Title | Cryptographic Applications of Analytic Number Theory [electronic resource] : Complexity Lower Bounds and Pseudorandomness / edited by Igor Shparlinski |
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Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2003 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8037-4 |
Descript | IX, 414 p. online resource |
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