thesis.txt

DIAMOND2加密算法的原代码

the same system & key, (6) compromised keys, (7) as much computational 
and analytical power as can be obtained, and (8) mistakes made in 
the users of the cryptographic system.  The cryptographer can make 
life as difficult as possible for the cryptanalyst by depriving him 
of some of these things by (1) using redundancy reduction before encryption, 
(2) using an algorithm that is resistant to the known plain text attack, 
(3) & (4) using a strong enough algorithm that these clues aren't 
really useful, (5) changing keys often and selecting them properly, 
(6) guarding keys as closely as the data they protect justifies, (7) 
ensuring that there aren't enough computers in the world to do a brute 
force attack on the algorithm, and (8) making sure users of the system 
understand how to properly use it.

This thesis proposes one solution to the above challenge by proposing 
(1) an approach to linguistically based redundancy reduction, and 
(2) proposing a new data encryption algorithm (MPJ) that can be used 
where DES is in use now, but is more secure.

A.  Motivation

There has been a great deal of discussion of the security of DES in 
the open literature.  Most of it has been favorable to DES [MEY], 
but there are a few indications that it would be wise to supplement 
the aging DES and eventually replace it.

DES has been in use since 1977, and has been used in a large number 
of applications where people have had many possible motivations for 
trying to break this cipher.  During this time, it is possible that 
someone has discovered a computationally feasible method for doing 
so [KRU].  Under such circumstances, it is highly unlikely that such 
a discovery would be made known.  There is no way to really know this 
for sure, unless you are one of the ones who has broken DES.  The 
closest thing that I have found to an open admission of breaking DES 
is a story of the FBI successfully decrypting a file of drug transaction 
records that were encrypted on a PC using a DES board. [MCL] The DES 
board that the criminal used has an algorithm to generate a key from 
a word or phrase.  By an exhaustive search of an English dictionary 
and key names from the criminal's family & friends using a supercomputer, 
the file was solved.  This indicates some weakness in DES, but even 
more weakness in the way the key was chosen. The key was not chosen 
randomly, so the FBI's job was much easier.

DES is subject to attacks that require precomputation that could tie 
up a supercomputer for a few years, after which it would take only 
a few days to solve a DES cryptogram.  This is becoming less of a 
barrier as the price of computers drops and the speed and storage 
capacity of computers increase.

The U. S. National Security Agency (NSA) is acting to release some  of  its 
own algorithms for ``sensitive but unclassified'' applications, such 
as communications between government contractors.  The NSA also releases 
some classified algorithms to chip manufacturers for use in classified 
devices, but under strict controls [ULT].  This will take some of 
the load off of the DES algorithm, but there is a catch.  They intend 
to keep the algorithms secret and control the keys.  Since the security 
of the algorithm is dependent on the key in a way that only  the NSA  knows, 
this gives the NSA the exclusive ability to read everybody's' communications.  That 
is not all bad, as it discourages the use of one of those systems 
by someone engaged in spying or other illegal activity.  Unfortunately, 
these systems are not an option for protection of a corporations proprietary 
data that may have a great deal to do  with profits and  losses, but 
are not really in the domain of the NSA.

There are other alternatives to DES now, but none of them in the public 
domain are even as good, let alone better, for general cryptography.  For 
example, RSA encryption has great advantages in the authentication 
of digital signatures, but the complications of selecting good keys 
and the fact that the security of RSA relies heavily on the failure 
of the state of the art in mathematics to progress makes it at least 
inconvenient to use and at most insecure.

Because of the above considerations, it is my intentions to suggest 
a better algorithm (MPJ) for general use in the private sector.  Although 
the MPJ algorithm might be useful for government applications, too, 
the design requirements for the two areas of application vary [CHA] 
and the latter is kept shrouded in secrecy, so we shall leave it to 
the NSA.

B.  Approach

First, the problem is defined.  As explained in the above section, 
the basic problem is to create an algorithm to supplement DES.  Design 
criteria are then conceived such that an algorithm that meets those 
criteria will solve the problem as defined.  The design criteria chosen 
for the MPJ algorithm are discussed in chapter VI.  To avoid repetition 
of one or more of the many mistakes that have been made throughout 
history with cryptography, it is, of course, necessary to research 
what was done in the past, both distant and recent.  From this, many 
good ideas can be gleaned that apply to the problem at hand.  These 
ideas, along with a knowledge of current technology are then applied 
to design criteria with a bit of creativity and a lot of hard work 
to define the new algorithm.

