Information Technology Reference
In-Depth Information
To help prevent decoding by statistical analysis, encoders can code
several letters at once, rather than coding letter by letter. For example,
a code could be constructed so that pairs of letters were coded together
(coding “ED” by “RM,” for instance.) With this approach, counts of
individual letters would not give much information to potential crypt
analysts, because the code was not based on individual letters. Even
here, however, when reasonably large amounts of text are collected,
patterns could be observed and statistical analysis of groups of letters
may provide insights. Coding pairs of letters may create some difficul
ties for cryptanalysts, but these are rarely insurmountable.
Increasing the size of the groups, however, can greatly complicate
the work required to break a code. When 50 or 100 letters are encoded
as a group, for example, the task of cryptanalysis may be sufficiently
timeconsuming such that codes can be cracked only after many years
(at which time, the data may no longer be sensitive or even relevant).
Encoding reasonably large groups of letters together is the basis
for one of today's most popular encryption schemes, called
public
key systems
, which are often used with modern computer systems.
Public key systems typically involve three main elements.
3
First, each group of letters is interpreted as a number
n
. (If a
group had only one letter, we might consider A as 01, B as 02, C as
03, and so on. If a group had two letters, then the combination CA
might be 0301—putting the numbers for C and A next to each
other. The number
n
in what follows would be 01 or 0301 or what
ever letters formed a group within our message.)
Second, the number
n
is put into an arithmetic formula to get a
coded form. For example, the formula might specify numbers
e
and
m
, so that the coded number
c
is
c
n
e
mod
m
; that is, the group's
number
n
is raised to the power
e
, and the remainder is computed
after dividing by
m
. With this approach,
c
is easily computed (as
suming you have a good calculator that raises numbers to powers
and also takes remainders).
Third, when
e
and
m
have been chosen carefully, it turns out
that a similar formula may be used to decipher the message. In par
ticular, there may be a number
d
where
n
c
d
mod
m
. The security
of the code then depends upon the difficulty of computing
d
. For a
public key system, a person wishing to receive coded messages will
publish
m
and
e
, so anyone can send him or her information. The
3 For more information, see Donald W. Davies,
Tutorial: The Security of Data in Networks,
IEEE Computer Society, Los Angeles, CA, 1981. The discussion here follows the general
treatment given in Part II of Davies' tutorial, pp. 115-134.
