Cryptographic Applications of Analytic Number Theory : Complexity Lower Bounds and Pseudorandomness / edited by Igor Shparlinski
(Progress in Computer Science and Applied Logic ; 22)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Basel : Birkhäuser Basel : Imprint: Birkhäuser |
| 出版年 | 2003 |
| 本文言語 | 英語 |
| 大きさ | IX, 414 p : online resource |
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| 内容注記 | 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 |
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| 一般注記 | 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 |
| 著者標目 | Shparlinski, Igor editor SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Data encryption (Computer science) LCSH:Applied mathematics LCSH:Engineering mathematics LCSH:Number theory FREE:Mathematics FREE:Number Theory FREE:Data Encryption FREE:Applications of Mathematics |
| 分 類 | DC23:512.7 |
| 巻冊次 | ISBN:9783034880374 
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| ISBN | 9783034880374 |
| URL | http://dx.doi.org/10.1007/978-3-0348-8037-4 |
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