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# 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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### 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 ...
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### Usage of GF(p^m) fields, where p != 2

$GF(2^m)$ 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 $... 2answers 1k views ### How does hash function in Elgamal signature scheme prevent existential forgery attack? I have heard that hashing the message M prevents an existential forgery attack. I was wondering how. 1answer 244 views ### ElGamal signature scheme: Why is r included in s In the ElGamal signature scheme we calculate a signature for a (hashed) message$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$... 1answer 571 views ### ElGamal digital signature. why mod p-1 in delta? Im trying to figure out why$\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$1answer 200 views ### Is ElGamal still unforgable if the adversary knows r Is ElGamal still unforgable if the adversary knows the value of$r$that was calculated by$g^k$? When we do sign the message$msg$, we calculate$r = g^k$. As we know the regular ElGamal ... 1answer 456 views ### Generating a valid signature on El-Gamal without knowing the private key Suppose we are given$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$...
For a padded message, M, using the El Gamal encryption schema, how can we determine the random number $r$, when we are given $p$, the prime number, $g$ which is the primitive root of $p$, $b$ and $x$ ...