# Questions tagged [elgamal-signature]

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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### ElGamal signature scheme problem and unsure whether my calculations are wrong or that's the answer

Trying to solve problem with verifying a message through the ElGamal signature scheme and I end up getting two different values. I'm given a prime number p=881 , e1=3, d=60 , and a random value r=11 . ...
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### What is the purpose of $k \in \{2, \dots, p-2\}$ in ElGamal signatures on ${\mathbb{Z_{p}^{*}}}$?

The question is mainly stated in the title. I had to do a refreshment on public key cryptography. The algorithms are pretty straightforward however, I always stumbled upon this question. Is it in ...
81 views

### Occasional failure of an attack on ElGamal signature

I am following the procedure described on p. 319 of the fourth edition of Douglas Stinson and (since that edition) Maura Paterson's Cryptography − Theory and Practice (IBSN 978-1-03-247604-9). The ...
965 views

### Is it insecure to sign the value 0 with ElGamal?

Is it insecure to sign the plaintext 0 with ElGamal signature algorithm? Can this leak the private key, give the possibility to forge other signatures or does provide any other attack vector?
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### Difference between ElGamal and Schnorr signature

A question about Schnorr group. Am I right that this is basically a protection against discrete-log solvers? So Schnorr signature is better than ElGamal in that sense?
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1 vote
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### How to compute certificates using Diffie-Hellman key exchange with certificates and Elgamal signature scheme

We consider the Diffie–Hellman key exchange scheme with certificates. We have a system with the three users Alice, Bob and Charley. The Diffie–Hellman algorithm uses p = 61 and α = 18. The three ...
382 views

### Elgamal security if same key used twice

Assume that user A sends to user B a message, unencrypted, and signs it with an Elgamal signature. Can some adversary, call it C, who eavesdrops, learn the private key if user A signed both messages ...
122 views

### In ElGamal, how does knowing the secret number used for a signature reveal the signer's private key?

In ElGamal, how does knowing the secret number used for a signature reveal the signer's private key? How do two signatures using the same secret number reveal the signer's private key? [Hint: p-1 is ...
1 vote
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### How to properly sign and verify using DSA? Can anyone spot my mistake?

The question that I am trying to answer is as follows: 10.14. The parameters of DSA are given by p = 59,q = 29,α = 3, and Bob’s private key is d = 23. Show the process of signing (Bob) and ...
2k views

### What is largest prime factor in Diffie-Hellman?

I was reading the paper of A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms by TAHER ELGAMAL to better understand ElGamal public-key scheme, and he stated that for any ...
522 views

### Why ElGamal signature is insecure with nonrandom k?

In ElGamal signature scheme like: Keygen: $\beta:=\alpha^a\bmod p$ where $\alpha$ and $p$ are large prime numbers. Public key is $(p,\alpha,\beta)$ and secret key is $a$. Sign: Choosing random $k$ ...
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### In DSA digital signature, why does k have to be random and unique each for each signing? [duplicate]

If we repeat k, I think there is little chance for s to repeat since user's private key x is ...
529 views

### How to compute ElGamal decryption by hand

Lets say that $u=3, x=5, v=2$, how do we work out $u^{-x}*v$, so $3^{-5} * 2$. I know how to work out the answer if it was $3^5 * 2$ but how do we do it with negative exponents?
493 views

### Whats wrong with my El Gamal signature example

I'm trying to digitally sign a message m using El Gamal. So far I've been unable to verify the digital signature ive made using El Gamal. I am using prime number, p = 8369. prime root g = 3031. ...
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### Find private key from knowing random exponents are an arithmetic series

Let $p$ be a large prime and $g$ a primitive root modulo $p$, and $h$ a collision-resistant hash function. Person A chooses a random integer $1 < u< p$ and $y \equiv g^u \pmod p$ is publicly ...
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### Recovering private key from Secp256k1 signatures

I've seen many answers here and many articles that says we can recover the private key from reused R signatures. But, what if the r,s signatures are different in transaction of bitcoin then is there a ...
1 vote
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### primitive root of a very big prime number (Elgamal DS)

For encryption methods there is a need for (very large) prime numbers. So for Elgamal digital signature there is the problem of finding a primitive root of $(p)$ where $p$ must be very large prime ...
320 views

### Signature Scheme with proof of data possession

Most signature schemes first hash the data and than sign the hash. Correct me if I am wrong: The signature does not prove that the signatory was in possession of the document itself? In cases where ...
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### Any scenario for using ElGamal-SIGNATURE over RSA?

On a homework assignment, we're asked to give an example in which scenario one would use an ElGamal-Signature over an RSA-Signature. I found this question, but the answer also only describes why RSA ...
1 vote
270 views

### Does ElGamal authentication exist?

Are there any natural ways to transform ElGamal encryption system or ElGamal signature scheme into an authentication protocol?
1 vote
### Given 2 Digital Signature generated by $S=D\times k^r$ how do you solve for $k$?
Given 2 signature $(D_1, r_1, S_1)$ and $(D_2, r_2, S_2)$ and the Signature is generated as $S=D\times k^r \mod N$ where $N$ is a product of 2 primes and $r_1$, $r_2$ is co-prime. How do you solve for ...