A digital signature scheme based on the discrete logarithm problem, published by Taher ElGamal in 1984. Not to be confused with the ElGamal encryption system.

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Generating a valid signature on El-Gamal without knowing the private key

Suppose we are given $p$, the large prime, $g$ which is the primitive root for $p$, $b$ which is calculated as $b=g^x$ mod $p$ where $x$ is the private key and $0<x<p-1$. Also suppose we know ...
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Why do we need to hash both the message and the $h$ value in ElGamal signature?

The professor left us a question on ElGamal signatures: Given the hash function $H$ and message $M$, choose a random $r$ and compute $h=g^r$ and $H(M||h)$. Show that, if $H(M)$ is used instead of ...
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ElGamal signatures' secret key

Assume I recovered the ElGamal signatures (75,18) and (75,67) Alice produced on the messages 81 and 14, respectively. Alice's public key is (alpha,beta,p)=(2,35,101). How can I recover Alice secret ...
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How does hash function in Elgamal signature scheme prevent existential forgery attack?

I have heard that hashing the message M prevents an existential forgery attack. I was wondering how.
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Validity of ElGamal signature variation

I'm trying to solve excersise 7.6 from Hoffstein - Introduction to Mathematical Cryptography page 459 (http://goo.gl/oRyInT) Let $p$ be a prime and let $i$ and $j$ be integers with $gcd(j, p − 1) = ...