Progress in Computer Science and Applied Logic

Cryptographic Applications of Analytic Number Theory

Complexity Lower Bounds and Pseudorandomness

Authors: Shparlinski, Igor

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About this book

The book introduces new ways of using analytic number theory in cryptography and related areas, such as complexity theory and pseudorandom number generation.

Key topics and features:

- various lower bounds on the complexity of some number theoretic and cryptographic problems, associated with classical schemes such as RSA, Diffie-Hellman, DSA as well as with relatively new schemes like XTR and NTRU

- a series of very recent results about certain important characteristics (period, distribution, linear complexity) of several commonly used pseudorandom number generators, such as the RSA generator, Blum-Blum-Shub generator, Naor-Reingold generator, inversive generator, and others

- one of the principal tools is bounds of exponential sums, which are combined with other number theoretic methods such as lattice reduction and sieving

- a number of open problems of different level of difficulty and proposals for further research

- an extensive and up-to-date bibliography

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.

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)

Table of contents (33 chapters)

Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-3-0348-8037-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-3-7643-6654-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.00
price for USA
  • ISBN 978-3-0348-9415-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Cryptographic Applications of Analytic Number Theory
Book Subtitle
Complexity Lower Bounds and Pseudorandomness
Authors
Series Title
Progress in Computer Science and Applied Logic
Series Volume
22
Copyright
2003
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8037-4
DOI
10.1007/978-3-0348-8037-4
Hardcover ISBN
978-3-7643-6654-4
Softcover ISBN
978-3-0348-9415-9
Series ISSN
2297-0576
Edition Number
1
Number of Pages
IX, 414
Topics