Black-Box Models of Computation in Cryptology

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Springer Science & Business Media, Mar 23, 2012 - Mathematics - 86 pages
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Generic 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
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About the author (2012)

Dr. Tibor Jager completed his doctoral thesis at the Horst Görtz Institute for IT Security at Ruhr-Universität Bochum under the supervision of Prof. Dr. Jörg Schwenk. He is now a postdoctoral researcher at the Karlsruhe Institute of Technology.

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