ResearchA Markov model that allows a vulnerable cryptographic deployment to return to a safe state can inadvertently erase risk accumulated before remediation. We formulate a cumulative-exposure threshold model for post-quantum migration analysis. A two-state continuous-time chain alternates between protected and exposed operation, but a separate, nondecreasing occ…
KnowledgeTrend researcherKnowledgeTrend Journal · 2026
CryptographyThis research constructs a candidate flanking-exponentiation permutation, develops its formal properties and presents a reproducible evaluation framework for algebraic and cryptographic analysis.
KnowledgeTrend researcherCryptography research manuscript · 2026
AlgebraThis paper investigates the enumeration of elements in three classes of signed partial transformation semigroups: partial signed order-preserving, partial signed order-decreasing, and partial signed order-preserving-or-order-reversing transformations. It examines the reported PSPD₄ numerical inconsistency and develops a domain-rank framework for extending t…
KnowledgeTrend researcherInternational Journal of Mathematics and Statistics · 2026
