Code and ciphers: Julius Caesar, the Enigma and the internet

100
chapter 8
If we replace each term by its remainder (mod 2) as soon as it is calculated
the binary equivalent is
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
which is clearly correct since, obviously,
U n �2 n �1
and all the terms after U 0 are odd.
This particular sequence is clearly of no use to a cryptographer since it
is exceptionally non-random. Is it possible however that some binary
linear sequences might be suitable, and how would they be used? We look
first at the practical problem of how a binary stream of key could be used
for encipherment.
Using a binary stream of key for encipherment
The cryptographer would first have to convert the text of the message
from an alphabetic/numeric to binary form. In the early days of computers
five or six bits were used to represent the most important characters.
Since these provided for only 32 or 64 characters respectively, which
imposed limitations on the character set that could be used, they were
eventually replaced by an eight-bit representation, which became known
as a byte, allowing 256 characters, sufficient to include not only lower and
upper case letters, numbers and punctuation but also numerous other
symbols such as brackets of various kinds and accents. Today an eight-bit
representation is standard, for example,
etc. and
whilst
and
A�65�01000001,
B�66�01000010
a�97�01100001,
b�98�01100010,
$�36�00100100
ê�136�10001000.