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Black-Box Models of Computation in Cryptology

Tibor Jager

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Naturwissenschaften, Medizin, Informatik, Technik / Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik

Beschreibung

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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Schlagwörter

Cryptographic Hardness Assumptions, Computational Complexity, Generic Group Model, Black-Box Models of Computation, Computational Number Theory and Algebra