A Cryptographic Truss

Universal algebra requires native structures where the failure of distributivity is an inherent geometric feature, not an artificial amputation. The introduction of the Truss by Brzezi\'{n}ski \cite{Brzezinski2017} provided a rigorous category for algebras residing between braces and rings. However, the examples currently populating the literature are frequently trivial: taking a standard ring $(R, +, \cdot)$, deleting the zero element, and defining a heap $[x,y,z] = x - y + z$. This paper introduces a native, exotic Truss derived from the discrete logarithm problem (DLP) over characteristic 2 finite fields. By weaponizing the failure of base distributivity inherent in power-logarithmic operations, we construct a mathematically flawless Truss that acts simultaneously as a sandbox for algebraic ideal theory and a NOBUS (Nobody But Us) cryptographic trapdoor.