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There are different crypto-systems that have been called Hash-Elgamal. The one your exam refers to is likely whatever was included in your course. Without knowing that, we can't necessarily answer your question. The most common is the Elgamal variant defined with encryption function: $c=\mathsf{Enc}(m,r)=\langle g^r, \mathcal{H}(y^r)\oplus m \rangle$ This ...


What you are saying for hashing is actually more commonly known as Cramer-Shoup's crypto-system and yes it is non-malleable. You can read Lecture notes 22 given by Boaz Barak in Fall 2007 for more details.


There seem to be no standardized ElGamal test vectors available in the public domain. However, there are some ElGamal test vectors generated with libgcrypt 1.5.0 available in this fork of the pycrypto project.

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