Number Theoretic Methods in Cryptography: Complexity lower bounds [Softcover reprint of the original 1st ed. 1999] 3034897235, 9783034897235, 9783034886642, 3034886640

The book introduces new techniques which imply rigorous lower bounds on the complexity of some number theoretic and cryp

427 35 1MB

English Pages 182 [181] Year 1999

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Number Theoretic Methods in Cryptography: Complexity lower bounds [Softcover reprint of the original 1st ed. 1999]
3034897235, 9783034897235, 9783034886642, 3034886640

Author / Uploaded
Igor Shparlinski

Table of contents :
Front Matter....Pages i-ix
Front Matter....Pages 1-1
Introduction....Pages 3-12
Basic Notation and Definitions....Pages 13-18
Auxiliary Results....Pages 19-36
Front Matter....Pages 37-37
Approximation of the Discrete Logarithm Modulo p ....Pages 39-47
Approximation of the Discrete Logarithm Modulo p - 1....Pages 49-52
Approximation of the Discrete Logarithm by Boolean Functions....Pages 53-65
Approximation of the Discrete Logarithm by Real and Complex Polynomials....Pages 67-80
Front Matter....Pages 81-81
Polynomial Approximation and Arithmetic Complexity of the Diffie—Hellman Key....Pages 83-96
Boolean Complexity of the Diffie—Hellman Key....Pages 97-106
Front Matter....Pages 107-107
Trade-off between the Boolean and Arithmetic Depths of Modulo p Functions....Pages 109-123
Special Polynomials and Boolean Functions....Pages 125-130
RSA and Blum—Blum—Shub Generators of Pseudo-Random Numbers....Pages 131-141
Front Matter....Pages 143-143
Generalizations and Open Questions....Pages 145-157
Further Directions....Pages 159-164
Back Matter....Pages 165-182

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