A Formal Model and Lower-Bound Intuition for Cryptographic Migration

We present a novel approach to gaining insight into the structure of cryptographic migration problems which are classic problems in applied cryptography. We use a formal model to capture the inherent dependencies and complexities of such transitions. Using classical mathematical results from combinatorics, probability theory, and combinatorial analysis, we evaluate the challenges of migrating large cryptographic IT infrastructures. We show mathematical rigorously that for certain idealized random partitions and under some standard Erdős-Rényi-type assumptions our model exhibits a certain expected structural complexity and provide numerical data for selected parameter sets. This work paves the way for future advancements in both the theoretical understanding and practical implementation of cryptographic migration strategies.