In the process of doing all of the above, it became apparent that 
the security of encrypted data was vastly improved by first removing 
as much redundancy from the data as possible.  Therefore, as sort 
of a bonus, a linguistic approach to data compression is also presented 
that can either be used in conjunction with the MPJ encryption algorithm, 
another encryption method, or just by itself for the savings that 
it gains in communications channel capacity and/or data storage space.

II.       HISTORY OF CRYPTOGRAPHY

One of the best works on the history of cryptography is <MI>The Codebreakers, 
by David Kahn [KAH].  In that book, David Kahn discusses cryptography 
from the prehistory to World War II.  The first codes and ciphers 
were in written form, and used to protect the privacy of communications 
sent by courier or mail through hostile or unknown territory.  Some 
of these were reasonably good, but most were not difficult to break 
using manual methods, provided that the interceptor had sufficient 
cipher text and perhaps some probable text.  The use of radio, especially 
by the military, increased the need for cryptography, as well as increasing 
the rewards for those who could break the encryption schemes in use.  Kahn's 
documentation of the efforts of those who broke some very complex 
encryption schemes, like the German Enigma and the Japanese Purple 
ciphers, lend great insight to the kind of process cryptanalysis really 
is.

Kahn points out the kinds of mistakes the inventors and users of cryptographic 
algorithms tend to make that reduce the security of their communications.  For 
example, German users of Enigma tended to choose a three-letter indicator 
for their messages that consisted of three consecutive letters on 
the keyboard.  This substantially reduced the number of keys that 
had to be searched to determine the one that they were using.  While 
the designer of an algorithm may calculate the great number of combinations 
of keys that there are, the cryptanalyst looks at ways to isolate 
parts of the key so that the difficulty of a solution is much less 
than the size of the key space indicates.  The difference in mind 
set between the concealer of secrets and the one who prys into them 
has caused many an inventor of an encryption algorithm to be overconfident.

The job of the cryptanalyst is a tedious one.  He tries all kinds 
of things to try to unscramble the cipher text in front of him.  Sometimes 
the search is fruitless.  Sometimes the search yields something that 
looks like a meaningful language.  It is this ability to recognize 
a meaningful message when it comes out of the various operations that 
the cryptanalyst tries that makes the whole process possible.  It 
is also helpful for the cryptanalyst to know some probable plain text 
that is contained in a message.  This is almost always the case.  For 
example, military messages even now have a very stereotyped format, 
with the from, to, and date indicators in the same places in the message. 
The cryptanalyst almost always knows what language to expect a message 
to be written in, and this is a great help.  Natural languages contain 
a great deal of redundancy.  A message that is only 90% recovered 
is usually readable.  Natural languages also have very consistent 
statistical properties that are very useful in cryptanalysis, especially 
when the cryptanalysis is automated.  The only time that these things 
don't help the cryptanalyst is in the ``one-time pad.''

III.      ELEMENTS OF ENCRYPTION

Several basic elements make up the basis of a multitude of possible 
encryption algorithms, either alone or in combination [BEK][BAL].  Although 
most of these elements may be used to form the basis of an encryption 
method all by itself, the most secure methods of encryption will several 
of them.  For example, substitution and permutation are basic elements 
of both DES and MPJ encryption algorithms.  These algorithms, in turn, 
are best used with some form of feedback.

A.  Substitution

A substitution cipher simply substitutes one symbol from the plain 
text alphabet for another one from a cipher text alphabet.  The plain 
text alphabet can be a natural language alphabet, ASCII, EBCDIC, Baudot, 
the set {0,1}, or any other finite set.  Cipher text alphabets, likewise, 
may be any finite set.  To be able to easily apply computer methods 
to the manipulation of these alphabets, it is preferable to use alphabets 
that are groups of binary digits (bits).  This is not a severe limitation, 
since a correspondence can be set up between any finite set and a 
set of binary numbers.

