Overview

The book introduces new ways of using analytic number theory in cryptography and related areas, such as complexity theory and pseudorandom number generation.Cryptographers and number theorists will find this book useful. The former can learn about new number theoretic techniques which have proved to be invaluable cryptographic tools, the latter about new challenging areas of applications of their skills.

Full Product Details

Author:   Igor Shparlinski
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2003 ed.
Volume:   22
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   1.710kg
ISBN:  

9783764366544

ISBN 10:   3764366540
Pages:   414
Publication Date:   11 December 2002
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

I Preliminaries.- 1 Basic Notation and Definitions.- 2 Polynomials and Recurrence Sequences.- 3 Exponential Sums.- 4 Distribution and Discrepancy.- 5 Arithmetic Functions.- 6 Lattices and the Hidden Number Problem.- 7 Complexity Theory.- II Approximation and Complexity of the Discrete Logarithm.- 8 Approximation of the Discrete Logarithm Modulop.- 9 Approximation of the Discrete Logarithm Modulop -1.- 10 Approximation of the Discrete Logarithm by Boolean Functions.- 11 Approximation of the Discrete Logarithm by Real Polynomials.- III Approximation and Complexity of the Diffie-Hellman Secret Key.- 12 Polynomial Approximation and Arithmetic Complexity of the.- Diffie-Hellman Secret Key.- 13 Boolean Complexity of the Diffie-Hellman Secret Key.- 14 Bit Security of the Diffie-Hellman Secret Key.- IV Other Cryptographic Constructions.- 15 Security Against the Cycling Attack on the RSA and Timed-release Crypto.- 16 The Insecurity of the Digital Signature Algorithm with Partially Known Nonces.- 17 Distribution of the ElGamal Signature.- 18 Bit Security of the RSA Encryption and the Shamir Message Passing Scheme.- 19 Bit Security of the XTR and LUC Secret Keys.- 20 Bit Security of NTRU.- 21 Distribution of the RSA and Exponential Pairs.- 22 Exponentiation and Inversion with Precomputation.- V Pseudorandom Number Generators.- 23 RSA and Blum-Blum-Shub Generators.- 24 Naor-Reingold Function.- 25 1/M Generator.- 26 Inversive, Polynomial and Quadratic Exponential Generators.- 27 Subset Sum Generators.- VI Other Applications.- 28 Square-Freeness Testing and Other Number-Theoretic Problems.- 29 Trade-off Between the Boolean and Arithmetic Depths of ModulopFunctions.- 30 Polynomial Approximation, Permanents and Noisy Exponentiation in Finite Fields.- 31 Special Polynomials and BooleanFunctions.- VII Concluding Remarks and Open Questions.

Reviews

From the reviews: Igor Shparlinski is a very prolific mathematician and computer scientist ! . The book is written at a very high level, suitable for graduate students and researchers in computer science and mathematics. ! book has a unique perspective, and is not really comparable to other books in the area. ! book contains many deep results, and the mathematically-sophisticated reader can find much that is novel. ! this is an impressive work that will be of significant interest to researchers in cryptography and algorithmic number theory. (Jeffrey Shallit, SIGACT News, Vol. 41 (3), September, 2010)

From the reviews: Igor Shparlinski is a very prolific mathematician and computer scientist ... . The book is written at a very high level, suitable for graduate students and researchers in computer science and mathematics. ... book has a unique perspective, and is not really comparable to other books in the area. ... book contains many deep results, and the mathematically-sophisticated reader can find much that is novel. ... this is an impressive work that will be of significant interest to researchers in cryptography and algorithmic number theory. (Jeffrey Shallit, SIGACT News, Vol. 41 (3), September, 2010)

From the reviews: “Igor Shparlinski is a very prolific mathematician and computer scientist … . The book is written at a very high level, suitable for graduate students and researchers in computer science and mathematics. … book has a unique perspective, and is not really comparable to other books in the area. … book contains many deep results, and the mathematically-sophisticated reader can find much that is novel. … this is an impressive work that will be of significant interest to researchers in cryptography and algorithmic number theory.” (Jeffrey Shallit, SIGACT News, Vol. 41 (3), September, 2010)

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