
plaintext xor KEYKEYKEYKEY (and so on), is called a Vigenere cipher.
If the key is not too long and the plaintext is in English, do the
following:
1. Discover the length of the key by counting coincidences.
(See Gaines [GAI44], Sinkov [SIN66].) Trying each displacement of
the ciphertext against itself, count those bytes which are equal.
If the two ciphertext portions have used the same key, something
over 6% of the bytes will be equal. If they have used different
keys, then less than 0.4% will be equal (assuming random 8-bit bytes
of key covering normal ASCII text). The smallest displacement which
indicates an equal key is the length of the repeated key.
2. Shift the text by that length and XOR it with itself. This
removes the key and leaves you with text XORed with itself. Since
English has about 1 bit of real information per byte, 2 streams of
text XORed together has 2 bits of info per 8-bit byte, providing
plenty of redundancy for choosing a unique decryption. (And in fact
one stream of text XORed with itself has just 1 bit per byte.)
If the key is short, it might be even easier to treat this as a
standard polyalphabetic substitution. All the old cryptanalysis
texts show how to break those. It's possible with those methods, in
the hands of an expert, if there's only ten times as much text as key.
See, for example, Gaines [GAI44], Sinkov [SIN66].
8.3. How do I send encrypted mail under UNIX? [PGP, RIPEM, PEM, ...]
Here's one popular method, using the des command:
cat file | compress | des private_key | uuencode | mail
Meanwhile, there is a de jure Internet standard in the works called
PEM (Privacy Enhanced Mail). It is described in RFCs 1421 through
1424. To join the PEM mailing list, contact pem-dev-request@tis.com.
There is a beta version of PEM being tested at the time of this
writing.
There are also two programs available in the public domain for encrypting
mail: PGP and RIPEM. Both are available by FTP. Each has its own
newsgroup: alt.security.pgp and alt.security.ripem. Each has its own FAQ
as well.
PGP is most commonly used outside the USA since it uses the RSA algorithm
without a license and RSA's patent is valid only (or at least primarily)
in the USA.
RIPEM is most commonly used inside the USA since it uses the RSAREF which
is freely available within the USA but not available for shipment outside
the USA.
Since both programs use a secret key algorithm for encrypting the body of
the message (PGP used IDEA; RIPEM uses DES) and RSA for encrypting the
message key, they should be able to interoperate freely. Although there
have been repeated calls for each to understand the other's formats and
algorithm choices, no interoperation is available at this time (as far as
we know).
8.4. Is the UNIX crypt command secure?
No. See [REE84]. There is a program available called cbw (crypt
breaker's workbench) which can be used to do ciphertext-only attacks
on files encrypted with crypt. One source for CBW is [FTPCB].
8.5. How do I use compression with encryption?
A number of people have proposed doing perfect compression followed by
some simple encryption method (e.g., XOR with a repeated key). This
would work, if you could do perfect compression. Unfortunately, you can
only compress perfectly if you know the exact distribution of possible
inputs, and that is almost certainly not possible.
Compression aids encryption by reducing the redundancy of the plaintext.
This increases the amount of ciphertext you can send encrypted under a
given number of key bits. (See "unicity distance")
Nearly all practical compression schemes, unless they have been designed
with cryptography in mind, produce output that actually starts off with
high redundancy. For example, the output of UNIX compress begins with a
well-known three-byte ``magic number''. This produces a field of "known
plaintext" which can be used for some forms of cryptanalytic attack.
Compression is generally of value, however, because it removes other
known plaintext in the middle of the file being encrypted. In general,
the lower the redundancy of the plaintext being fed an encryption
algorithm, the more difficult the cryptanalysis of that algorithm.
In addition, compression shortens the input file, shortening the output
file and reducing the amount of CPU required to do the encryption
algorithm, so even if there were no enhancement of security, compression
before encryption would be worthwhile.
Compression after encryption is silly. If an encryption algorithm is
good, it will produce output which is statistically indistinguishable
from random numbers and no compression algorithm will successfully
compress random numbers. On the other hand, if a compression algorithm
succeeds in finding a pattern to compress out of an encryption's output,
then a flaw in that algorithm has been found.
8.6. Is there an unbreakable cipher?
Yes. The one-time pad is unbreakable; see part 4. Unfortunately the
one-time pad requires secure distribution of as much key material as
plaintext.
