Introduction To Number Theory With Computing
Download Introduction To Number Theory With Computing PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Introduction To Number Theory With Computing book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Number Theory for Computing
Author: Song Y. Yan
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-11-11
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.
Number Theory for Computing
Author: Song Y. Yan
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-09
Mathematicians do not study objects, but relations among objectsj they are indifferent to the replacement of objects by others as long as relations do not change. Matter is not important, only form interests them. HENRI POINCARE (1854-1912) Computer scientists working on algorithms for factorization would be well advised to brush up on their number theory. IAN STEWART [219] The theory of numbers, in mathematics, is primarily the theory of the prop erties of integers (i.e., the whole numbers), particularly the positive integers. For example, Euclid proved 2000 years aga in his Elements that there exist infinitely many prime numbers. The subject has long been considered as the purest branch of mathematics, with very few applications to other areas. How ever, recent years have seen considerable increase in interest in several central topics of number theory, precisely because of their importance and applica tions in other areas, particularly in computing and information technology.
Introduction to Number Theory with Computing
This introduction to number theory has been written specifically for mathematics and computing undergraduates. Computer programs in BASIC are accompanied by basic text which explains the subject and demonstrates how computers have opened up new horizons for number theorists.