Number Theoretic Methods in Cryptography: Complexity lower bounds

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.