ElGamal Signature Scheme - Correctness

Correctness

The algorithm is correct in the sense that a signature generated with the signing algorithm will always be accepted by the verifier.

The signature generation implies

Hence Fermat's little theorem implies

\begin{align} g^{H(m)} & \equiv g^{xr} g^{ks} \\ & \equiv (g^{x})^r (g^{k})^s \\ & \equiv (y)^r (r)^s \pmod p.\\ \end{align}

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