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The modulus p was wrong, since we are tracking the exponents in the group of unit Z/pZ^x, hence the modulus p-1 should be right (by Fermat's little theorem). |
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g(x,n) &= \begin{cases}
n & x\in S_0\\
2n \pmod {p-1} & x\in S_1\\
n+1 \pmod {p-1} & x\in S_2
\end{cases}
\\
h(x,n) &= \begin{cases}
n+1 \pmod {p-1} & x\in S_0\\
2n \pmod {p-1} & x\in S_1\\
n & x\in S_2
\end{cases}
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