Black-Box Models of Computation in Cryptology [electronic resource] /
Jager, Tibor.author.
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?
"Dissertation Ruhr-Universitat Bochum, 2011"--T.p. verso.
Includes bibliographical references.
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?
Computer mathematics.
Computational Mathematics and Numerical Analysis.