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

If the cryptographer were prepared to have two tables on hand, listing
the 17 576 (�26�26�26) plaintext and cipher trigraphs, an even more
secure system, trigraph substitution, could be used.
Clearly, one could devise increasingly secure systems in this way but,
in practice, the tables would be unwieldy and even a system based on
strings of 4 letters (i.e. tetragraphs) is hardly practicable.
Suppose, however, that a system could be devised which took a string
of letters of fixed length and somehow converted them automatically into
another string and which guaranteed that changing any of the letters in
the first string would produce an entirely different second string. Such a
system would not require printed tables and could be very secure indeed,
depending upon the method by which the string is converted and the
number of letters in the strings. At the lower end of the scale of such
systems we have the Julius Caesar method: the conversion being done by
moving each letter three places forward in the alphabet and the fixed
length of the string being 1. At the top end of the scale we have a method
known as RSA, after Rivest, Shamir and Adelman who devised the
method in 1978 [13.1], which can be used to encipher very long strings,
e.g. 100 letters, and which provides an extremely high degree of security.
This may seem remarkable enough but even more remarkable is the fact
that the RSA is a public key system, which means, as was explained in
Chapter 12, that the details of how to encrypt a message are made publicly
available, but only the ‘owner’ of the public key knows how to decrypt the
messages which are sent to him. The owner can, however, reply to his correspondents
by encrypting his messages in such a way that they can
decrypt them.
Although in theory RSA encryption could be carried out by hand the
computations, which involve modular arithmetic with very large integers,
could only realistically be carried out on a computer with facilities
for multi-length arithmetic.
Factorisation of large integers
Encipherment and the internet 171
It is a relatively easy task to multiply two numbers together, particularly
if we have a calculator available, provided that they are not too large. If
the numbers are both less than 10 a child should be able to do it unaided.
If they are both less than 100 most people, hopefully, could get the answer
with paper and pencil. If both numbers are bigger than 10 000 it is likely
that a calculator would be employed.