  Recently, much work has been done to investigate Galois module structure of
local field extensions, particularly through the use of Galois scaffolds. Given
a totally ramified $p$-extension of local fields $L/K$, a Galois Scaffold gives
us a $K$-basis for $K[G]$ whose effect on the valuation of elements of $L$ is
easy to determine. In 2013, N.P. Byott and G.G. Elder gave sufficient
conditions for the existence of Galois scaffolds for cyclic extensions of
degree $p^2$ in characteristic $p$. We take their work and adapt it to cyclic
extensions of degree $p^2$ in characteristic $0$.
