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Well, $\operatorname{GHASH}$ might be better understood as the polynomial: $$\operatorname{GHASH}_H(X_1, X_2, ... , X_{m-1}, X_m) = X_1 H^{m} + X_2 H^{m-1} + ... + X_{m-1} H^2 + X_m H^1$$ where addition, multiplication and exponentiation are in the field $GF(2^{128})$. These addition, multiplication and exponentiation operations act algebraically quite a ...



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