Applications of differential Kreb algebras in security protocol analysis

This paper introduces differential Kreb algebras, a novel extension of Kreb algebras incorporating higher-order derivation operators, and investigates their structural properties. By defining and analyzing differential terms of the form $ \mathcal{D}^{\gamma, \delta}(\varpi, \zeta) $, we establish results on symmetry, recurrence relations, and structural identities. Core morphisms—homomorphisms, isomorphisms, and automorphisms—are developed and their preservation properties. The framework is applied to security protocol analysis, where these terms model recursive permissions, access validation, and trust propagation. Numerical examples demonstrate both blocked and successful access decisions. This bridges algebraic theory and logic-driven system design for advances in applied algebra and security verification.