We 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.

# Posts for July 20, 2009.

We 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.

We 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.

We discuss the discrete logarithm problem, its use in cryptography, and two possible directions of generalization to other algebraic structures.