R$1$a$.$ Alice has enough information to compute S$,$ accessing only $\backslash$alpha $,$a and the public directory.

R$1$b$.$ Bob has enough information to compute S$,$ accessing only $\backslash$alpha $,$b and the public directory.

R$1$q$.$ Quinn has enough information to compute S$,$ accessing only $\backslash$alpha $,$ q and the public directory.

R$2.$ No eavesdroppers can compute S based on information from the public directory, assuming that they cant solve the Discrete Logarithm Problem.

For each of the following schemes, verify R$1$a$,$ R$1$b$,$ R$1$q$,$ R$2$ in that order, justifying whether the rule is met or broken. Once you have justified why a rule is broken, you are done with that scheme.