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A Course in Number Theory and Cryptography (Record no. 75109)

000 -LEADER
fixed length control field 04103nam a22005055i 4500
001 - CONTROL NUMBER
control field 978-1-4419-8592-7
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20220801140037.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 121227s1994 xxu| s |||| 0|eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 9781441985927
-- 978-1-4419-8592-7
082 04 - CLASSIFICATION NUMBER
Call Number 512.7
100 1# - AUTHOR NAME
Author Koblitz, Neal.
245 12 - TITLE STATEMENT
Title A Course in Number Theory and Cryptography
250 ## - EDITION STATEMENT
Edition statement 2nd ed. 1994.
300 ## - PHYSICAL DESCRIPTION
Number of Pages X, 235 p.
490 1# - SERIES STATEMENT
Series statement Graduate Texts in Mathematics,
505 0# - FORMATTED CONTENTS NOTE
Remark 2 I. Some Topics in Elementary Number Theory -- 1. Time estimates for doing arithmetic -- 2. Divisibility and the Euclidean algorithm -- 3. Congruences -- 4. Some applications to factoring -- II. Finite Fields and Quadratic Residues -- 1. Finite fields -- 2. Quadratic residues and reciprocity -- III. Cryptography -- 1. Some simple cryptosystems -- 2. Enciphering matrices -- IV. Public Key -- 1. The idea of public key cryptography -- 2. RSA -- 3. Discrete log -- 4. Knapsack -- 5 Zero-knowledge protocols and oblivious transfer -- V. Primality and Factoring -- 1. Pseudoprimes -- 2. The rho method -- 3. Fermat factorization and factor bases -- 4. The continued fraction method -- 5. The quadratic sieve method -- VI. Elliptic Curves -- 1. Basic facts -- 2. Elliptic curve cryptosystems -- 3. Elliptic curve primality test -- 4. Elliptic curve factorization -- Answers to Exercises. .
520 ## - SUMMARY, ETC.
Summary, etc . . . both Gauss and lesser mathematicians may be justified in rejoic­ ing that there is one science [number theory] at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean. - G. H. Hardy, A Mathematician's Apology, 1940 G. H. Hardy would have been surprised and probably displeased with the increasing interest in number theory for application to "ordinary human activities" such as information transmission (error-correcting codes) and cryptography (secret codes). Less than a half-century after Hardy wrote the words quoted above, it is no longer inconceivable (though it hasn't happened yet) that the N. S. A. (the agency for U. S. government work on cryptography) will demand prior review and clearance before publication of theoretical research papers on certain types of number theory. In part it is the dramatic increase in computer power and sophistica­ tion that has influenced some of the questions being studied by number theorists, giving rise to a new branch of the subject, called "computational number theory. " This book presumes almost no background in algebra or number the­ ory. Its purpose is to introduce the reader to arithmetic topics, both ancient and very modern, which have been at the center of interest in applications, especially in cryptography. For this reason we take an algorithmic approach, emphasizing estimates of the efficiency of the techniques that arise from the theory.
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier https://doi.org/10.1007/978-1-4419-8592-7
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Koha item type eBooks
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-- New York, NY :
-- Springer New York :
-- Imprint: Springer,
-- 1994.
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-- computer
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650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1
-- Number theory.
650 14 - SUBJECT ADDED ENTRY--SUBJECT 1
-- Number Theory.
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
-- 2197-5612 ;
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