E-Sources Informatics

CRYPTOGRAPHY IS AN ANCIENT ART, well over two thousand years old. The need
to keep certain information secret has always existed, and attempts to preserve
secrets have therefore existed as well. But it is only in the last thirty years that
cryptography has developed into a science that has offered us needed security in
our daily lives. Whether we are talking about automated teller machines, cellular
telephones, Internet commerce, or computerized ignition locks on automobiles,
there is cryptography hidden within. And what is more, none of these applications
would work without cryptography!
The history of cryptography over the past thirty years is a unique success story.
The most important event was surely the discovery of public key cryptography in
the mid 1970s. It was truly a revolution: We know today that things are possible
that previously we hadn’t even dared to think about. Diffie and Hellman were
the first to formulate publicly the vision that secure communication must be
able to take place spontaneously. Earlier, it was the case that sender and receiver
had first to engage in secret communication to establish a common key. Diffie
and Hellman asked, with the naivety of youth, whether one could communicate
secretly without sharing a common secret. Their idea was that one could encrypt
information without a secret key, that is, one that no one else could know. This
idea signaled the birth of public key cryptography. That this vision was more
than just wild surmise was shown a few years later with the advent of the RSA
algorithm.
Modern cryptography has been made possible through the extraordinarily
fruitful collaboration between mathematics and computer science. Mathematics
provided the basis for the creation and analysis of algorithms. Without
mathematics, and number theory in particular, public key cryptography
would be impossible. Mathematics provides the results on the basis of which the
algorithms operate.
If the cryptographic algorithms are to be realized, then one needs procedures
that enable computation with large integers: The algorithms must not function
only in theory; they must perform to real-world specifications. That is the task of
computer science.
This book distinguishes itself from all other books on the subject in that it
makes clear this relationship between mathematics and computing. I know of no
book on cryptography that presents the mathematical basis so thoroughly while
providing such extensive practical applications, and all of this in an eminently
readable style.