1.  Monoalphabetic

A monoalphabetic substitution cipher is one in which each letter of 
the plain text alphabet is always substituted for by the same cipher 
text alphabet. The cipher text alphabet need not be in any particular 
order.  A subset of the monoalphabetic substitution cipher is the 
Caesar cipher.  This cipher replaces each letter with a letter that 
is n letters later in the alphabet.  This cipher is so named because 
it was reportedly first used by Caesar. [KAH]  With only 26 possible 
keys, this is obviously not very secure.  In fact, any substitution 
cipher that substitutes one letter for another is vulnerable to solution 
by frequency analysis, and can be solved, given enough cipher text 
with the same key.  How much cipher text is enough depends on the 
nature of the plain text, but for plain English, as many characters 
as there are letters in the alphabet is sufficient for the probabilities 
of occurrences of letters to betray enough letter identities to make 
solution probable.  While ciphers of this type no longer have any 
value for serious cryptography, they do make fun puzzles for elementary 
school children.  For example, the following cryptogram is presented 
for your solution:

UIJT JT B DBFTBS TVCTUJUVUO DJQIFS/  XPVME ZPV USVTU VPVS TFDSFST 
UP JU@

Substitution ciphers can be made more secure by operating on substitutions 
of more than one letter at a time.  For example, the substitution 
could be made on digraphs or trigraphs (groups of two or three letters).  A 
more practical example is the Data Encryption Standard.  DES is actually 
a substitution cipher with an effective alphabet size of 2^64, 
or about 1.84 x 10^19, and the MPJ Encryption Algorithm is a 
substitution cipher with an effective alphabet size of 2^128 
or about 3.4 x 10^38.   Not only is it difficult to get that 
large of a sample to analyze for statistics, but the memory required 
to store the substitution table is impractical even for computer systems 
using large optical storage disks.

2.  Polyalphabetic

A polyalphabetic substitution cipher is one in which each letter of 
the plain text alphabet may be replaced a letter from one of many 
cipher alphabets. The selection of which alphabet to take the substitution 
from may be determined in many ways.  The most usual method is by 
selecting the cipher alphabet by a combination of a message indicator 
and the number of characters from the beginning of the message.  The 
classic example of this type of cipher is the rotor-based machine.  The 
substitution occurs by physical wire crossings within rotors.  After 
each character is enciphered, one or more rotors are rotated by a 
ratchet mechanism.  The message indicator, which is part of the key, 
determines the starting position of the rotors.  This effectively 
allows the use of more cipher alphabets than there are letters in 
the message.  Because of this, the use of statistical analysis on 
any one message to guess at the substitutions is useless.  There is, 
however a good way to attack this kind of cipher when it is used heavily. 
This is by analyzing the statistics of the first character in each 
message, then the second, etc.  This is called analyzing the messages 
``in depth.''

Although the rotor-based polyalphabetic ciphers used by Germany and 
Japan in World War II contributed greatly to their losses because 
their messages were read regularly by the allies, it is possible to 
create a more secure polyalphabetic substitution with computer technology. 
The primary weakness of the mechanical rotor machines was the infrequent 
changing of many of the parts of the key such as rotor wiring and 
ratchet construction.  A more general method of using a different 
set of alphabets for each message would be very secure.  Unfortunately, 
it would result in keys larger than the message.  Since the minimum 
key length for absolute, provable cryptographic security, as determined 
by C. E. Shannon [SHA], is exactly the length of the message, this 
solution is not very efficient with respect to key management.

B.  Permutation

Permutation is taking the same symbols and writing them in a different 
order to confuse an interceptor.  There are many ways of doing this 
geometrically. For example, words may be written vertically then transcribed 
horizontally, or they may be written on a strip of paper wrapped along 
the length of a rod of a given diameter, then unwrapped for delivery.

In general, a permutation operation may be considered as an operation 
on a block of symbols, where each symbol's position is changed to 
another position within the block according to some rule.  The blocks 
may overlap each other if the permutation is undone from the end of 
the message to the beginning.

The rule(s) determining how the permutation is done may be fixed, 
or they may depend in some way on a key.  Although historical permutation 
ciphers tended to be rather simple, computer methods allow them to 
be potentially rather complex, especially if the symbols that are 
scrambled are individual bits.

Permutation, when used in combination with substitution, is very useful 
in further increasing the complexity of a cipher, since the two algorithms 
act in different ways to baffle the interceptor.  This is significant, 
since it is not possible to actually increase the security of a substitution 
cipher by simply repeating the same thing with a different key.  The 
result in such a case would be another substitution cipher with the 
same complexity.

C.  Noise Addition