Posts Tagged ‘giant steps’
Infrastructures and Global Fields.
Thursday, July 23rd, 2009The following posts give an introduction to infrastructures and how to obtain these from global fields:
The Discrete Logarithm Problem and Generalizations.
One-dimensional Infrastructures.
Interpreting One-dimensional Infrastructures as Groups: f-Representations.
n-dimensional Infrastructures.
How to Obtain Reduction Maps for n-dimensional Infrastructures.
Obtaining Infrastructures from Global Fields.
See also my article on infrastructures at Wikipedia.
Obtaining Infrastructures from Global Fields.
Tuesday, July 21st, 2009We show how to obtain n-dimensional infrastructures from global fields of unit rank n. We will also discuss how to obtain baby steps in these cases, and show graphical representations of certain two-dimensional infrastructures obtained from function fields.
n-dimensional Infrastructures.
Monday, July 20th, 2009We will introduce n-dimensional infrastructures and briefly discuss reductions, f-representations and giant steps. We will also discuss how infrastructures can be obtained from finite abelian groups.
Interpreting One-dimensional Infrastructures as Groups: f-Representations.
Monday, July 20th, 2009We introduce the notion of f-representations and relate them to reduction maps. Moreover, we equip a set of f-representations with a group operation which can be computed purely with baby steps, giant steps and relative distances.
One-dimensional Infrastructures.
Monday, July 20th, 2009We give the definition of one-dimensional infrastructures and construct baby and giant steps. Moreover, we show that one-dimensional infrastructures generalize finite cyclic groups. Finally, we give some remarks on our choice of the giant step definition.