Of course, a cryptosystem need not be utterly unbreakable to be
useful. Rather, it needs to be strong enough to resist attacks by
likely enemies for whatever length of time the data it protects is
expected to remain valid.
8.7. What does ``random'' mean in cryptography?
Cryptographic applications demand much more out of a pseudorandom
number generator than most applications. For a source of bits to be
cryptographically random, it must be computationally impossible to
predict what the Nth random bit will be given complete knowledge of
the algorithm or hardware generating the stream and the sequence of
0th through N-1st bits, for all N up to the lifetime of the source.
A software generator (also known as pseudo-random) has the function
of expanding a truly random seed to a longer string of apparently
random bits. This seed must be large enough not to be guessed by
the opponent. Ideally, it should also be truly random (perhaps
generated by a hardware random number source).
Those who have Sparcstation 1 workstations could, for example,
generate random numbers using the audio input device as a source of
entropy, by not connecting anything to it. For example,
cat /dev/audio | compress - >foo
gives a file of high entropy (not random but with much randomness in
it). One can then encrypt that file using part of itself as a key,
for example, to convert that seed entropy into a pseudo-random
string.
When looking for hardware devices to provide this entropy, it is
important really to measure the entropy rather than just assume that
because it looks complicated to a human, it must be "random". For
example, disk operation completion times sound like they might be
unpredictable (to many people) but a spinning disk is much like a
clock and its output completion times are relatively low in entropy.
8.8. What is the unicity point (a.k.a. unicity distance)?
See [SHA49]. The unicity distance is an approximation to that amount
of ciphertext such that the sum of the real information (entropy) in
the corresponding source text and encryption key equals the number
of ciphertext bits used. Ciphertexts significantly longer than this
can be shown probably to have a unique decipherment. This is used to
back up a claim of the validity of a ciphertext-only cryptanalysis.
Ciphertexts significantly shorter than this are likely to have
multiple, equally valid decryptions and therefore to gain security
from the opponent's difficulty choosing the correct one.
Unicity distance, like all statistical or information-theoretic
measures, does not make deterministic predictions but rather gives
probabilistic results: namely, the minimum amount of ciphertext
for which it is likely that there is only a single intelligible
plaintext corresponding to the ciphertext, when all possible keys
are tried for the decryption. Working cryptologists don't normally
deal with unicity distance as such. Instead they directly determine
the likelihood of events of interest.
Let the unicity distance of a cipher be D characters. If fewer than
D ciphertext characters have been intercepted, then there is not
enough information to distinguish the real key from a set of
possible keys. DES has a unicity distance of 17.5 characters,
which is less than 3 ciphertext blocks (each block corresponds to
8 ASCII characters). This may seem alarmingly low at first, but
the unicity distance gives no indication of the computational work
required to find the key after approximately D characters have been
intercepted.
In fact, actual cryptanalysis seldom proceeds along the lines used
in discussing unicity distance. (Like other measures such as key
size, unicity distance is something that guarantees insecurity if
it's too small, but doesn't guarantee security if it's high.) Few
practical cryptosystems are absolutely impervious to analysis; all
manner of characteristics might serve as entering ``wedges'' to crack
some cipher messages. However, similar information-theoretic
considerations are occasionally useful, for example, to determine a
recommended key change interval for a particular cryptosystem.
Cryptanalysts also employ a variety of statistical and
information-theoretic tests to help guide the analysis in the most
promising directions.
Unfortunately, most literature on the application of information
statistics to cryptanalysis remains classified, even the seminal
1940 work of Alan Turing (see [KOZ84]). For some insight into the
possibilities, see [KUL68] and [GOO83].
8.9. What is key management and why is it important?
One of the fundamental axioms of cryptography is that the enemy is in
full possession of the details of the general cryptographic system,
and lacks only the specific key data employed in the encryption. (Of
course, one would assume that the CIA does not make a habit of telling
Mossad about its cryptosystems, but Mossad probably finds out anyway.)
Repeated use of a finite amount of key provides redundancy that can
eventually facilitate cryptanalytic progress. Thus, especially in
modern communication systems where vast amounts of information are
transferred, both parties must have not only a sound cryptosystem but
also enough key material to cover the traffic.
Key management refers to the distribution, authentication, and
handling of keys.
A publicly accessible example of modern key management technology
is the STU III secure telephone unit, which for classified use
employs individual coded ``Crypto Ignition Keys'' and a central Key
Management Center operated by NSA. There is a hierarchy in that
certain CIKs are used by authorized cryptographic control
personnel to validate the issuance of individual traffic keys and
to perform installation/maintenance functions, such as the
reporting of lost CIKs.
