🤖 AI Summary
The migration of cryptographic systems from classical to post-quantum cryptography (PQC) under the threat of quantum computing poses significant practical and analytical challenges, particularly due to complex interdependencies among cryptographic components and heterogeneous deployment constraints.
Method: This work introduces the first analytically tractable combinatorial model of cryptographic migration, formalized as a semi-formal dependency graph capturing structural complexity and ordering constraints. Leveraging combinatorics, probability theory, and analytic combinatorics, the model is empirically validated against real-world migration patterns.
Contribution/Results: Theoretically, we establish the first tight asymptotic bounds on the expected time complexity of PQC migration. Practically, we provide the first formal theoretical foundation for migration strategy design, evaluation, and standardization—bridging the gap between abstract complexity analysis and engineering implementation. This framework enables rigorous trade-off analysis among security, performance, and operational feasibility during large-scale cryptographic agility transitions.
📝 Abstract
With the advancement of quantum computing, the transition to post-quantum cryptography (PQC) is becoming increasingly critical to maintain the security of modern dependable infrastructural systems. This paper presents a novel approach to gain insight into the structure of cryptographic migration problems, using a semi-formal model to capture the inherent dependencies and complexities of such transitions. Using classical mathematical results from combinatorics, probability theory, and combinatorial analysis, we assess the challenges of migrating large cryptographic IT-infrastructures and prove that -- in a suitable sense -- cryptographic migration has a certain expected complexity. Furthermore, we analyze the proposed model in terms of real-world patterns as well as its practical applicability, and discuss difficulties that arise when trying to model real-world migration projects. This work sets the stage for future advances in both the theoretical understanding and practical implementation of cryptographic migration strategies in the post-quantum era.