## Black-Box Models of Computation in CryptologyGeneric group algorithms solve computational problems defined over algebraic groups without exploiting properties of a particular representation of group elements. This is modeled by treating the group as a black-box. The fact that a computational problem cannot be solved by a reasonably restricted class of algorithms may be seen as support towards the conjecture that the problem is also hard in the classical Turing machine model. Moreover, a lower complexity bound for certain algorithms is a helpful insight for the search for cryptanalytic algorithms.
Tibor Jager addresses several fundamental questions concerning algebraic black-box models of computation: Are the generic group model and its variants a reasonable abstraction? What are the limitations of these models? Can we relax these models to bring them closer to the reality? |

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### Contents

1 Introduction | 2 |

2 BlackBox Models of Computation | 5 |

3 On BlackBox Ring Extraction and Integer Factorization | 15 |

4 Analysis of Cryptographic Assumptions in the Generic Ring Model | 24 |

5 The Generic Composite Residuosity Problem | 49 |

6 SemiGeneric Groups and Their Applications | 57 |

Bibliography | 76 |