In the non$-$interactive version of Schnorr's protocol $($see ZK lecture $-$ slide $42)$ the challenge is computed as c :$=$ H$($h$||$y$),$ where y is the first message of the prover and

h the prover's public key. Let the variation with c :$=$ H$($y$),$ i$.$e$.$ without including the public key of the prover. Prove that this version does not have the property

of correctness.