# 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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### 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 ...
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### 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 ...
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### 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 ...
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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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
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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 ...
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### 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 ...
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### Does ElGamal authentication exist?

Are there any natural ways to transform ElGamal encryption system or ElGamal signature scheme into an authentication protocol?
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### 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 ...
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### ElGamal signatures systems

Let $p$ prime number $q/p-1$ prime and $g\in (Z/pZ)^*$ element of order $q$.Also $a\in \{1,...,q-1\}$ the private key and $y\equiv g^a\pmod p$ the correspoding public key.For each of the following ...
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### El-Gamal signature with two messages

Alice uses an ElGamal signature with base the group $Z^*_{107}$ and parameter $g=3$ of order $q=53$.The private key of Alice is some $x \in \{0,1,.....,52\}$ and the public key of her is $y=10$. To ...
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### Why does the ElGamal signature have the specific form that it does?

In the original paper, ElGamal(1985) starts his discussion of signatures by saying: "The signature ..... is chosen such that the equation: $\alpha^m = y^r r^s \text{mod p}$ (equation 3 from the ...
$GF(2^m)$ Galois fields are widely used in different cryptographic algorithms, for example, in Rijndael. However, $GF(p^m)$ fields are possible with any prime $p$, not only 2, but $GF(2^m)$ fields ...
Assume out of a set of ElGamal signatures, I've discovered that two have the same y i.e. $signature_{1}$ on $m_{1}$ = $(y,s_{1})$ and $signature_{2}$ on $m_{2}$ = $(y,s_{2})$. The public keys for \$...