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Modern cryptography depends heavily on number theory, with primality test ing, factoring, discrete logarithms (indices), and elliptic curves being perhaps the most prominent subject areas. Since my own graduate study had empha sized probability theory, statistics, and real analysis, when I started work ing in cryptography around 1970, I found myself swimming in an unknown, murky sea. I thus know from personal experience how inaccessible number theory can be to the uninitiated. Thank you for your efforts to case the transition for a new generation of cryptographers. Thank you also for helping Ralph Merkle receive the credit he deserves. Diffie, Rivest, Shamir, Adleman and I had the good luck to get expedited review of our papers, so that they appeared before Merkle's seminal contribu tion. Your noting his early submission date and referring to what has come to be called "Diffie-Hellman key exchange" as it should, "Diffie-Hellman-Merkle key exchange", is greatly appreciated. It has been gratifying to see how cryptography and number theory have helped each other over the last twenty-five years. :'-Jumber theory has been the source of numerous clever ideas for implementing cryptographic systems and protocols while cryptography has been helpful in getting funding for this area which has sometimes been called "the queen of mathematics" because of its seeming lack of real world applications. Little did they know! Stanford, 30 July 2001 Martin E. Hellman Preface to the Second Edition Number theory is an experimental science.
List of contents
Foreword by Martin E. Hellman.- Preface to the Second Edition.- Preface to the First Edition.- 1. Elementary Number Theory.- 2. Computational/Algorithmic Number Theory.- 3. Applied Number Theory.- Bibliography.- Index.
Summary
This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this 2nd edition proofs of many theorems have been provided, further additions and corrections were made.
Additional text
From the reviews of the second edition:
"This book gives a profound and detailed insight at an undergraduate level in abstract and computational number theory as well as in applications in computing and cryptography. … The author has done a lot of work in providing a plenty of examples, in adding many historical comments including sketchy biographies … and in presenting the whole topic in a very accessible style. So the book can be recommended warmly for the laymen as well as for the mathematician without experience in applied number theory." (G. Kowol, Monatshefte für Mathematik, Vol. 140 (4), 2003)
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From the reviews of the second edition:
"This book gives a profound and detailed insight at an undergraduate level in abstract and computational number theory as well as in applications in computing and cryptography. ... The author has done a lot of work in providing a plenty of examples, in adding many historical comments including sketchy biographies ... and in presenting the whole topic in a very accessible style. So the book can be recommended warmly for the laymen as well as for the mathematician without experience in applied number theory." (G. Kowol, Monatshefte für Mathematik, Vol. 140 (4), 2003)
