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Cryptographic Applications of Analytic Number Theory : Complexity Lower Bounds and Pseudorandomness

Author: Igor Shparlinski
Publisher: Basel : Birkhäuser Basel : Imprint : Birkhäuser, 2003.
Series: Progress in computer science and applied logic, 22.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Igor Shparlinski
ISBN: 9783034880374 3034880375
OCLC Number: 851759813
Description: 1 online resource (ix, 414 pages).
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 Boolean Functions --
VII Concluding Remarks and Open Questions.
Series Title: Progress in computer science and applied logic, 22.
Responsibility: edited by Igor Shparlinski.

Abstract:

The book introduces new techniques that imply rigorous lower bounds on the com- plexity of some number-theoretic and cryptographic problems. These functions are considered over the residue ring  Read more...

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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 Read more...

 
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