# 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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### RSA Digital Signature vs Elgamal Digital Signature

What are the advantages of RSA signatures against ElGamal signatures? Is there a situation in which it would be better e.g. to use RSA signatures?
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### El Gamal existential forgery using Pointchevalâ€“Stern signature algorithm

I found that there exists an algorithm that claims to make the El Gamal signature generation more secure. The algorithm can be found here as a pdf. I'm mainly interested in the two-parameter forgery ...
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### How to generate an El Gamal signature without knowing the private key x?

Let $x$ be the private key. Let $k$ be a random generated number $< p-1$, with $p$ the large prime. Let $g$ be the generator of $p$ the large prime. Let $r$ be the equality $r=g^k$ Let $m_e$ be an ...
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### Combining Elgamal encryption with the Elgamal signature scheme - Security issues?

For didactic (not real-world) purposes, I would like to teach other students the Elgamal encryption system and the Elgamal signature scheme. Are there known security issues when combining them? (i.e. ...
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### Attacks on schemes based on elliptic curves when the transmitted points are not on the curve

Some elliptic curve schemes require to send a curve point during the normal execution of the protocol. For example, ElGamal encryption and ElGamal signature require this. On the other hand, ECDSA does ...
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### ElGamal scheme signature: if private key a mod p is equal to private sig. key k mod p-1, can an attacker notice and determine the value of a?

If someone is signing a document using the ElGamal signature scheme, and if the random involved in the signature $k \mod (p-1)$ is equal to $a$ (the private key), can an attacker notice? If so can he ...
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### Inverse in ElGamal signature

I am learning about ElGamal signature verification. During the signature generation one has to choose a k such that ...
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### Role of Fermat's little theorem in the proof of correctness of ElGamal signature

In the Wikipedia article about the ElGamal signature scheme it is written, that Fermat's little theorem is used in the following proof of correctness: From the signature generation in ElGamal we can ...
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### ElGamal Signatures

I know various applications of RSA signatures. I wonder, is there any real-world applications of ElGamal signatures and encryption?
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### Batch ElGamal Scheme

I know about ElGamal scheme and its key generation, encryption, and decryption methods. I'm not sure about what is meant by batch ElGamal. Can someone please clarify it. How it differs from ElGamal ...
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### ElGamal in $Z^*_{p^n}$

If $p$ is an odd prime and $n$ natural,it is known that the group $Z^*_{p^n}$ is cyclic.Explain why the selection-choice of the group $Z^*_{{3^{1000}}}$ for the construction of a cryptosystem ElGamal ...
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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 signature scheme: Why is r included in s

In the ElGamal signature scheme we calculate a signature for a (hashed) message $m$ as $r \equiv_p g^k$, $s \equiv_{p-1} (m - xr) k^{-1}$ and verify it by checking $g^m \equiv_p y^r r^s$. Here $r$...
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### ElGamal digital signature. why mod p-1 in delta?

Im trying to figure out why $\delta$ in the signature part of ElGamal has mod $p-1$ when $\gamma$ has mod $p$? $\gamma = \alpha^k \mod p$ $\delta = (x-a\gamma)k^{-1} \mod p-1$
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### Is ElGamal still unforgable if the adversary knows r

Is ElGamal still unforgable if the adversary knows the value of $r$ that was calculated by $g^k$? When we do sign the message $msg$, we calculate $r = g^k$. As we know the regular ElGamal ...
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### ElGamal signature: Forging a signature of a specific form

I have a question I can't solve from one of the courses I'm currently taking: Show that given a legitimate ElGamal signature $(S,R)$ on a given message $m$, an attacker can compute a signature ...
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### Can ElGamal encryption and ElGamal signatures be used together sharing the same key-pairs?

I'm working on a encryption system where each party can store exactly a single ElGamal private key in a device. This is a hardware limit. The system must be expanded to support signatures and ...
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### Safe generator for ElGamal signature

What are the properties a generator $g$ should have to be secure for ElGamal signatures (original scheme)? I am aware that it is poorly chosen and not secure when $g|p-1$ or $g^{-1}|p-1$, where $p$ ...
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### Recovering the key in an ElGamal Signature Scheme variant

From page 318 in Stinson's "Cryptography: Theory and Practice", question 7.3: Suppose that Alice is using ElGamal Signature Scheme. In order to save time in generating >the random numbers k that ...
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### Elgamal test vectors

I know that Elgamal algorithms have fallen out of fashion, and they are not included in any widespread cryptographic standard nowadays. However, they are still present in several popular crypto ...
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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. ...