# Tagged Questions

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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### EL-Gammal 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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### ElGamal message signatures retrieving the secret value x

If the GCD(r, p-1) is small and the value k is used to sign a message using ElGamal is also small. Then the secret value of x can be determined. Why is this true? How would one retrieve x?
I stumbled upon this question in some textbook. Propose a variant of ElGamal signature scheme such that there is no need to calculate the inverse $k^{-1}$ as it is usually done using the EEA. ...