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Black-Box Models of Computation in Cryptology [electronic resource] /by Tibor Jager.

by Jager, Tibor [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: Wiesbaden : Vieweg+Teubner Verlag, 2012.Description: XII, 86p. online resource.ISBN: 9783834819901.Subject(s): Mathematics | Computer science -- Mathematics | Mathematics | Computational Mathematics and Numerical AnalysisDDC classification: 518 | 518 Online resources: Click here to access online
Contents:
Black-Box Models of Computation -- On Black-Box Ring Extraction and Integer Factorization -- On the Analysis of Cryptographic Assumptions in the Generic Ring Model -- The Generic Composite Residuosity Problem -- Semi-Generic Groups and Their Applications.
In: Springer eBooksSummary: 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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Black-Box Models of Computation -- On Black-Box Ring Extraction and Integer Factorization -- On the Analysis of Cryptographic Assumptions in the Generic Ring Model -- The Generic Composite Residuosity Problem -- Semi-Generic Groups and Their Applications.

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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