Number Theoretic Methods in Cryptography: Complexity lower bounds / Edition 1

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The book introduces new techniques which imply rigorous lower bounds on the complexity of some number theoretic and cryptographic problems. These methods and techniques are based on bounds of character sums and numbers of solutions of some polynomial equations over finite fields and residue rings. It also contains a number of open problems and proposals for further research.

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Editorial Reviews

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"This volume gives a thorough treatment of the complexity of the discrete logarithm problem in a prime field, as well as related problems. The final chapter on further directions gives an interesting selection of problems."

--Zentralblatt Math

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Product Details

Table of Contents

I Preliminaries
1 Introduction
2 Basic Notation and Definitions
3 Auxiliary Results
II Approximation and Complexity of the Discrete Logarithm
4 Approximation of the Discrete Logarithm Modulo p
5 Approximation of the Discrete Logarithm Modulo p - 1
6 Approximation of the Discrete Logarithm by Boolean Functions
7 Approximation of the Discrete Logarithm by Real and Complex Polynomials
III Complexity of Breaking the Diffie-Hellman Cryptosystem
8 Polynomial Approximation and Arithmetic Complexity of the Diffie-Hellman Key
9 Boolean Complexity of the Diffie-Hellman Key
IV Other Applications
10 Trade-off between the Boolean and Arithmetic Depths of Modulo p Functions
11 Special Polynomials and Boolean Functions
12 RSA and Blum-Blum-Shub Generators of Pseudo-Random Numbers
V Concluding Remarks
13 Generalizations and Open Questions
14 Further Directions
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