## Number Theoretic Methods in Cryptography: Complexity Lower Bounds |

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### Contents

Basic Notation and Definitions | 13 |

Approximation and Complexity of the Discrete Logarithm | 37 |

Approximation of the Discrete Logarithm | 53 |

Copyright | |

7 other sections not shown

### Other editions - View all

Number Theoretic Methods in Cryptography: Complexity lower bounds Igor Shparlinski Limited preview - 2012 |

Number Theoretic Methods in Cryptography: Complexity lower bounds Igor Shparlinski No preview available - 1999 |

### Common terms and phrases

absolute constant absolutely irreducible algebraic arithmetic circuits Assume binary binary entropy function bit of ind bit representation Blum integer Boolean function B(U1 breaking the Diffie-Hellman Chapter character sums congruence consider CREW PRAM complexity decision tree define denote derive Diffie-Hellman cryptosystem discrete logarithm modulo disjunctive normal form divisor exponential sums fan-in Boolean circuits finite fields Fourier coefficients gates holds indx inequality ISBN least Lemma Let a Boolean Let f(X linear complexity linear recurring sequence log log logp modulo a prime monomials non-trivial lower bound non-zero polynomial number of monomials number of solutions obtain lower bounds particular polynomial f(X polynomial of degree private key proof of Theorem quadratic character quadratic non-residue quadratic non-residue modulo quadratic residue modulo Question rational function rightmost bit second leftmost bit set S C smallest non-negative residue spr f square-free Theorem 6.1 UBC(d unbounded fan-in Boolean values variables vector