Cryptography Reference
In-Depth Information
same probability, then there are said to be 8 bits of information in
this byte. On the other hand, if only two values like 00101110 and
10010111 happen to appear in a message, then there is only one bit
of information in each byte. The two values could be replaced with
just a 0 and a 1 and the entire file would be reduced to one-eighth
the size. The number of bits of information in a file is called, in this
context, its
entropy
.
Shannon also provided a precise formula for measuring the size
of information, a topic found later in Section 2.3. This measurement
of information offered some important insights to cryptographers.
Mathematicians who break codes rely on deep statistical analysis to
ferret out patterns in files. In English, the letter “q” is often followed
by the letter “u” and this pattern is a weak point that might be ex-
ploited by attackers trying to get at the underlying message. A good
encryption program would leave no such patterns in the final file.
Every one of the 256 possible values of a byte would occur with equal
probability. It would seem to be filled chock-full with information.
One-time pads
are an encryption system that is a good example
of the basic structure behind information theory. The one-time pad
received its name because spies often carried pads of random num-
bers that served as the encryption key. They would use each sheet
once and then dispose of it.
Asecretcanbesplitinto
parts using an extension
of one-time pads
described on page 58.
Aone-timepadcanbebuiltbyusingastandardmethodofen-
cryption. Assume for the moment that a key is just a number like 5
and a message consists of all uppercase letters. To encrypt a letter
like “C” with a key number like 5, count over five letters to get “H”. If
the counting goes past “Z” at the end of the alphabet, simply go back
to “A” and keep going. The letter “Y” encrypted with the key number
6 would produce “E”. To decrypt work backward.
Here is a sample encryption:
HELLO
90210
QENMO
In this case, the key is the five numbers 9, 0, 2, 1, and 0. They
would constitute the one-time pad that encrypted this message. In
practice, the values should be as random as possible. A humanmight
reveal some hidden short circuits in its brain.
1
Shannon proved that a one-time pad is an unbreakable cipher be-
cause the information in the final file is equal to the information in
the key. An easy way to see why this is true is to break the message,
1
Or the limitations of creativity brought on by too much television.
