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Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness (Progress in Computer Science and Applied Logic) - Hardcover
Synopsis
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.
"synopsis" may belong to another edition of this title.
From the Back Cover
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.
Review
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)"About this title" may belong to another edition of this title.
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