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.

learn more… | top users | synonyms

0
votes
1answer
23 views

El Gamal existential forgery using Pointcheval–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 ...
0
votes
0answers
17 views

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 ...
0
votes
0answers
21 views

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. ...
3
votes
1answer
112 views

ElGamal Signatures

I know various applications of RSA signatures. I wonder, is there any real-world applications of ElGamal signatures and encryption?
0
votes
2answers
472 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.
1
vote
1answer
39 views

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 ...
0
votes
1answer
36 views

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 ...
1
vote
2answers
69 views

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 ...
0
votes
1answer
27 views

Inverse in ElGamal signature

I am learning about ElGamal signature verification. During the signature generation one has to choose a k such that ...
4
votes
2answers
281 views

Why do we need to hash both the message and the $h$ value in ElGamal signature?

The professor left us a question on ElGamal signatures: Given the hash function $H$ and message $M$, choose a random $r$ and compute $h=g^r$ and $H(M||h)$. Show that, if $H(M)$ is used instead of ...
8
votes
1answer
2k views

DSA vs. ElGamal vs. Schnorr

It has been well known for a long time that NSA played a primary role in the development of the Digital Signature Algorithm (DSA). DSA is a sort of hybrid of the ElGamal and Schnorr signature ...
1
vote
2answers
101 views

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 ...
0
votes
0answers
43 views

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 ...
0
votes
1answer
53 views

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 ...
1
vote
0answers
74 views

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 ...
1
vote
1answer
55 views

For $p=23$, $g=2$, $q=11$ you are given the signature $(18,3)$ in the message $m=2$. Construct a signature in the message $m'=3$

Alice uses an ElGamal signature in group $(Z/pZ)^{*}$ without using hash function. To sign the message $m \in (Z/pZ)^*$ calculates the signature $(r,s)$ as follows: choose random $k \in \{0, 1, ...
1
vote
0answers
78 views

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 ...
1
vote
2answers
129 views

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 ...
2
votes
0answers
103 views

Recovering El Gamal secret key from signatures [duplicate]

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 ...
3
votes
1answer
351 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 ...
3
votes
1answer
106 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 ...
1
vote
1answer
230 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 $p$? $\gamma = \alpha^k \mod p$ $\delta = (x-a\gamma)k^{-1} \mod p-1$
1
vote
1answer
135 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 ...
5
votes
2answers
928 views

ElGamal signature without calculating the inverse

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. ...
3
votes
1answer
323 views

ElGamal signature - exploiting fallacious implementation

This question is related to ElGamal signature scheme as defined here ElGamal signature without calculating the inverse Show how one could exploit an implementation ElGamal signature scheme in which ...
3
votes
1answer
504 views

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?
7
votes
1answer
2k views

How can one show that an ElGamal-like signature verification scheme is valid?

For an ElGamal-like signature scheme, I am given two things: The signing function, the verification function. How can I show that the verification function is valid? Example 1: Signing: $s := ...
9
votes
1answer
3k views

ElGamal Signature Scheme: Recovering the key when reusing randomness

Show how if Alice uses the same value of $k$ to sign two different messages $m_1$ and $m_2$, using the ElGamal signature scheme, Eve can recover the value of $a$ from the corresponding signatures ...
5
votes
1answer
529 views

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 $p$ ...
1
vote
2answers
477 views

ElGamal: Generation of “g” value?

I haven't been able to find a clear explanation on this (and I'm probably just confused in general). I have the following parameters of ElGamal signatures: $p$ = safe prime $q = (p-1)/2$ $g$ = an ...
1
vote
1answer
159 views

Recovering the random number r

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 $x$ ...
2
votes
1answer
394 views

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 ...
4
votes
1answer
536 views

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 ...
0
votes
0answers
116 views

RSA vs El Gamal digital signature. Which is more secure? [duplicate]

I'm reading about the notions of security concerning digital signatures and I can't understand whether RSA is more secure than El Gamal digital signature. Well, they are both prone to forgery, but I ...
3
votes
1answer
271 views

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 ...
2
votes
1answer
910 views

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 ...
4
votes
1answer
1k views

Why is ElGamal considered non-deterministic?

One difference between RSA and ElGamal is that ElGamal isn't necessarily deterministic (while RSA is). What makes it non-deterministic? Is this advantageous to security? How else does this property ...