| Category | : Security | | Added on | : 15/06/2007 10:06:44 | | Added by | : ganelon | | Archive password | : www.megapid.net | | Total size | : 2 MB | | Description | : |
| | This book originated in a well-established yet
constantly evolving course on Complexity and Cryptography which we have both given to final year Mathematics
undergraduates at Oxford for many years. It has also formed part of an M.Sc. course on Mathematics and the
Foundations of Computer Science, and has been the basis for a more recent course on Randomness and Complexity
for the same groups of students. One of the main motivations for setting up the course was to give
mathematicians, who traditionally meet little in the way of algorithms, a taste for the beauty and importance
of the subject. Early on in the book the reader will have gained sufficient background to understand what is
now regarded as one of the top ten major open questions of this century, namely the P = NP question. At the
same time the student is exposed to the mathematics underlying the security of cryptosystems which are now an
integral part of the modern ‘email age’. Although this book provides an introduction to many of
the key topics in complexity theory and cryptography, we have not attempted to write a comprehensive text.
Obvious omissions include cryptanalysis, elliptic curve cryptography, quantum cryptography and quantum
computing. These omissions have allowed us to keep the mathematical prerequisites to a minimum. Throughout the
text the emphasis is on explaining the main ideas and proving the mathematical results rigorously. Thus we
have not given every result in complete generality. The exercises at the end of many sections of the book are
in general meant to be routine and are to be used as a check on the understanding of the preceding principle;
the problems at the end of each chapter are often harder. TABLE OF CONTENT: Chapter 01: Basics of
cryptography Chapter 02: Complexity theory Chapter 03: Non-deterministiccomputation Chapter
04: Probabilistic computation Chapter 05: Symmetric cryptosystems Chapter 06: One
wayfunctions Chapter 07: Public key cryptography Chapter 08: Digital signatures Chapter 09:
Key establishment protocols Chapter 10: Secure encryption Chapter 11: Identification schemes
Appendix 1: Basic mathematical background Appendix 2: Graph theory definitions Appendix 3:
Algebra and number theory Appendix 4: Probability theory Appendix 5: Hints to selected exercises
and problems Appendix 6: Answers to selected exercises and problems>Password:
ganelon |
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