Show that the GHASH function calculates [left(X_{1} cdot H^{m}ight) oplusleft(X_{2} cdot H^{m-1}ight) oplus cdots oplusleft(X_{m-1} cdot H^{2}ight)

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Show that the GHASH function calculates

\[\left(X_{1} \cdot H^{m}ight) \oplus\left(X_{2} \cdot H^{m-1}ight) \oplus \cdots \oplus\left(X_{m-1} \cdot H^{2}ight) \oplus\left(X_{m} \cdot Hight)\]

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