This should give an inkling of the extent of the key management
problem. For public-key systems, there are several related issues,
many having to do with ``whom do you trust?''
8.10. Can I use pseudo-random or chaotic numbers as a key stream?
Chaotic equations and fractals produce an apparent randomness from
relatively compact generators. Perhaps the simplest example is a
linear congruential sequence, one of the most popular types of random
number generators, where there is no obvious dependence between seeds
and outputs. Unfortunately the graph of any such sequence will, in a
high enough dimension, show up as a regular lattice. Mathematically
this lattice corresponds to structure which is notoriously easy for
cryptanalysts to exploit. More complicated generators have more
complicated structure, which is why they make interesting pictures---
but a cryptographically strong sequence will have no computable
structure at all.
See [KNU81], exercise 3.5-7; [REE77]; and [BOY89].
8.11. What is the correct frequency list for English letters?
There are three answers to this question, each slightly deeper than
the one before. You can find the first answer in various books:
namely, a frequency list computed directly from a certain sample of
English text.
The second answer is that ``the English language'' varies from author
to author and has changed over time, so there is no definitive list.
Of course the lists in the books are ``correctly'' computed, but
they're all different: exactly which list you get depends on which
sample was taken. Any particular message will have different
statistics from those of the language as a whole.
The third answer is that yes, no particular message is going to have
exactly the same characteristics as English in general, but for all
reasonable statistical uses these slight discrepancies won't matter.
In fact there's an entire field called ``Bayesian statistics'' (other
buzzwords are ``maximum entropy methods'' and ``maximum likelihood
estimation'') which studies questions like ``What's the chance that a
text with these letter frequencies is in English?'' and comes up with
reasonably robust answers.
So make your own list from your own samples of English text. It will
be good enough for practical work, if you use it properly.
8.12. What is the Enigma?
``For a project in data security we are looking for sources of
information about the German Enigma code and how it was broken by
the British during WWII.''
See [WEL82], [DEA85], [KOZ84], [HOD83], [KAH91].
8.13. How do I shuffle cards?
Card shuffling is a special case of the permutation of an array of
values, using a random or pseudo-random function. All possible output
permutations of this process should be equally likely. To do this, you
need a random function (modran(x)) which will produce a uniformly
distributed random integer in the interval [0..x-1]. Given that
function, you can shuffle with the following [C] code: (assuming ARRLTH
is the length of array arr[] and swap() interchanges values at the two
addresses given)
for ( n = ARRLTH-1; n > 0 ; n-- ) swap( &arr[modran( n+1 )], &arr[n] ) ;
modran(x) can not be achieved exactly with a simple (ranno() % x) since
ranno()'s interval may not be divisible by x, although in most cases the
error will be very small. To cover this case, one can take ranno()'s
modulus mod x, call that number y, and if ranno() returns a value less
than y, go back and get another ranno() value.
See [KNU81] for further discussion.
8.14. Can I foil S/W pirates by encrypting my CD-ROM?
Someone will frequently express the desire to publish a CD-ROM with
possibly multiple pieces of software, perhaps with each encrypted
separately, and will want to use different keys for each user (perhaps
even good for only a limited period of time) in order to avoid piracy.
As far as we know, this is impossible, since there is nothing in standard
PC or workstation hardware which uniquely identifies the user at the
keyboard. If there were such an identification, then the CD-ROM could be
encrypted with a key based in part on the one sold to the user and in
part on the unique identifier. However, in this case the CD-ROM is one
of a kind and that defeats the intended purpose.
If the CD-ROM is to be encrypted once and then mass produced, there must
be a key (or set of keys) for that encryption produced at some stage in
the process. That key is useable with any copy of the CD-ROM's data.
The pirate needs only to isolate that key and sell it along with the
illegal copy.
8.15. Can you do automatic cryptanalysis of simple ciphers?
Certainly. For commercial products you can try AccessData; see
question 8.1. We are not aware of any FTP sites for such software,
but there are many papers on the subject. See [PEL79], [LUC88],
[CAR86], [CAR87], [KOC87], [KOC88], [KIN92], [KIN93], [SPI93].
8.16. What is the coding system used by VCR+?
One very frequently asked question in sci.crypt is how the VCR+ codes
work. The codes are used to program a VCR based on numerical input.
See [SHI92] for an attempt to describe it.