Security
A third party can forge signatures either by finding the signer's secret key x or by finding collisions in the hash function . Both problems are believed to be difficult. However, as of 2011 no tight reduction to a computational hardness assumption is known.
The signer must be careful to choose a different k uniformly at random for each signature and to be certain that k, or even partial information about k, is not leaked. Otherwise, an attacker may be able to deduce the secret key x with reduced difficulty, perhaps enough to allow a practical attack. In particular, if two messages are sent using the same value of k and the same key, then an attacker can compute x directly.
Read more about this topic: ElGamal Signature Scheme
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