Cryptographic Applications of Analytic Number Theory

Table of Contents

1. Altmetric Badge
   Book Overview
2. Altmetric Badge
   Chapter 1 Introduction
3. Altmetric Badge
   Chapter 2 Basic Notation and Definitions
4. Altmetric Badge
   Chapter 3 Polynomials and Recurrence Sequences
5. Altmetric Badge
   Chapter 4 Exponential Sums
6. Altmetric Badge
   Chapter 5 Distribution and Discrepancy
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   Chapter 6 Arithmetic Functions
8. Altmetric Badge
   Chapter 7 Lattices and the Hidden Number Problem
9. Altmetric Badge
   Chapter 8 Complexity Theory
10. Altmetric Badge
    Chapter 9 Approximation of the Discrete Logarithm Modulo p
11. Altmetric Badge
    Chapter 10 Approximation of the Discrete Logarithm Modulo p — 1
12. Altmetric Badge
    Chapter 11 Approximation of the Discrete Logarithm by Boolean Functions
13. Altmetric Badge
    Chapter 12 Approximation of the Discrete Logarithm by Real Polynomials
14. Altmetric Badge
    Chapter 13 Polynomial Approximation and Arithmetic Complexity of the Diffie-Hellman Secret Key
15. Altmetric Badge
    Chapter 14 Boolean Complexity of the Diffie-Hellman Secret Key
16. Altmetric Badge
    Chapter 15 Bit Security of the Diffie—Hellman Secret Key
17. Altmetric Badge
    Chapter 16 Security Against the Cycling Attack on the RSA and Timed-release Crypto
18. Altmetric Badge
    Chapter 17 The Insecurity of the Digital Signature Algorithm with Partially Known Nonces
19. Altmetric Badge
    Chapter 18 Distribution of the ElGamal Signature
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    Chapter 19 Bit Security of the RSA Encryption and the Shamir Message Passing Scheme
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    Chapter 20 Bit Security of the XTR and LUC Secret Keys
22. Altmetric Badge
    Chapter 21 Bit Security of NTRU
23. Altmetric Badge
    Chapter 22 Distribution of the RSA and Exponential Pairs
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    Chapter 23 Exponentiation and Inversion with Precomputation
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    Chapter 24 RSA and Blum—Blum—Shub Generators
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    Chapter 25 Naor—Reingold Function
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    Chapter 26 1/ M Generator
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    Chapter 27 Inversive, Polynomial and Quadratic Exponential Generators
29. Altmetric Badge
    Chapter 28 Subset Sum Generators
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    Chapter 29 Square-Freeness Testing and Other Number-Theoretic Problems
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    Chapter 30 Trade-off Between the Boolean and Arithmetic Depths of Modulo p Functions
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    Chapter 31 Polynomial Approximation, Permanents and Noisy Exponentiation in Finite Fields
33. Altmetric Badge
    Chapter 32 Special Polynomials and Boolean Functions
34. Altmetric Badge
    Chapter 33 Concluding Remarks and Open Questions